Dahlberg's bilinear estimate for solutions of divergence form complex elliptic equations

Comparative analysis of creative and classic training methods in health,safety and environment (HSE)participation improvementI.Mohammad Fam a ,*,H.Nikoomaram b ,A.Soltanian caDepartment of Occupational Health and Safety,Faculty of Health,Hamadan University of Medical Sciences,Iran bDepartment of HSE,Science and Research Branch,Islamic Azad University,Tehran,Iran cDepartment of Bio Statistics and Epidemiology,Faculty of Health,Hamadan University of Medical Sciences,Irana r t i c l e i n f oArticle history:Received 5June 2011Received in revised form 7November 2011Accepted 7November 2011Keywords:SafetyParticipation Training CreativeInterventiona b s t r a c tThe increasing trend of deaths and injuries in industries has led their authorities to develop accident investigation plans.One of the underlying aspects of such plans is hazard identi fication and incidents reporting which can be met by an appropriate employees ’participation.So far,several studies have con firmed the effect of training in participation improvement.So the main objective of the present study was to compare two training approaches,classic and creative,in improving health,safety and envi-ronment (HSE)supervisors ’participation.The study was carried out in an Iranian petrochemical complex where the safety supervisors had been encouraged to report incidents through the Green Card system.Classic and creative training approaches were applied to increase supervisors ’participation.To do so,the supervisors were divided into Case and Control groups.In order to determine the level of supervisors ’participation,the mean of completed green cards by each person at six month intervals was used.In this way,the level of participation in the two groups was measured before,during and after the intervention.To analyze the results,Student ’s t -test,Longitudinal Data Analysis and Mixed Model were employed.The results showed that both during and after the intervention,the effect of the creative approach was more than that of the classic approach.After twelve months of intervention stop,the participation trend in both groups was downward.However,this decrease was only signi ficant in the control group.To conclude,the creative approach emphasizing on the participatory training could be an effective approach in improving the safety and consequently the health of supervisors in industries.Ó2011Elsevier Ltd.All rights reserved.1.IntroductionWork related accidents are one of the most important problems being faced by industries (Aksorn &Hadikusumo,2008;Cheng,Leu,Lin,&Fan,2010).Researches on occupational accidents con firm the negative impacts these events have on their victims,families,co-workers and the whole society (Azadeh &Mohammad Fam,2009;Chi,Chang,&Ting,2005).Apart from the humanitarian aspect of reducing occupational deaths and injuries in developing countries,a strong case can be made for reducing work related accidents on economic grounds alone,as they consume massive financial resources that the countries can ill afford to lose (Boden &Galizzi,1999;Keller,2001;Koegh,Nuwayhid,Gordon,&Gucer,2000;Ramessur,2009;Weil,2001).The total number of work related accidents each year has grown to an estimated 125million worldwide (Kirschenbaum,Ludmilla,&Goldberg,2000).Workplace deaths comprise 0.9%of all disability adjusted for life years (DALY ’s)in the world (13.1million)and 16%of inadvertent DALY ’s occurs in working group with 15e 69years old.It is noteworthy that more than 11.3million US employees are seriously injured,and nearly 11,000are killed on the job (Hämäläinen,Takala,&Saarela,2006;Salminen,2008).In Iran,there are not accurate statistics of all work related accidents since the accidents are not fully reported and recorded.Moreover,many Iranian workers are not insured against occupa-tional injuries.However,in the year 2000,about 724,000burns,2,810,000falls,425,000violence cases and 2million traf fic acci-dents were reported (DHS,2000,p.10).The number of deaths is estimated to be about 25,365(DHS,2000,p.10).The increasing trends of deaths and injuries in both developed and developing countries have led industries to accurately inves-tigate the accidents in order to maintain preventive mechanisms (Hämäläinen,Saarela,&Takala,2009;Hintikka &Saarela,2010;*Corresponding author.Tel.:þ988118255963;fax:þ988118255301.E-mail addresses:mohammadfam@umsha.ac.ir (I.M.Fam),h.nikoomaram@srbiau.ac.ir (H.Nikoomaram),a_sultanian@ (A.Soltanian).Contents lists available at SciVerse ScienceDirectJournal of Loss Prevention in the Process Industriesjou rn al homepage :/locate/jlp0950-4230/$e see front matter Ó2011Elsevier Ltd.All rights reserved.doi:10.1016/j.jlp.2011.11.003Journal of Loss Prevention in the Process Industries 25(2012)250e 253Ooteghem,2006).To do so,it is required to identify workplace hazards and to report incidents’data including near-misses and accidents(Baybutt,2003;Einarsson&Brynjarsson,2008;Jacinto& Aspinwall,2004;Nouri,Azadeh,Mohammad Fam,&Azadeh,2007). Although it is necessary for all employees at different organiza-tional levels to participate in incidents reporting,evidence from industries suggests that the involvement of supervisors is of a great importance(Barach&Small,2000).Supervisors have comprehen-sive knowledge about their workplace and in many instances they provide applied solutions to accident prevention.Further,involving supervisors in accident prevention decisions builds trust, commitment and good will,which leads to increased job satisfac-tion and ultimately improved health,safety and environmental (HSE)performance(Probst&Estrada,2010;Seppala,1995).One of the basic principles of participation promoting is proved to be appropriate education and training conducted in different methods (Limbo,Peterson,&Pridham,2003;Rooney,1992;Seppala,1995).Although several studies have confirmed the effect of training in participation improvement(Fakhrul Razi,Iyuke,Hassan,&Aini, 2003;Mohammad Fam&Moghimbeigi,2009;Rall,Ev,& Staender,2011),there have not been researches on comparison of different training methods as well as determining their consistency. Assessment of consistency would help HSE managers to plan refresher courses effectively(Hung&Huyen,2011).Therefore,the main objective of the present study is to compare two training approaches,classic and creative,in improving HSE supervisors’participation.Moreover,the study identifies the increase of the level of participation,i.e.the increase in the mean of completed hazards and incidents report cards by each supervisor,in the two approaches and determines the consistency of the trainings.2.Material and methodsThe present study was carried out in an Iranian petrochemical complex where the safety supervisors had been encouraged to report workplace hazards,near-misses and minor accidents through the“Green Card”system.In this system,the supervisors filled in the cards and put them into special boxes.The cards then were submitted to the specialized committee and if approved,the award of5e20US dollars was given to the supervisors to reward them for reporting incidents.To assess the level of supervisors’participation in the green card system,the means of cards completed by supervisors were calculated in thefirst and the second six months of2008.Two training approaches were applied to increase supervisors’participation.To do so,the supervisors were divided into Case and Control groups,containing40and35male individuals,respectively. Table1shows the details of the supervisors under study.Each group was trained12months(4h per month).The training main syllabuses included hazard identification and incidents reporting through the green card system.In this way,supervisors were trained how to identify hazards,near-misses and minor accidents,to report them andfinally to follow up the corrective measures.The Fishbowl and Samoan Circle methods,which are considered as a creative approach,were used to train the case group in the above issues while the classic approach was used for the control group.It is noteworthy that the creative training approach helps trainees to use their ability and imagination to produce new ideas in a participatory environment whereas in the classic approach the trainees have no participation in the training process(Mohammad Fam,Simayee,&Zolnoornia,2009,p.65).Fishbowls involve a small group of people seated in circle and having a conversation(fish).They are surrounded by a larger group of observers,seated in an outer circle(bowl).The facilitator gives a short input of5e10min which sets out the general outline of the discussion and after that the inner circle starts to discuss.The outer circle usually listens and observes.Whenever someone wants to contribute and move to the inner circle,a participant from the fishbowl must free a chair and move to the outer circle.At the end of the session,a debriefing is held in a whole group conversation.The Samoan Circle is a leaderless meeting intended to help negotiations in controversial issues.While there is no‘leader’, a professional facilitator can welcome participants and explain the seating arrangements,rules,timelines and the process.The Samoan Circle has people seated in a circle within a circle,however only those in the inner circle are allowed to speak.The inner circle should represent all the different viewpoints present,and all others must remain silent.The process offers others a chance to speak only if they join the‘inner circle’.Descriptive statistics were used to explain the data.In order to determine the level of supervisors’participation,the mean of completed green cards by each person at six month intervals was used.In this way,the level of participation in the two groups was measured after six and twelve months during the intervention. Furthermore,the measurement was exactly repeated after the intervention was stopped.Table1Details of the supervisors.Case group Control groupNumber of supervisors4035Average age(year)28.15Æ3.0430.62Æ2.45Average work experience(year)7.11Æ2.67.74Æ2.2Average salary(US Dollar)571.37Æ108.21584.61Æ84.35Holding high school Diploma27.1%31.2%Holding BSc/BA50.4%49%Holding MSc/MA and higher22.5%19.8%Table2Comparison of supervisors’participation before,during and after the intervention.Period Year Group Mean Standard deviation P e valueBefore the intervention2008First6months e 2.37 2.470.037a(3.142*,110.506**)Second6months 1.75 1.16During the intervention2009First6months Case 3.29 1.710.021b(2.03*,61.184**)Control 2.58 1.23Second6months Case 3.83 1.29<0.001b(3.56*,73**)Control 3.4 1.49After the intervention2010First6months Case 4.04 1.130.4b(2.581*,72.93**)Control 3.98 2.36Second6months Case 3.69 1.940.001b(3.27*,73**)Control 2.02 1.59*Denotes independent t value;**Denotes degree of freedom.a Denote P-value based on twoÀtailed.b Denote P-value based on oneÀtailed test.I.M.Fam et al./Journal of Loss Prevention in the Process Industries25(2012)250e253251The trend of supervisors ’participation was shown through application of Spline Smoothing method.Student ’s t -test was used to compare the means of supervisors ’participation in case and control groups.Two-tailed hypothesis test was applied to compare the means of participation level and one-tailed hypothesis test was used to determine the increase or decrease in the supervisors ’participation average.To determine the relationship between such variables as salary,educational level etc and supervisors ’partici-pation in the two groups,Longitudinal Data Analysis and Mixed Model were employed and the data gathered was analyzed using R2.12.1software.All statistical tests were performed at the 0.05level of signi ficance.3.ResultsAs mentioned in section 2,the mean of completed green cards by each supervisor at six month intervals was used to measure the level of their participation.Table 2compares the level of supervi-sors ’participation before,during and after the intervention.It is noteworthy that in 2008,there was no intervention,i.e.no case/control group,and the level of supervisors ’participation was only assessed.As Table 2shows,before the intervention,the level of supervi-sors ’participation signi ficantly decreased in the second six months comparing with the first six months (p <0.05).During the inter-vention,the increase of participation in the case group was signi ficantly more than the control group and this happened after both the first and the second six months (p <0.05).However,comparing first 2009with second 2009,the increase of mean values in the control group was more than that of the case group.At first sight,this may look rather strange but the launch of Targeted Subsidies Scheme in Iran in the second six months of 2009and consequently public concerns about increasing of living costs seem to be the main reason.In this way,control group members,who were less-educated and low-paid workers,were trying to submit more green cards,thus to be awarded more.In other words,they found it as a way of income rise.Targeted Subsidies Scheme also resulted in increasing the participation level in the control group comparing with the case group after the first six months of stopping the intervention,although this increase was not signi ficant.After one year of the Scheme implementation (in second 2010)public concerns about its consequences were removed so in this period the level of partici-pation in the case group was signi ficantly more than the control group (p <0.05).Fig.1shows the trend of the case and control participation levels in the three years.Finally,after twelve months of stopping the intervention,the trend of supervisors ’participation in the two groups wasdownward.As the P -values con firm the decrease of participation was only signi ficant in the control group (Table 3).However,more surveys would be needed to strongly con firm more consistency of the creative trainings.Meanwhile,no relationship was observed between the super-visors ’age/work experience and their participation level while the relationship between the amounts of salary/education and the participation mean was signi ficant (p <0.05).4.DiscussionWork related accidents are of a great importance to the public health spectrum around the world (Kirschenbaum et al.,2000;Mohammad Fam &Moghimbeigi,2009).In developing countries such as Iran,the mortality and disability rates resulting from work related accidents are rather high in comparison with developed countries (Hämäläinen,2009;Maghsoudi &Gabraely,2008;McAlinden,Sitoh,&Norman,1997).Facing this fact and realizing the negative effects of occupational accidents on the whole society,Iranian researchers,industries authorities and safety engineers have conducted research and developed measures to evaluate and consequently to improve workplace safety (Azadeh,Keramati,Mohammad Fam,&Jamshidnedjad,2006;McAlinden et al.,1997).So far,guidelines to develop occupational safety measures have classi fied measures into groups based on their oriented objectives (Mohammad Fam,2006).Such systems as 3E (engineering,enforcement and education)are currently being applied to assess and to enhance workplace safety in Iran (Mohammad Fam,2007).As outlined above,education and training are the basic elements focusing on human factors and aiming at employees ’behavior change in line with safety improvement (Lingrad,2002;Swuste &Arnoldy,2003).Thus,training activities which serves to promote employees ’participation,as a sign of behavior change,are considered necessary to both workplace and personnel safety and health protection and improvement (Bell &Grushecky,2006;Lingard &Holmes,2001).The findings of the study revealed that the two trainings resulted in promoting supervisors ’participation in incidents reporting both during and after the intervention.This result is similar to the findings of Inness,Turner,Barling,and Stride (2010)and of Sanaei Nasab,Ghofranipour,Kazemnejad,Khavanin,and Tavakoli (2008).The study also con firmed that both during and after the inter-vention,the effectiveness of the creative approach was more than that of the classic approach.The reason behind this is the emphasis of creative trainings on the participatory approach (Culvenor &Else,1997;Otsuka,Misawa,Noguchi,&Yamaguchi,2010).By partici-pating in the case group,the supervisors increased their ability to improve their work condition and were motivated to participate in the problem solving process.Moreover,after six months of stopping the intervention,the participation increasing trend in the two groups still continued although its pace was slower.After twelve months of intervention stop,the participation trend in both groups was downward.However,this decrease was only signi ficant in the controlgroup.Fig.1.Trend of the case and control participation levels in the three years.Table 3Comparison of supervisors ’participation after 6and 12months of intervention stop.Group6months 12months Meandifference P e value (one-tailed)Mean ÆSDMean ÆSD Case 4.04Æ1.13 3.69Æ1.940.350.712(0.562a ,68b )Control3.98Æ2.262.02Æ1.591.960.023(1.366a ,78b )a Denotes independent t value.bDenotes degree of freedom.I.M.Fam et al./Journal of Loss Prevention in the Process Industries 25(2012)250e 253252This implies that the consistency of creative trainings was more than that of the classic ones.The case group awareness and perception of participation necessity through intra-group interac-tions,discussions and team works may be one of its main reasons. However,more surveys would be needed to strongly confirm more consistency of the creative trainings.The result is similar to the findings of Chang and Liao(2009).The study of Edwards(2005) also mentioned that the effects of trainings decreased after a year when they were stopped.Hung and Huyen(2011)suggested managers conduct refresher courses to increase the consistency of trainings.Moreover,the study of Matthews,Gallus,and Henning (2011)confirmed the more consistency of participatory trainings.Thefindings of the study showed there was a significant rela-tionship between employees’salary/education and their partici-pation level.Since the correlation coefficient of the mentioned variables was high(r¼0.86),this can be inferred that highly paid supervisors were more educated,thus more aware of workplace hazards and of their roles in controlling such hazards through participation.Moreover,higher salary may also promote supervi-sors to take responsibility of their role of encouraging safety management activities.This result confirms thefindings of Eklöf, Ingelgård,and Hagberg(2004)and of Rivilis et al.(2008).5.ConclusionsFinally,the present research demonstrated that all steps of the participatory training aim at promoting the supervisors’capacity to self development in safety aspects.As a result,the creative approach emphasizing on the participatory training could be an effective approach in improving the safety and consequently the health of supervisors in developing countries.In other words,this approach would help motivate these groups to voluntarily engage in improving quality of their working life.ReferencesAksorn,T.,&Hadikusumo,B.H.W.(2008).Critical success factors influencing safety program performance in Thai construction projects.Safety Science,46,709e727. 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Personality and environmental concernJacob B.Hirsh *Department of Psychology,Sidney Smith Hall,100St.George Street,Toronto,Ontario,Canada M5S 3G3a r t i c l e i n f oArticle history:Available online 25January 2010Keywords:Personality Big fiveEnvironmental concern Environmentalism GSOEPa b s t r a c tPeople vary considerably in their attitudes toward environmental issues.Although some individuals view the environment from a purely utilitarian perspective,others are concerned about environmental sustainability and maintaining an ecological balance.The current study examines the relationship between personality characteristics and environmental concern in a community sample of 2690German adults.Structural equation modeling revealed that greater environmental concern was related to higher levels of Agreeableness and Openness,with smaller positive relationships emerging with Neuroticism and Conscientiousness.Ó2010Elsevier Ltd.All rights reserved.1.IntroductionFor better or for worse,human behavior has a large influence on the global ecology.Many of the environmental challenges facing us today are a direct result of human actions,and as such may require behavioral solutions (Oskamp,2000;Saunders,2003).In recogni-tion of this fact,many researchers have investigated the social and psychological factors that influence environmental attitudes and behaviors.Much of this research has focused on the role of specific values,beliefs,and norms as predictors of environmental concern (Dietz,Fitzgerald,&Shwom,2005;Dietz,Stern,&Guagnano,1998;Schultz,2001;Van Liere &Dunlap,1980).More recently,environmentalism has been examined from the perspective of the ‘‘Big Five’’taxonomy of personality traits,which describes variation in human personality across the five broad dimensions of Extraversion,Agreeableness,Conscientiousness,Neuroticism,and Openness to Experience (Goldberg,1993).These broad trait dimensions can be used to predict more specific atti-tudes and value orientations (McCrae &Costa,2008;Roccas,Sagiv,Schwartz,&Knafo,2002).Two of these traits,Agreeableness and Openness,have emerged as significant predictors of pro-environ-mental values (Hirsh &Dolderman,2007).These findings are consistent with theoretical models that relate pro-environmental attitudes to higher levels of empathy and self-transcendence (Schultz,2000;Schultz &Zelezny,1999),which appear to be related to Agreeableness and Openness,respectively.Individuals who are more empathic and less self-focused appear more likely to develop a personal connection with nature,which in turnpredicts their pro-environmental attitudes (Bragg,1996;Mayer &Frantz,2004).Indeed,developing such an emotional affinity toward the natural environment can bolster one’s motives for environmental protection (Kals,Schumacher,&Montada,1999).While both Agreeableness and Openness fit well into theoretical models of pro-environmental attitudes,the initial study demon-strating their predictive utility was limited to a relatively small sample of undergraduate students (N ¼106).The initial study was also limited by the imbalance of male (n ¼32)and female (n ¼74)participants,making it difficult to examine the importance of gender as a moderating variable.The current study extends this previous research by examining the personality predictors of environmental concern in a much larger community sample of German adults (N ¼2690).Additionally,structural equation modeling was used to provide error-reduced estimates of the true relationships between the variables of interest.It was hypothesized that both Agreeableness and Openness would remain significant predictors of increased environmental concern.2.Methods 2.1.ParticipantsData analyses were based on the responses of 2690participants of the German Socio-Economic Panel Study (GSOEP),a longitudinal research project that polls a large and diverse sample of German households (Haisken-DeNew &Frick,2005).While the full GSOEP sample is considerably larger,the current analysis could only be conducted on the subset of respondents who completed the available measures of personality and environmental concern,described below.The age of participants in the current sample ranged from 26to 93years (M ¼54.1,SD ¼14.6).A reasonably*Fax:þ14169784811.E-mail address:jacob.hirsh@utoronto.caContents lists available at ScienceDirectJournal of Environmental Psychologyjournal homepa ge:/locate/jep0272-4944/$–see front matter Ó2010Elsevier Ltd.All rights reserved.doi:10.1016/j.jenvp.2010.01.004Journal of Environmental Psychology 30(2010)245–248balanced proportion of male(47%)and female(53%)respondents were included.2.2.Materials2.2.1.PersonalityIn2005,GSOEP participants completed a15-item version of the Big Five Inventory(BFI;Gerlitz&Schupp,2005;John,Donahue,& Kentle,1991),which measures the Big Five personality traits of Extraversion,Agreeableness,Conscientiousness,Neuroticism,and Openness to Experience.This shortened version of the BFI,known as the BFI-S,demonstrates good internal coherence and has been validated against longer inventories assessing thefive major factors of personality.Each trait domain is represented by3descriptive phrases to which respondents must rate their agreement on a scale ranging from1(Does not apply)to7(Does apply).Sample phrases include‘‘Worry a lot’’and‘‘Value artistic experiences’’.2.2.2.Environmental concernAlthough there is no standard scale measuring environmental concern in the GSOEP dataset,there are a number of specific items that probe respondents’environmental attitudes.In the current analysis,we used3items administered at multiple time points as indicators of a latent environmental concern factor.In particular, the items of interest were‘‘Environmentally Conscious’’,‘‘Importance of Environmental Protection’’,and‘‘Worried about Environment’’. Each of these items was administered on multiple occasions.To the extent that there is a stable dispositional component to environ-mental concern,it should be captured by the shared variance of these cross-time measures(cf.Kenny&Zautra,1995).The‘‘Environmentally conscious’’item was administered in 1998and2003;the‘‘Importance of environment’’item was administered in1994,1998,and1999;finally,the‘‘Worried about environment’’item was based on data collected in2005–2007. Examining the shared variance amongst these items allowed for an error-reduced estimate of environmental concern across a large time period.2.3.Analytic techniqueStructural equation modeling was used to explicitly model sources of error in the dataset,thereby providing more accurate estimates of the true relationships between the variables of interest.In particular,we employed a measurement model that accounts for acquiescence bias,halo bias,and the observed corre-lations among Big Five personality traits(Anusic,Schimmack, Pinkus,&Lockwood,2009).First,each Big Five domain was modeled as a latent factor reflected in the3indicator items(e.g.,‘‘Value artistic experiences’’).Second,a halo bias factor was modeled as the shared variance among each of these latent Big Five domains. Third,an acquiescence factor was modeled as the shared variance amongst each of the individual questionnaire items.Fourth,the higher-order Big Five factors(DeYoung,2006;Digman,1997; McCrae et al.,2008)were modeled as reflecting the shared vari-ance among Agreeableness,Conscientiousness,and Neuroticism (Stability or Alpha),and Extraversion and Openness(Plasticity or Beta).In order to ensure the model would be identified,the regression weights werefixed to be equal for the loadings within each of the halo,acquiescence,and higher-order personality factors.Note,however,that while such equality constraints force the unstandardized coefficients to be equal,the standardized coefficients(as will be reported below)also depend upon the variance of the indicators and may thus differ from one another.Environmental concern was modeled in a two-step hierarchical process.First,three latent variables were constructed,one for each set of the environmental items described above.For example,the three separate assessments of‘‘Importance of environmental protection’’were used as indicators of a latent factor.Second,an overall environmental concern factor was modeled as the shared variance amongst each of the three item-based environmental factors.Regression lines predicting this overall environmental concern variable were drawn from each of the latent Big Five trait factors.The resulting model allowed for an error-reduced exami-nation of the contributions of the Big Five personality traits to environmental concern over time.3.Results3.1.ModelfitReasonablefit is provided by a model when CFI>.90,RMSEA<.08, and SRMR<.10(Kline,2005).The current model demonstrated acceptable to goodfit,with a CFI of.91,RMSEA of.045(90%confidence interval of.043–.047),and SRMR of.05.The chi-square value of 1406.46(df¼218)was significant at p<.001;however,because the current sample is relatively large,the chi-square test is not an optimal indicator offit.3.2.Personality and environmental concernThe model and estimated parameters are presented in Fig.1.The latent environmental concern factor was strongly related to each of the three item-based environmental factors,including‘‘importance of environmental protection’’(b¼.94),‘‘worried about environ-ment’’(b¼.64),and‘‘environmentally conscious’’(b¼.62).Envi-ronmental concern was in turn significantly predicted by individual differences in the Big Five personality traits.In particular,greater environmental concern was significantly associated with higher levels of Agreeableness(b¼.22),Openness(b¼.20),Neuroticism (b¼.16),and Conscientiousness(b¼.07).In contrast,no significant relationship was observed with Extraversion(b¼.02).3.3.Demographic variablesAge,gender,and household income were added to the model in order to examine the importance of demographic variables in predicting environmental concern.A regression line predicting the latent environmental concern factor was drawn from each of the demographic variables.Including these variables did not change the relationships between personality and environmental concern, although it did decrease the overallfit of the model(CFI¼.84; RMSEA¼.053;SRMR¼.06).Nonetheless,significant relationships were observed,with environmental concern being positively associated with age(b¼.13)and negatively with household income (b¼À.06).Women also displayed higher levels of environmental concern than men(b¼.07),consistent with previous research (Davidson&Freudenburg,1996).3.4.Examination of possible gender moderationBecause the sample contained a large number of both males and females,it was possible to examine the possible interactions between gender and personality in the prediction of environmental concern. The model depicted in Fig.1was therefore extended to a multiple-groups confirmatory factor analysis,with the model being estimated simultaneously for males and females.The model again demonstrated acceptablefit when no equality constraints were imposed across groups(CFI¼.91;RMSEA¼.031;SRMR¼.054).Constraining the factor loadings and structural covariances to be equal across the groups did not significantly reduce modelfit(CFI¼.91;RMSEA¼.030;J.B.Hirsh/Journal of Environmental Psychology30(2010)245–248 246SRMR ¼.056;D c 2¼31.67,D df ¼26,p ¼.20).Conversely,with this fully constrained model in place,allowing the regression weights of the Big Five domains on the Environmental Concern variable to vary freely did not improve model fit (CFI ¼.91;RMSEA ¼.031;SRMR ¼.056;D c 2¼2.73,D df ¼5,p ¼.74).The relationship between the Big Five and environmental concern thus did not appear to be moderated by gender.4.DiscussionAs in previous research,greater environmental concern was related to higher levels of the Big Five personality traits of Agree-ableness and Openness (Hirsh &Dolderman,2007).These rela-tionships appear to be relatively robust,given that they were replicated using different measures,obtained from an adult rather than student population,and in a German rather than Canadian sample.Additionally,these effects were observed despite the removal of error variance through structural equation modeling.The current study thus provides additional support for the impor-tance of these two personality traits in predicting environmental attitudes,while further demonstrating that their importance does not appear to be moderated by gender.Both Agreeableness and Openness have been related to the higher-order personal value of self-transcendence,reflecting an expanded sense of self and a greater concern for others (Olver &Mooradian,2003;Roccas et al.,2002).Agreeableness,for instance,is related to higher levels of empathy (Ashton,Paunonen,Helmes,&Jackson,1998),which is thought to support pro-environmental motives (Schultz,2000).Individuals who are lower in Agreeableness tend to be more selfish generally speaking,and are less concerned about the welfare of others.Openness,meanwhile,is associated with increased cognitive ability and flexibility in thought (DeYoung,Peterson,&Higgins,2005),potentially affording a broader perspective on humanity’s place in the larger ecology and a greater aesthetic appreciation of natural beauty.Less open individuals,in contrast,are likely to have a narrower and more conservative perspective on nature’s value.An unexpected finding was the effect of Neuroticism,with more neurotic individuals demonstrating significantly higher levels of environmental concern.Although this relationship was not found in the preliminary study that employed the Big Five (Hirsh &Dolderman,2007),it was previously found to predict support for environmental preservation (Wiseman &Bogner,2003)when measured with the Eysenck Personality Questionnaire (Eysenck &Eysenck,1975).One explanation for this finding is that neurotic individuals tend to be more worried about negative outcomes in general,and so concern about the environment may reflect anxiety about the consequences of environmental degradation (whereas emotionally stable individuals would potentially experience less affective disturbance when thinking about this topic).It isthusFig.1.Structural regression model with the Big Five traits predicting environmental concern.Halo represents an evaluative bias factor.Acquiescence represents acquiescence bias in scale usage.Stability and Plasticity represent the two higher-order Big Five traits.EC1¼‘‘Importance of Environmental Protection’’items;EC2¼‘‘Worried about Environment’’items;EC3¼‘‘Environmentally Conscious’’items.Structural error terms are presented for all endogenous variables,with the critical ratios in parentheses.Measurement error terms were omitted from the figure to improve readability.J.B.Hirsh /Journal of Environmental Psychology 30(2010)245–248247possible that neurotic individuals would demonstrate a more egoistic form of environmental concern,rather than an altruistic one(Schultz,2001).A secondfinding that was unpredicted from previous research on this topic is the fact that Conscientiousness had a small but signifi-cant positive association with environmental concern.Given the relatively small magnitude of this relationship,it is perhaps unsur-prising that the previous study employing a smaller sample size did not uncover this result.The importance of Conscientiousness for environmental concern is consistent with studies that link this trait to higher levels of social investment and prudent rule-adherence in general(Lodi-Smith&Roberts,2007).Highly conscientious indi-viduals might be expected to carefully follow social guidelines and norms for appropriate environmental action,whereas less consci-entious individuals might be more willing to‘‘cut corners’’when it comes to environmentally responsible behavior.The current analysis has a number of strengths over previous inquiries into the relationship between personality and environ-mental concern.First,the large sample provided by the longitudinal GSOEP study allowed for a more detailed structural analysis of the relevant variables.Second,the sample was more representative of the larger population in terms of age and gender distribution.While previous research has mostly employed undergraduate students, the current sample had a much broader age range that stretched further into the lifespan.Third,the inclusion of multiple time-lagged measures allowed for an examination of the personality predictors of environmental concern across long periods of time.Despite the strengths of the study,there are also some note-worthy limitations.These limitations are primarily related to the measures that were administered as part of the GSOEP project.In particular,while the15-item BFI-S provides a good measure of the broad Big Five factors,it does not allow for an assessment of lower-order personality traits.It is possible that certain aspects of each Big Five domain would be more strongly related to environmental concern than others,but this could not be examined in the current data.Similarly,the measures of environmental concern were derived from the available items,but they did not reflect a compre-hensive coverage of the entire domain of environmental attitudes.It is certainly possible that personality traits may be differentially related to the various aspects of environmental concern(Milfont& Duckitt,2004;Schultz,2001;Wiseman&Bogner,2003).Future research could explore these possibilities by employing more detailed measures of personality and environmental concern. Nonetheless,the current study provides support for the importance of personality traits in relation to environmental attitudes,and thereby provides a useful framework for more targeted investiga-tions into the processes underlying these relationships. 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Draft:Deep Learning in Neural Networks:An OverviewTechnical Report IDSIA-03-14/arXiv:1404.7828(v1.5)[cs.NE]J¨u rgen SchmidhuberThe Swiss AI Lab IDSIAIstituto Dalle Molle di Studi sull’Intelligenza ArtificialeUniversity of Lugano&SUPSIGalleria2,6928Manno-LuganoSwitzerland15May2014AbstractIn recent years,deep artificial neural networks(including recurrent ones)have won numerous con-tests in pattern recognition and machine learning.This historical survey compactly summarises relevantwork,much of it from the previous millennium.Shallow and deep learners are distinguished by thedepth of their credit assignment paths,which are chains of possibly learnable,causal links between ac-tions and effects.I review deep supervised learning(also recapitulating the history of backpropagation),unsupervised learning,reinforcement learning&evolutionary computation,and indirect search for shortprograms encoding deep and large networks.PDF of earlier draft(v1):http://www.idsia.ch/∼juergen/DeepLearning30April2014.pdfLATEX source:http://www.idsia.ch/∼juergen/DeepLearning30April2014.texComplete BIBTEXfile:http://www.idsia.ch/∼juergen/bib.bibPrefaceThis is the draft of an invited Deep Learning(DL)overview.One of its goals is to assign credit to those who contributed to the present state of the art.I acknowledge the limitations of attempting to achieve this goal.The DL research community itself may be viewed as a continually evolving,deep network of scientists who have influenced each other in complex ways.Starting from recent DL results,I tried to trace back the origins of relevant ideas through the past half century and beyond,sometimes using“local search”to follow citations of citations backwards in time.Since not all DL publications properly acknowledge earlier relevant work,additional global search strategies were employed,aided by consulting numerous neural network experts.As a result,the present draft mostly consists of references(about800entries so far).Nevertheless,through an expert selection bias I may have missed important work.A related bias was surely introduced by my special familiarity with the work of my own DL research group in the past quarter-century.For these reasons,the present draft should be viewed as merely a snapshot of an ongoing credit assignment process.To help improve it,please do not hesitate to send corrections and suggestions to juergen@idsia.ch.Contents1Introduction to Deep Learning(DL)in Neural Networks(NNs)3 2Event-Oriented Notation for Activation Spreading in FNNs/RNNs3 3Depth of Credit Assignment Paths(CAPs)and of Problems4 4Recurring Themes of Deep Learning54.1Dynamic Programming(DP)for DL (5)4.2Unsupervised Learning(UL)Facilitating Supervised Learning(SL)and RL (6)4.3Occam’s Razor:Compression and Minimum Description Length(MDL) (6)4.4Learning Hierarchical Representations Through Deep SL,UL,RL (6)4.5Fast Graphics Processing Units(GPUs)for DL in NNs (6)5Supervised NNs,Some Helped by Unsupervised NNs75.11940s and Earlier (7)5.2Around1960:More Neurobiological Inspiration for DL (7)5.31965:Deep Networks Based on the Group Method of Data Handling(GMDH) (8)5.41979:Convolution+Weight Replication+Winner-Take-All(WTA) (8)5.51960-1981and Beyond:Development of Backpropagation(BP)for NNs (8)5.5.1BP for Weight-Sharing Feedforward NNs(FNNs)and Recurrent NNs(RNNs)..95.6Late1980s-2000:Numerous Improvements of NNs (9)5.6.1Ideas for Dealing with Long Time Lags and Deep CAPs (10)5.6.2Better BP Through Advanced Gradient Descent (10)5.6.3Discovering Low-Complexity,Problem-Solving NNs (11)5.6.4Potential Benefits of UL for SL (11)5.71987:UL Through Autoencoder(AE)Hierarchies (12)5.81989:BP for Convolutional NNs(CNNs) (13)5.91991:Fundamental Deep Learning Problem of Gradient Descent (13)5.101991:UL-Based History Compression Through a Deep Hierarchy of RNNs (14)5.111992:Max-Pooling(MP):Towards MPCNNs (14)5.121994:Contest-Winning Not So Deep NNs (15)5.131995:Supervised Recurrent Very Deep Learner(LSTM RNN) (15)5.142003:More Contest-Winning/Record-Setting,Often Not So Deep NNs (16)5.152006/7:Deep Belief Networks(DBNs)&AE Stacks Fine-Tuned by BP (17)5.162006/7:Improved CNNs/GPU-CNNs/BP-Trained MPCNNs (17)5.172009:First Official Competitions Won by RNNs,and with MPCNNs (18)5.182010:Plain Backprop(+Distortions)on GPU Yields Excellent Results (18)5.192011:MPCNNs on GPU Achieve Superhuman Vision Performance (18)5.202011:Hessian-Free Optimization for RNNs (19)5.212012:First Contests Won on ImageNet&Object Detection&Segmentation (19)5.222013-:More Contests and Benchmark Records (20)5.22.1Currently Successful Supervised Techniques:LSTM RNNs/GPU-MPCNNs (21)5.23Recent Tricks for Improving SL Deep NNs(Compare Sec.5.6.2,5.6.3) (21)5.24Consequences for Neuroscience (22)5.25DL with Spiking Neurons? (22)6DL in FNNs and RNNs for Reinforcement Learning(RL)236.1RL Through NN World Models Yields RNNs With Deep CAPs (23)6.2Deep FNNs for Traditional RL and Markov Decision Processes(MDPs) (24)6.3Deep RL RNNs for Partially Observable MDPs(POMDPs) (24)6.4RL Facilitated by Deep UL in FNNs and RNNs (25)6.5Deep Hierarchical RL(HRL)and Subgoal Learning with FNNs and RNNs (25)6.6Deep RL by Direct NN Search/Policy Gradients/Evolution (25)6.7Deep RL by Indirect Policy Search/Compressed NN Search (26)6.8Universal RL (27)7Conclusion271Introduction to Deep Learning(DL)in Neural Networks(NNs) Which modifiable components of a learning system are responsible for its success or failure?What changes to them improve performance?This has been called the fundamental credit assignment problem(Minsky, 1963).There are general credit assignment methods for universal problem solvers that are time-optimal in various theoretical senses(Sec.6.8).The present survey,however,will focus on the narrower,but now commercially important,subfield of Deep Learning(DL)in Artificial Neural Networks(NNs).We are interested in accurate credit assignment across possibly many,often nonlinear,computational stages of NNs.Shallow NN-like models have been around for many decades if not centuries(Sec.5.1).Models with several successive nonlinear layers of neurons date back at least to the1960s(Sec.5.3)and1970s(Sec.5.5). An efficient gradient descent method for teacher-based Supervised Learning(SL)in discrete,differentiable networks of arbitrary depth called backpropagation(BP)was developed in the1960s and1970s,and ap-plied to NNs in1981(Sec.5.5).BP-based training of deep NNs with many layers,however,had been found to be difficult in practice by the late1980s(Sec.5.6),and had become an explicit research subject by the early1990s(Sec.5.9).DL became practically feasible to some extent through the help of Unsupervised Learning(UL)(e.g.,Sec.5.10,5.15).The1990s and2000s also saw many improvements of purely super-vised DL(Sec.5).In the new millennium,deep NNs havefinally attracted wide-spread attention,mainly by outperforming alternative machine learning methods such as kernel machines(Vapnik,1995;Sch¨o lkopf et al.,1998)in numerous important applications.In fact,supervised deep NNs have won numerous of-ficial international pattern recognition competitions(e.g.,Sec.5.17,5.19,5.21,5.22),achieving thefirst superhuman visual pattern recognition results in limited domains(Sec.5.19).Deep NNs also have become relevant for the more generalfield of Reinforcement Learning(RL)where there is no supervising teacher (Sec.6).Both feedforward(acyclic)NNs(FNNs)and recurrent(cyclic)NNs(RNNs)have won contests(Sec.5.12,5.14,5.17,5.19,5.21,5.22).In a sense,RNNs are the deepest of all NNs(Sec.3)—they are general computers more powerful than FNNs,and can in principle create and process memories of ar-bitrary sequences of input patterns(e.g.,Siegelmann and Sontag,1991;Schmidhuber,1990a).Unlike traditional methods for automatic sequential program synthesis(e.g.,Waldinger and Lee,1969;Balzer, 1985;Soloway,1986;Deville and Lau,1994),RNNs can learn programs that mix sequential and parallel information processing in a natural and efficient way,exploiting the massive parallelism viewed as crucial for sustaining the rapid decline of computation cost observed over the past75years.The rest of this paper is structured as follows.Sec.2introduces a compact,event-oriented notation that is simple yet general enough to accommodate both FNNs and RNNs.Sec.3introduces the concept of Credit Assignment Paths(CAPs)to measure whether learning in a given NN application is of the deep or shallow type.Sec.4lists recurring themes of DL in SL,UL,and RL.Sec.5focuses on SL and UL,and on how UL can facilitate SL,although pure SL has become dominant in recent competitions(Sec.5.17-5.22). Sec.5is arranged in a historical timeline format with subsections on important inspirations and technical contributions.Sec.6on deep RL discusses traditional Dynamic Programming(DP)-based RL combined with gradient-based search techniques for SL or UL in deep NNs,as well as general methods for direct and indirect search in the weight space of deep FNNs and RNNs,including successful policy gradient and evolutionary methods.2Event-Oriented Notation for Activation Spreading in FNNs/RNNs Throughout this paper,let i,j,k,t,p,q,r denote positive integer variables assuming ranges implicit in the given contexts.Let n,m,T denote positive integer constants.An NN’s topology may change over time(e.g.,Fahlman,1991;Ring,1991;Weng et al.,1992;Fritzke, 1994).At any given moment,it can be described as afinite subset of units(or nodes or neurons)N= {u1,u2,...,}and afinite set H⊆N×N of directed edges or connections between nodes.FNNs are acyclic graphs,RNNs cyclic.Thefirst(input)layer is the set of input units,a subset of N.In FNNs,the k-th layer(k>1)is the set of all nodes u∈N such that there is an edge path of length k−1(but no longer path)between some input unit and u.There may be shortcut connections between distant layers.The NN’s behavior or program is determined by a set of real-valued,possibly modifiable,parameters or weights w i(i=1,...,n).We now focus on a singlefinite episode or epoch of information processing and activation spreading,without learning through weight changes.The following slightly unconventional notation is designed to compactly describe what is happening during the runtime of the system.During an episode,there is a partially causal sequence x t(t=1,...,T)of real values that I call events.Each x t is either an input set by the environment,or the activation of a unit that may directly depend on other x k(k<t)through a current NN topology-dependent set in t of indices k representing incoming causal connections or links.Let the function v encode topology information and map such event index pairs(k,t)to weight indices.For example,in the non-input case we may have x t=f t(net t)with real-valued net t= k∈in t x k w v(k,t)(additive case)or net t= k∈in t x k w v(k,t)(multiplicative case), where f t is a typically nonlinear real-valued activation function such as tanh.In many recent competition-winning NNs(Sec.5.19,5.21,5.22)there also are events of the type x t=max k∈int (x k);some networktypes may also use complex polynomial activation functions(Sec.5.3).x t may directly affect certain x k(k>t)through outgoing connections or links represented through a current set out t of indices k with t∈in k.Some non-input events are called output events.Note that many of the x t may refer to different,time-varying activations of the same unit in sequence-processing RNNs(e.g.,Williams,1989,“unfolding in time”),or also in FNNs sequentially exposed to time-varying input patterns of a large training set encoded as input events.During an episode,the same weight may get reused over and over again in topology-dependent ways,e.g.,in RNNs,or in convolutional NNs(Sec.5.4,5.8).I call this weight sharing across space and/or time.Weight sharing may greatly reduce the NN’s descriptive complexity,which is the number of bits of information required to describe the NN (Sec.4.3).In Supervised Learning(SL),certain NN output events x t may be associated with teacher-given,real-valued labels or targets d t yielding errors e t,e.g.,e t=1/2(x t−d t)2.A typical goal of supervised NN training is tofind weights that yield episodes with small total error E,the sum of all such e t.The hope is that the NN will generalize well in later episodes,causing only small errors on previously unseen sequences of input events.Many alternative error functions for SL and UL are possible.SL assumes that input events are independent of earlier output events(which may affect the environ-ment through actions causing subsequent perceptions).This assumption does not hold in the broaderfields of Sequential Decision Making and Reinforcement Learning(RL)(Kaelbling et al.,1996;Sutton and Barto, 1998;Hutter,2005)(Sec.6).In RL,some of the input events may encode real-valued reward signals given by the environment,and a typical goal is tofind weights that yield episodes with a high sum of reward signals,through sequences of appropriate output actions.Sec.5.5will use the notation above to compactly describe a central algorithm of DL,namely,back-propagation(BP)for supervised weight-sharing FNNs and RNNs.(FNNs may be viewed as RNNs with certainfixed zero weights.)Sec.6will address the more general RL case.3Depth of Credit Assignment Paths(CAPs)and of ProblemsTo measure whether credit assignment in a given NN application is of the deep or shallow type,I introduce the concept of Credit Assignment Paths or CAPs,which are chains of possibly causal links between events.Let usfirst focus on SL.Consider two events x p and x q(1≤p<q≤T).Depending on the appli-cation,they may have a Potential Direct Causal Connection(PDCC)expressed by the Boolean predicate pdcc(p,q),which is true if and only if p∈in q.Then the2-element list(p,q)is defined to be a CAP from p to q(a minimal one).A learning algorithm may be allowed to change w v(p,q)to improve performance in future episodes.More general,possibly indirect,Potential Causal Connections(PCC)are expressed by the recursively defined Boolean predicate pcc(p,q),which in the SL case is true only if pdcc(p,q),or if pcc(p,k)for some k and pdcc(k,q).In the latter case,appending q to any CAP from p to k yields a CAP from p to q(this is a recursive definition,too).The set of such CAPs may be large but isfinite.Note that the same weight may affect many different PDCCs between successive events listed by a given CAP,e.g.,in the case of RNNs, or weight-sharing FNNs.Suppose a CAP has the form(...,k,t,...,q),where k and t(possibly t=q)are thefirst successive elements with modifiable w v(k,t).Then the length of the suffix list(t,...,q)is called the CAP’s depth (which is0if there are no modifiable links at all).This depth limits how far backwards credit assignment can move down the causal chain tofind a modifiable weight.1Suppose an episode and its event sequence x1,...,x T satisfy a computable criterion used to decide whether a given problem has been solved(e.g.,total error E below some threshold).Then the set of used weights is called a solution to the problem,and the depth of the deepest CAP within the sequence is called the solution’s depth.There may be other solutions(yielding different event sequences)with different depths.Given somefixed NN topology,the smallest depth of any solution is called the problem’s depth.Sometimes we also speak of the depth of an architecture:SL FNNs withfixed topology imply a problem-independent maximal problem depth bounded by the number of non-input layers.Certain SL RNNs withfixed weights for all connections except those to output units(Jaeger,2001;Maass et al.,2002; Jaeger,2004;Schrauwen et al.,2007)have a maximal problem depth of1,because only thefinal links in the corresponding CAPs are modifiable.In general,however,RNNs may learn to solve problems of potentially unlimited depth.Note that the definitions above are solely based on the depths of causal chains,and agnostic of the temporal distance between events.For example,shallow FNNs perceiving large“time windows”of in-put events may correctly classify long input sequences through appropriate output events,and thus solve shallow problems involving long time lags between relevant events.At which problem depth does Shallow Learning end,and Deep Learning begin?Discussions with DL experts have not yet yielded a conclusive response to this question.Instead of committing myself to a precise answer,let me just define for the purposes of this overview:problems of depth>10require Very Deep Learning.The difficulty of a problem may have little to do with its depth.Some NNs can quickly learn to solve certain deep problems,e.g.,through random weight guessing(Sec.5.9)or other types of direct search (Sec.6.6)or indirect search(Sec.6.7)in weight space,or through training an NNfirst on shallow problems whose solutions may then generalize to deep problems,or through collapsing sequences of(non)linear operations into a single(non)linear operation—but see an analysis of non-trivial aspects of deep linear networks(Baldi and Hornik,1994,Section B).In general,however,finding an NN that precisely models a given training set is an NP-complete problem(Judd,1990;Blum and Rivest,1992),also in the case of deep NNs(S´ıma,1994;de Souto et al.,1999;Windisch,2005);compare a survey of negative results(S´ıma, 2002,Section1).Above we have focused on SL.In the more general case of RL in unknown environments,pcc(p,q) is also true if x p is an output event and x q any later input event—any action may affect the environment and thus any later perception.(In the real world,the environment may even influence non-input events computed on a physical hardware entangled with the entire universe,but this is ignored here.)It is possible to model and replace such unmodifiable environmental PCCs through a part of the NN that has already learned to predict(through some of its units)input events(including reward signals)from former input events and actions(Sec.6.1).Its weights are frozen,but can help to assign credit to other,still modifiable weights used to compute actions(Sec.6.1).This approach may lead to very deep CAPs though.Some DL research is about automatically rephrasing problems such that their depth is reduced(Sec.4). In particular,sometimes UL is used to make SL problems less deep,e.g.,Sec.5.10.Often Dynamic Programming(Sec.4.1)is used to facilitate certain traditional RL problems,e.g.,Sec.6.2.Sec.5focuses on CAPs for SL,Sec.6on the more complex case of RL.4Recurring Themes of Deep Learning4.1Dynamic Programming(DP)for DLOne recurring theme of DL is Dynamic Programming(DP)(Bellman,1957),which can help to facili-tate credit assignment under certain assumptions.For example,in SL NNs,backpropagation itself can 1An alternative would be to count only modifiable links when measuring depth.In many typical NN applications this would not make a difference,but in some it would,e.g.,Sec.6.1.be viewed as a DP-derived method(Sec.5.5).In traditional RL based on strong Markovian assumptions, DP-derived methods can help to greatly reduce problem depth(Sec.6.2).DP algorithms are also essen-tial for systems that combine concepts of NNs and graphical models,such as Hidden Markov Models (HMMs)(Stratonovich,1960;Baum and Petrie,1966)and Expectation Maximization(EM)(Dempster et al.,1977),e.g.,(Bottou,1991;Bengio,1991;Bourlard and Morgan,1994;Baldi and Chauvin,1996; Jordan and Sejnowski,2001;Bishop,2006;Poon and Domingos,2011;Dahl et al.,2012;Hinton et al., 2012a).4.2Unsupervised Learning(UL)Facilitating Supervised Learning(SL)and RL Another recurring theme is how UL can facilitate both SL(Sec.5)and RL(Sec.6).UL(Sec.5.6.4) is normally used to encode raw incoming data such as video or speech streams in a form that is more convenient for subsequent goal-directed learning.In particular,codes that describe the original data in a less redundant or more compact way can be fed into SL(Sec.5.10,5.15)or RL machines(Sec.6.4),whose search spaces may thus become smaller(and whose CAPs shallower)than those necessary for dealing with the raw data.UL is closely connected to the topics of regularization and compression(Sec.4.3,5.6.3). 4.3Occam’s Razor:Compression and Minimum Description Length(MDL) Occam’s razor favors simple solutions over complex ones.Given some programming language,the prin-ciple of Minimum Description Length(MDL)can be used to measure the complexity of a solution candi-date by the length of the shortest program that computes it(e.g.,Solomonoff,1964;Kolmogorov,1965b; Chaitin,1966;Wallace and Boulton,1968;Levin,1973a;Rissanen,1986;Blumer et al.,1987;Li and Vit´a nyi,1997;Gr¨u nwald et al.,2005).Some methods explicitly take into account program runtime(Al-lender,1992;Watanabe,1992;Schmidhuber,2002,1995);many consider only programs with constant runtime,written in non-universal programming languages(e.g.,Rissanen,1986;Hinton and van Camp, 1993).In the NN case,the MDL principle suggests that low NN weight complexity corresponds to high NN probability in the Bayesian view(e.g.,MacKay,1992;Buntine and Weigend,1991;De Freitas,2003), and to high generalization performance(e.g.,Baum and Haussler,1989),without overfitting the training data.Many methods have been proposed for regularizing NNs,that is,searching for solution-computing, low-complexity SL NNs(Sec.5.6.3)and RL NNs(Sec.6.7).This is closely related to certain UL methods (Sec.4.2,5.6.4).4.4Learning Hierarchical Representations Through Deep SL,UL,RLMany methods of Good Old-Fashioned Artificial Intelligence(GOFAI)(Nilsson,1980)as well as more recent approaches to AI(Russell et al.,1995)and Machine Learning(Mitchell,1997)learn hierarchies of more and more abstract data representations.For example,certain methods of syntactic pattern recog-nition(Fu,1977)such as grammar induction discover hierarchies of formal rules to model observations. The partially(un)supervised Automated Mathematician/EURISKO(Lenat,1983;Lenat and Brown,1984) continually learns concepts by combining previously learnt concepts.Such hierarchical representation learning(Ring,1994;Bengio et al.,2013;Deng and Yu,2014)is also a recurring theme of DL NNs for SL (Sec.5),UL-aided SL(Sec.5.7,5.10,5.15),and hierarchical RL(Sec.6.5).Often,abstract hierarchical representations are natural by-products of data compression(Sec.4.3),e.g.,Sec.5.10.4.5Fast Graphics Processing Units(GPUs)for DL in NNsWhile the previous millennium saw several attempts at creating fast NN-specific hardware(e.g.,Jackel et al.,1990;Faggin,1992;Ramacher et al.,1993;Widrow et al.,1994;Heemskerk,1995;Korkin et al., 1997;Urlbe,1999),and at exploiting standard hardware(e.g.,Anguita et al.,1994;Muller et al.,1995; Anguita and Gomes,1996),the new millennium brought a DL breakthrough in form of cheap,multi-processor graphics cards or GPUs.GPUs are widely used for video games,a huge and competitive market that has driven down hardware prices.GPUs excel at fast matrix and vector multiplications required not only for convincing virtual realities but also for NN training,where they can speed up learning by a factorof50and more.Some of the GPU-based FNN implementations(Sec.5.16-5.19)have greatly contributed to recent successes in contests for pattern recognition(Sec.5.19-5.22),image segmentation(Sec.5.21), and object detection(Sec.5.21-5.22).5Supervised NNs,Some Helped by Unsupervised NNsThe main focus of current practical applications is on Supervised Learning(SL),which has dominated re-cent pattern recognition contests(Sec.5.17-5.22).Several methods,however,use additional Unsupervised Learning(UL)to facilitate SL(Sec.5.7,5.10,5.15).It does make sense to treat SL and UL in the same section:often gradient-based methods,such as BP(Sec.5.5.1),are used to optimize objective functions of both UL and SL,and the boundary between SL and UL may blur,for example,when it comes to time series prediction and sequence classification,e.g.,Sec.5.10,5.12.A historical timeline format will help to arrange subsections on important inspirations and techni-cal contributions(although such a subsection may span a time interval of many years).Sec.5.1briefly mentions early,shallow NN models since the1940s,Sec.5.2additional early neurobiological inspiration relevant for modern Deep Learning(DL).Sec.5.3is about GMDH networks(since1965),perhaps thefirst (feedforward)DL systems.Sec.5.4is about the relatively deep Neocognitron NN(1979)which is similar to certain modern deep FNN architectures,as it combines convolutional NNs(CNNs),weight pattern repli-cation,and winner-take-all(WTA)mechanisms.Sec.5.5uses the notation of Sec.2to compactly describe a central algorithm of DL,namely,backpropagation(BP)for supervised weight-sharing FNNs and RNNs. It also summarizes the history of BP1960-1981and beyond.Sec.5.6describes problems encountered in the late1980s with BP for deep NNs,and mentions several ideas from the previous millennium to overcome them.Sec.5.7discusses afirst hierarchical stack of coupled UL-based Autoencoders(AEs)—this concept resurfaced in the new millennium(Sec.5.15).Sec.5.8is about applying BP to CNNs,which is important for today’s DL applications.Sec.5.9explains BP’s Fundamental DL Problem(of vanishing/exploding gradients)discovered in1991.Sec.5.10explains how a deep RNN stack of1991(the History Compressor) pre-trained by UL helped to solve previously unlearnable DL benchmarks requiring Credit Assignment Paths(CAPs,Sec.3)of depth1000and more.Sec.5.11discusses a particular WTA method called Max-Pooling(MP)important in today’s DL FNNs.Sec.5.12mentions afirst important contest won by SL NNs in1994.Sec.5.13describes a purely supervised DL RNN(Long Short-Term Memory,LSTM)for problems of depth1000and more.Sec.5.14mentions an early contest of2003won by an ensemble of shallow NNs, as well as good pattern recognition results with CNNs and LSTM RNNs(2003).Sec.5.15is mostly about Deep Belief Networks(DBNs,2006)and related stacks of Autoencoders(AEs,Sec.5.7)pre-trained by UL to facilitate BP-based SL.Sec.5.16mentions thefirst BP-trained MPCNNs(2007)and GPU-CNNs(2006). Sec.5.17-5.22focus on official competitions with secret test sets won by(mostly purely supervised)DL NNs since2009,in sequence recognition,image classification,image segmentation,and object detection. Many RNN results depended on LSTM(Sec.5.13);many FNN results depended on GPU-based FNN code developed since2004(Sec.5.16,5.17,5.18,5.19),in particular,GPU-MPCNNs(Sec.5.19).5.11940s and EarlierNN research started in the1940s(e.g.,McCulloch and Pitts,1943;Hebb,1949);compare also later work on learning NNs(Rosenblatt,1958,1962;Widrow and Hoff,1962;Grossberg,1969;Kohonen,1972; von der Malsburg,1973;Narendra and Thathatchar,1974;Willshaw and von der Malsburg,1976;Palm, 1980;Hopfield,1982).In a sense NNs have been around even longer,since early supervised NNs were essentially variants of linear regression methods going back at least to the early1800s(e.g.,Legendre, 1805;Gauss,1809,1821).Early NNs had a maximal CAP depth of1(Sec.3).5.2Around1960:More Neurobiological Inspiration for DLSimple cells and complex cells were found in the cat’s visual cortex(e.g.,Hubel and Wiesel,1962;Wiesel and Hubel,1959).These cellsfire in response to certain properties of visual sensory inputs,such as theorientation of plex cells exhibit more spatial invariance than simple cells.This inspired later deep NN architectures(Sec.5.4)used in certain modern award-winning Deep Learners(Sec.5.19-5.22).5.31965:Deep Networks Based on the Group Method of Data Handling(GMDH) Networks trained by the Group Method of Data Handling(GMDH)(Ivakhnenko and Lapa,1965; Ivakhnenko et al.,1967;Ivakhnenko,1968,1971)were perhaps thefirst DL systems of the Feedforward Multilayer Perceptron type.The units of GMDH nets may have polynomial activation functions imple-menting Kolmogorov-Gabor polynomials(more general than traditional NN activation functions).Given a training set,layers are incrementally grown and trained by regression analysis,then pruned with the help of a separate validation set(using today’s terminology),where Decision Regularisation is used to weed out superfluous units.The numbers of layers and units per layer can be learned in problem-dependent fashion. This is a good example of hierarchical representation learning(Sec.4.4).There have been numerous ap-plications of GMDH-style networks,e.g.(Ikeda et al.,1976;Farlow,1984;Madala and Ivakhnenko,1994; Ivakhnenko,1995;Kondo,1998;Kord´ık et al.,2003;Witczak et al.,2006;Kondo and Ueno,2008).5.41979:Convolution+Weight Replication+Winner-Take-All(WTA)Apart from deep GMDH networks(Sec.5.3),the Neocognitron(Fukushima,1979,1980,2013a)was per-haps thefirst artificial NN that deserved the attribute deep,and thefirst to incorporate the neurophysiolog-ical insights of Sec.5.2.It introduced convolutional NNs(today often called CNNs or convnets),where the(typically rectangular)receptivefield of a convolutional unit with given weight vector is shifted step by step across a2-dimensional array of input values,such as the pixels of an image.The resulting2D array of subsequent activation events of this unit can then provide inputs to higher-level units,and so on.Due to massive weight replication(Sec.2),relatively few parameters may be necessary to describe the behavior of such a convolutional layer.Competition layers have WTA subsets whose maximally active units are the only ones to adopt non-zero activation values.They essentially“down-sample”the competition layer’s input.This helps to create units whose responses are insensitive to small image shifts(compare Sec.5.2).The Neocognitron is very similar to the architecture of modern,contest-winning,purely super-vised,feedforward,gradient-based Deep Learners with alternating convolutional and competition lay-ers(e.g.,Sec.5.19-5.22).Fukushima,however,did not set the weights by supervised backpropagation (Sec.5.5,5.8),but by local un supervised learning rules(e.g.,Fukushima,2013b),or by pre-wiring.In that sense he did not care for the DL problem(Sec.5.9),although his architecture was comparatively deep indeed.He also used Spatial Averaging(Fukushima,1980,2011)instead of Max-Pooling(MP,Sec.5.11), currently a particularly convenient and popular WTA mechanism.Today’s CNN-based DL machines profita lot from later CNN work(e.g.,LeCun et al.,1989;Ranzato et al.,2007)(Sec.5.8,5.16,5.19).5.51960-1981and Beyond:Development of Backpropagation(BP)for NNsThe minimisation of errors through gradient descent(Hadamard,1908)in the parameter space of com-plex,nonlinear,differentiable,multi-stage,NN-related systems has been discussed at least since the early 1960s(e.g.,Kelley,1960;Bryson,1961;Bryson and Denham,1961;Pontryagin et al.,1961;Dreyfus,1962; Wilkinson,1965;Amari,1967;Bryson and Ho,1969;Director and Rohrer,1969;Griewank,2012),ini-tially within the framework of Euler-LaGrange equations in the Calculus of Variations(e.g.,Euler,1744). Steepest descent in such systems can be performed(Bryson,1961;Kelley,1960;Bryson and Ho,1969)by iterating the ancient chain rule(Leibniz,1676;L’Hˆo pital,1696)in Dynamic Programming(DP)style(Bell-man,1957).A simplified derivation of the method uses the chain rule only(Dreyfus,1962).The methods of the1960s were already efficient in the DP sense.However,they backpropagated derivative information through standard Jacobian matrix calculations from one“layer”to the previous one, explicitly addressing neither direct links across several layers nor potential additional efficiency gains due to network sparsity(but perhaps such enhancements seemed obvious to the authors).。

极大似然估计:兰波特与丹尼尔 伯努利朱春浩(武汉船舶职业技术学院图书信息中心,湖北武汉 430050)摘 要 本文探讨了似然思想早期的历史,指出兰波特是发现极大似然估计法的第一人,与丹尼尔?伯努利共为似然思想的先驱。

关键词 极大似然估计;似然思想;兰波特;丹尼尔 伯努利中图分类号 C829.29 文献标志码 A 文章编号 1671-8100(2011)01-0105-06基金资助:教育部人文社会科学研究规划基金项目(项目批准号:09YJA910006),湖北省人文社会科学研究项目(项目编号:2008d153)。

收稿日期:2011-01-20作者简介:朱春浩,男,硕士,教授,主要研究方向:概率统计学及其历史研究。

众所周知,统计学中存在三大学派,即经典学派、贝叶斯学派、信念学派。

这三大学派由于其在统计哲学方面的分歧,使得它们对几乎所有的统计问题都有自己的一套解决方法。

如果说各个学派有什么共同点的话,那么 似然原理!肯定是一个。

经典学派大师奈曼和爱根 皮尔逊(E.S.Pearson)就是利用 似然原理!给出了著名的 似然比检验!,贝叶斯学派认为 似然函数!是 等同无知!情况下的后验分布,而 似然函数!更被信念学派的鼻祖费歇尔认为是统计推断的基础。

似然原理!看起来是如此地有魅力,这使得没有什么现代统计学家愿意完全拒绝它。

这一方面是因为 似然原理!的哲学基础既朴素又自然,另一方面是因为利用 似然原理!取得的成就有目共瞩。

因此研究 似然!的历史几乎不需要问为什么。

极大似然估计也称最大似然估计,是建立在极大似然原理的基础上的一个统计方法,极大似然原理的直观想法是:一个随机试验如有若干个可能的结果A,B,C,∀。

若在一次试验中,结果A 出现,则一般认为试验条件对A 出现有利,也即A 出现的概率很大。

下面我们对离散型与连续型母体两种情形阐述极大似然估计。

设 1, 2∀, n 为取自具有概率函数{f (x | ): # }的母体 的一个样本。

Introduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP / Methods / RefsA guide to Log P and pKa measurements andtheir useBy Mark Earll BSc(Hons) CChem MRSC (C) Copyright 1999-2006, All rights reserved.Return to Mark's Analytical Chemistry Index PageWinner of ACD Labs "Star Pick" AwardNB: You should have MDL's Chime installed to see these pages at their best!Disclaimer: This article is for guidance and educational purposes only. The author can accept no responsibility for loss or damage however caused. The author recommends that manufacturers advice be consulted exclusively when using any laboratory products.PREFACE TO 2006 REVISION: This page was written in 1999 and can be seen as summarising my practical knowledge of the field at that time. Things have moved onparticularly in the area of high throughput measurements. For the latest in high throughput pKa and LogP measurements I suggest you contact Sirius Analytical Instruments and for high throughput permeability contact Pion Inc . I will continue to add things to this site on the use of physical chemistry measurements in QSAR modelling. Please see section 1.7. to 1.9.Table of Contents:Introduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP / Methods / Refs / TopIntroductionz Introduction z ContentszUnderstanding pKa and Log P measurements.{The pH scale {Activity {Practical pH measurement {pKa or Dissociation Constant {Log P and Partition Coefficients {Choice of partition solvent{How are LogP results related to activity? {How are LogP results related to solubility? {What do LogP values mean in practice?zMeasurement strategyzLogP/pKa measurement techniques{Aqueous Titration using Sirius instruments {Yesuda-Shedlovsky experiment {Ion Pair Log P's {pKa by Manual Titration {pKa by U.V. Spectroscopy {pKa by Solubility Method {Filter Probe Measurements {Log D and Log P by Filter Probe Method {Log P by Shake Flask {Log P by HPLCz ReferenceszAppendix 1 - Calculating Log D and % ionisedzAppendix 2 - Worked example calculationsThe followingJavascript calculators will help you calculate % ionised and Log D from pKa and Log P values:Percent Ionised Log DTable of pKa values: (Coming soon)The pKa or 'Dissociation Constant' is a measure of the strength of an acid or a base. The pKa allows you to determine the charge on a molecule at any given pH.The Partition Coefficient is a measure of how well a substance partitions between a lipid (oil) and water. pKa and Log P measurements are useful parameters for use in understanding the behaviour of drug molecules. Different ionic species of a molecule differ in physical chemical and biological properties and so it is important to be able to predict which ionic form of the molecule is present at the site of action. The Partition Coefficient is also a very useful parameter which may be used in combination with the pKa to predict the distribution of a drug compound in a biological system. Factors such as absorption, excretion and penetration of the CNS may be related to the Log P value of a drug and in certain cases predictions made.The measurement of pKa and Log P values are not straightforward. Experiments must be very carefully performed under standard conditions to ensure the results are valid and require interpretation of data which takes time and experience. In addition no one method is available for all compounds due to problems of insolubility, lack of removable protons and extreme values.This guide gives the theoretical basis of the pKa and LogP parameters as well as describing the techniques that can be used to measure them indicating which methods are appropriate for problem samples. I have also briefly indicated the use of these measurements in rational drug design.For more information please see the References section.Introduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP / Methods / Refs / Top 1.0 Understanding pKa and Log P measurements.1.1 The pH scaleArrhenius 1887 was the first person to give a definition of an acid and a base, namely that an Acid gives rise to excess of H+ in aq solution whereas a Base gives rise to excess of OH- in solution. This was refined by Bronsted-Lowry in 1923 such that a proton donor was defined as an acid and a proton acceptor as a base They also introduced the familiar concept of the conjugate Acid - Base pair. The final refinement to Acid Base theory was completed by Lewis in 1923 who extended the concept to an Acids being an e -pair acceptor and a base a e -pair donor.The pH concept was introduced in 1909 by the Danish chemist S.P.L.SorensonpH is defined by the negative logarithm of the hydrogen ion activity:where aH = activity of the hydrogen ionThe pH scale derives from the characteristics of the auto-dissociation of Water. Pure water has a low conductivity and is only slightly ionised however does Water dissociate slightly into Hydronium ions and hydroxide ions:orThe concentration of H+ and OH- ions, which are equal, are 1x 10-7 ions per litre The equilibrium constant (or ion product ) for the dissociation of water, Kw, isby taking logs of both side we get:Using the standard abbreviation p for {-log10} we get:This equation sets the pH scale to 0-14, which gives a convenient way to express 14 orders of magnitude of [H+]. Any solution with pH>7 contains excess hydroxyl ions and is alkaline; those with pH<7 are acidic, containing excess hydrogen ionspH scaleIntroduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP / Methods / Refs / Top1.2 ActivityA complication arises in electrochemistry due to the non-ideal nature of ions in solution. The activity of an ion at infinite dilution is equal to its concentration but as the concentration increases ionic attraction and incomplete hydration results in a drop in effective concentration. This means the law of Mass Action is only valid when activities are used in place of concentrationsActivity is defined as the "apparent concentration" of an ionic species, due to the attraction which ions can exert on one another and the incomplete hydration of ions in solutions that are too concentrated. The lower the concentration the less the interaction becomes. At infinite dilution activity coefficients approach unityThe activity of a species X is equal to the product of its concentration and its activity coefficient,The pH from an electrode relates to {H+} not [H+] though below Ionic strength of 0.01 these terms are very close between pH 2 and pH 10Introduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP / Methods / Refs / Top1.3 Practical pH measurementA pH electrode consists of a pH sensor which varies in proportion to the {H+} of the solution and a reference electrode which provides a stable constant voltage. The output is in mV which needs to be converted to pH units.Where Ec = reference potentialNf = Nernstian slope factor = Nf=2.3RT/nF = 59.1 at 25 CWhere R=Gas constantT=abs Temp in KelvinF=faraday constantn=Valance factorAs can be seen from the equation the slope factor is temperature dependentthe pH is derived from:At pH 7 where {H+}={OH-} the voltage from the electrode is zero, this is called the Isopotential Point. In theory this point is temperature independent. IUPAC-NBS operational pH scale is defined as the pH relative to a standard buffer measured using hydrogen electrode. In practice a pH electrode is calibrated with a standard pH 7.00 buffer to determine the isoelectric point and a standard buffer at either pH 4 or 9 to determine the slope. Conventional pH meters will read accurately over a range 2.5 - 11. Beyond this their accuracy is dubious.In recent years Sirius Analytical Instruments have produced a series of dedicated pKa/LogP instruments. In the PCA 101 pKa instrument the calibration is carried out in a more sophisticated way adding empirical correction factors at the extreme ends of the pH spectrum where the electrode behaviour is non-ideal. In this way measurements at pH 1 or 13 are possible. This is based on the work of Alex Avdeef (1)Introduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP / Methods / Refs / Top 1.4 pKa or dissociation constantBronsted was the first to show the advantage of expressing the ionisation of both acids and bases the same scale. He made an important distinction between Strong and weak bases:Strong acids and bases - defined as completely ionised in pH range 0-14Weak acids and bases - defined as incompletely ionised in pH range 0-14The pKa or ionisation constant is defined as the negative logarithm of the equilibrium coefficient of the neutral and charged forms of a compound. This allows the proportion of neutral and charged species at any pH to be calculated, as well as the basic or acidic properties of the compound to be defined."Thermodynamic Ionisation Constants" require the use of activities, being an "Infinite Dilution" definition. The measurement of activities is highly impractical, so in practice a high ionic strength swamping background electrolyte is used to give a "Constant Ionic Medium" pH definition. This is closely related to the thermodynamic definition. Such pKa values are independent of concentration and are of the type usually quoted in the literature.Thermodynamic Ionisation constantsfor acids:where{ } = activity in Mole litre-1pKa = -log10(Ka)for basespKa = -log10(Ka)At a given temp these are Thermodynamic Ionisation constants, which are independent of concentration. KTa. Since log 1 = 0 the pKa corresponds to the pH at which the concentration of ionised and neutral forms are equal.Ionisation constants that measured by Spectroscopy are "Concentration Ionisation Constants" These constants are measured ignoring activity effects and are dependent on concentration. It is therefore important that the concentration of the compound measured is quoted. Comparison of different compounds is only valid if their concentrations are identical.Concentration Ionisation constantswhere [] = concThese result from spectroscopic measurements where concentrations are used due to the beer lambert law.The "Thermodynamic" Ionisation Coefficient is related to the "Concentration" Ionisation Coefficient by:where f=activity coefficientpKa values are temperature dependent in a non-linear and unpredictable way. Samples measured by potentiometry are held at a constant temperature using a water jacket and thermostated water bath. Spectroscopic values are measured at ambient temperature. No pKa value should ever be quoted without the temperature. There is the additional question of whether pKa values should be measured at biological temperature as well as the standard 25 degrees. The former would have more meaning to biologists and the latter to chemists. Standard practice is to measure pKa’s at 25’CA useful formula for calculating the % ionisation of a compound at a particular pH from its pKa is(Where charge = 1 for bases and -1 for acids)% ionised plots of an Acid and a Base with a pKa of 8.0:Introduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP / Methods / Refs / Top1.5 Log P and Partition CoefficientsThe Partition Coefficient itself is a constant. It is defined as the ratio of concentration of compound in aqueous phase to the concentration in an immiscible solvent, as the neutral molecule . In practical terms the neutral molecule exists for bases > 2 pKa units above the pKa and for acids > 2 pKa units below. In practice the Log P will vary according to the conditions under which it is measured and the choice of partitioning solvent.Partition CoefficientPartition Coefficient, P = [Organic] / [Aqueous] Where [] = concentration Log P= log 10 (Partition Coefficient)NOTE:Log P = 1 means 10:1 Organic:Aqueous Log P = 0 means 1:1 Organic:Aqueous Log P = -1 means 1:10 Organic:AqueousLog D is the log distribution coefficient at a particular pH. This is not constant and will vary according to the protogenic nature of the molecule. Log D at pH 7.4 is often quoted to give an indication of the lipophilicity of a drug at the pH of blood plasma.Distribution CoefficientDistribution Coefficient, D = [Unionised] (o) / [Unionised] (aq) + [Ionised] (aq) Log D = log 10 (Distribution Coefficient )LogD is related to LogP and the pKa by the following equations:for acids for basesAcid withpKa = 8.0Base with pKa = 8.0The graphs below show the distribution plots of an acid a base and a zwitterionIon Pair PartitioningIn practice not only neutral molecules but also ion pairs may partition. The charged species may pair with a reagent ion or even, in certain cases, itself. This leads to great complication of the experimental determination. Both the Log P and the LogD values may be affected if one or more of the charged species partitions. Ion pairing effects may be fully determined with the Sirius PCA101 or GL-pKa instrument, but at least two to three titrations need to be carried out. Ion pairing effects will cause errors in any spectroscopic measurements.Both the ionic strength and the type of counter ion used in solution have a pronounced effect on the ion pairing phenomenon. The high ionic strength used in the potentiometric determinations in the Sirius PCA101 instrument tends to encourage ion pairing effects. The spectroscopic measurements of Log P are measured at a much lower ionic strength, hence comparisons will be invalid.The question arises how valid is the use of a background electrolyte? Typically 0.1M of a background electrolyte is used. This is very close to the biological level of 0.16M. The type of electrolyte is also called into question. 0.15 M KCl is generally used due to its similarity with NaCl. NaCl cannot be used because of the "sodium effect" on the electrode at high pH. Measurements in KCl have been found to match those in NaCl almost exactly. Initially the Sirius Instruments used KNO 3, as used in thedevelopment of Metal Ligand binding titrations, from which the titrimetric method was developed. KNO 3 is obviously alien to most biological systems.Introduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP / Methods / Refs / Top1.6 Choice of Partition solventThe choice of partition solvent has been subject to debate in recent years. The most commonly used solvent has been octan-1-ol after the work of Leo and Hansch at Pomona college California. Octanol was chosen as a simple model of a phospholipid membrane; however it has shown serious shortcomings in predicting Blood-brain barrier or skin penetration. More recently a group at ICI in 1989, (Leahy, Taylor and Wait) have proposed the use of four critical solvents for modelling biological membranes. These are octanol, chloroform, cyclohexane and propylene glycol dipelargonate (PGDP). Log P values measured in these different solvents show differences principally due to hydrogen bonding effects. Octanol candonate and accept hydrogen bonds whereas cyclohexane is inert. Chloroform can donate hydrogen bonds whereas PGDP can only accept them.Acid pKa = 8Base pKa =8Zwitterion pKa (base) = 5.6 & (acid) = 7.0Octanolamphiprotic (H-bonding)Which solvent to use is debatable; however delta log P values have been found to be useful in several QSAR studies.Liposomes.Recently partitioning experiments have been carried out with Liposomes. Liposomes are self assemblingmodel membranes composed of phopholipid groups such as phosphatadylcholine. The lipid molecule isChloroformproton donor (H-bonding)PGDPproton acceptor (H-bonding)AlkaneinertPhospholipidPhospholipid Model: (ref 8)log P (octanol-water) - logP (PGDP-water) predicts cardioselectivity in oxypropanolamines (ref 5)log P (octanol-water) - logP (alkane-water)has been suggested reflects hydrogen bonding capacity, which has implications for skin penetration. Compounds with high log P values and low H bonding capacity can readily get past ester/phosphate groups in skin membranes. (ref 6)log P (octanol-water) -logP (cyclohexane-water)correlates inversely with Log(Cbrain/Cblood) for a series of H2-receptor histamine antagonists (ref 7)dissolved in chloroform and deposited by evaporation onto a large surface such as a large round bottomed flask. The liposome is then hydrated by adding water and agitated. The lipids then self assemble to form lipid bilayers which form spheres, often concentric (multilammellar). For partitioning experiments it has been found that Unilamellar (single layer) liposomes are required. These can be formed by a a combination of freeze-thawing and extrusion through a fine filter or french press under pressure.Neutral LogP values from liposomes tend to be very similar to those measured in octanol but the ion-pair LogP values differ. The "Surface Ion Pair" log P is found to be much higher in bases, zwitterions and amphophiles. The values for acids tend to be similar to the octanol values. This reflects the increased potential for partitioning of molecules with basic groups into membranes.QSAR studies have found improved correlations with liposome derived "Surface Ion Pair" LogP values. It should be realised that for some compounds it is not possible to make measurements due to insolubility, impurity or instability reasons. It is practically impossible to make measurements on highly insoluble compounds, although pKa values may sometimes be measurable by aqueous-methanol titrations. In practical terms results become meaningless for compounds with extreme insolubility.Introduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP / Methods / Refs / Top 1.7 How are Log P results related to biological activity?Relationships between Log P and activity are often found in series where structural modifications have not significantly affected the pKa values. Hansch in 1964 showed that these relationships were often parabolic hence the relationship often leads to an optimum value for the log P for a desired activity or selective distribution. Relationships of the type:Activity= m log P + k’ (linear)Activity= m log P - c(log P)2 - k(parabolic)Activity= m log P - c(blog P +1) - k (rectilinear) (where m, k and c are constants)are generated using regression analysis to correlate observed biological data with measured partition coefficients.The best way of relating LogP, pKa and other physico-chemical data to biological activity is using Multivariate techniques such as Principal Components Analysis and Partial Least Squares Regression. To understand these techniques and for software to do this please visit Umetrics at It must be remembered that measured log P values only correlate with activity in certain instances. The use of organic solvents to model complex biolipids is very simplistic and cannot explain phenomena such as the large difference in activity between molecules of wildly different structures or between enantiomers. In these cases it is very useful to combine physical measurements with molecular modelling, molecular property and spectroscopic data and use multivariate analysis.For both CNS penetration and gastric absorption many studies show a parabolic relationship with an optimum Log P value of around 2 ± 1. Evidence for this comes from a wide variety of experiments in the literature from brain concentration of radiolabelled compounds to CNS behavioural studies. Recently more sophisticated analysis of molecular properties such as "Partial Charged Surface Area" (PSA) and the hydrogen bonding properties of molecules have lead to better predictions of oral absorption.Although lipophilicity is just one of many factors involved in biological activity it is often one of the most influential. In PLS regression of molecular properties vs biological activity measurements of LogP almost always features in the more important coefficients. It is also a good idea to add a LogP squared to any regression analysis to take account of the non linearity mentioned above.1.8 How are Log P results related to solubility?Log P’s of neutral immiscible liquids run parallel with their solubilities in water; however for solids solubility also depends on the energy required to break the crystal lattice. Bannerjee, Yalkowsky and Valvoni (1980) Envir.Sci.Tech ,14,1227 have suggested the following empirical equation to relate solubility, melting point and Log P:where S is the solubility in water in micromoles per litre.It is therefore possible to have compounds with high Log P values which are still soluble on account oftheir low melting point. Similarly it is possible to have a low Log P compound with a high melting point, which is very insoluble.In cases of precipitation when titrating a basic compound, the solubility of the free base may be calculated using the equation:1.9 What do Log P values mean in practice?From a survey of the literature, it is possible to obtain some general guidelines about the optimum Log P values for certain classes of drugs. When designing drug molecules some thought should be given to the following:Studies have found: (bear in mind these may not apply to your class of chemicals)z OptimumCNS penetration around Log P = 2 +/- 0.7 (Hansch) z Optimum Oral absorption around Log P = 1.8 z Optimum Intestinal absorption Log P =1.35 z Optimum Colonic absorption LogP = 1.32 z Optimum Sub lingual absorption Log P = 5.5 zOptimum Percutaneous Log P = 2.6 (& low mw)Formulation and dosing forms:z Low Log P (below 0) Injectable z Medium (0-3) Oralz High (3-4) TransdermalzVery High (4-7) Toxic build up in fatty tissuesDrug Clearance and Toxicityz Increasing LogD 7.4 above 0 will decrease renal clearance and increase metabolic clearance. z High Log D7.4 compounds will tend to be metabolised by P450 enzymes in the liver. z A high degree of ionisation keeps drugs out of cells and decreases systemic toxicity. z pKa in range 6 to 8 is advantageous for membrane penetration.zDrugs should be designed with the lowest possible Log P , to reduce toxicity, non-specific binding, increase ease of formulation and bioavailability. Drugs should also be as low mw as possible to lower the risk of allergic reactions. (See principle of minimum hydrophobicity )Physiological pH values:zStomach 2Where: = solubility at= solubility of free basez Kidneys 4.2 (variable)z Small Intestine Fed 5.0 Fasted 6.8z Duodenal Mucus 5.5z Plasma 7.4Principle of minimum hydrophobicityTaken from the introductory chapter in "Lipophilicity in Drug Action and Toxicology" VCH 1995 Vol 4p22-24 Bernard Testa, Vladimir Pliska and Han van de Waterbeemd."Both parabolic and bilinear relationships allow one to derive the optimum value of log P for transport to a givenlocation, within the time of a biological assay. Evidence for an optimum lipophilicity for CNS depressants wasfound by 1968. Hancsh was then able to assert that in order for drugs to gain rapid access to the CNS, theyshould preferably have a logP value near 2.0. Subsequently, studies on anesthetics, hypnotics and other CNSagents have lead to the "Principle of Minimum Hydrophobicity in Drug Design" The thrust of this is to keepdrugs out of the CNS, and thereby avoid CNS related side effects such as depression, weird dreams andsedation, one should design drugs so that logP is considerably lower than 2.0. This ploy has been successful inthe new generation of non-sedative antihistamines.That we require drugs to have lower rather than higher lipophilicity depends also on other observations madeover the past 30 years. Many studies on plants animals, fish various organelles such as liver microsomes, andenzymes have shown a linear increase in toxicity or inhibitory action in a series of compounds as LogP or piincreases.A very high lipophilicity should also be avoided because of adverse effects on protein binding and on drugabsorption, including solubility.Linear and sometimes parabolic relationships have been found between lipophilicity and drug metabolism, eitherin whole animals, in liver microsomes, or by specific enzymes such as cytochrome P450. Metabolism can beundesirable for two reasons; it may limit drug bioavailability, or it may produce toxic metabolites.The ideal drug candidate, going into human studies, should have already been designed with the idea of keepinglipophilicity as low as possible, provided this can be done without loss of affinity to the target receptor." Lipinski's "Rule of 5" for DrugsChris Lipinski of Pfizer derived an easy to use 'rule of thumb' for drug likeness in molecules after surveying the worlds marketed drugs.The rule states that for reasonable absorptionz Keep H-Bond donors below 5 (sum of OH and NHs)z Keep mW below 500z Log P should be below 5z No more than 10 H bond acceptors (sum of Ns and Os)Like all rules they are there to be broken and a number of exceptions exist. I have personally worked on a couple of well-absorbed drugs which broke this rule but as a general guide it works well. Remember that you may have charge in your molecule so that LogD(7.4) or LogD(5.5) is really the important parameter rather than Log P. Keeping LogD(7.4) around 2 seem generally good advice. Manipulating the pKa can be a way of improving a molecule.Clarke-Delaney "Guide of 2" for AgrochemicalsErik Clarke and John Delaney of Syngenta have derived a set of guidelines for agrochemicalsz Mw 200-400z Mpt <200z LogPoct <2z pKa (base) 7+/- 2z Log Sw 2+/-1z Stability alerts <2For other attempts at rules for agrochemicals see references 19 and 20 RefsIntroduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP / Methods / Refs / Top 2.0 Measurement StrategyThe strategy for measuring pKa and Log P is determined by the solubility of a compound. The compound must be soluble (and stable) during any procedure to ensure equilibrium is maintained.Typically in titration methods the compound is titrated towards the direction of its neutral form, resulting in a dramatic drop in solubility. Often several experiments are required to determine the concentration required for the compound to stay in solution. Data collected while precipitation is occurring produces incorrect results. Sometimes if sufficient data is collected while the compound is in solution the pKa may still be calculated.The pKa's of poorly soluble compounds must be measured in aqueous-methanol solution. If several titrations are carried out with different ratios of Methanol:Water the Yesuda-Shedlovsky equation can reveal the theoretical pKa in purely aqueous solution.Log P determination of poorly soluble compounds is a problem. Provided the Log P is high enough the compound may be determined by titration, adding the sample to the octanol first. The compound will then back partition into the aqueous layer. If this fails then spectroscopic methods have to be employed since more dilute solutions may be used.Substances submitted for pKa and LogP need to be pure, of accurately known composition and be submitted as free bases or inorganic acid salts. In general no reliable measurements can be made on organic acid salts.A good strategy is to submit compounds in a series. The reasons for this are:z to compare and contrast the properties of a closely related series, using directly comparabletechniques.z to find a common measurement strategy for all the compounds in a seriesz to identify experimental problems common to the seriesz to prevent unnecessary measurements, only key members of the series should be chosenz to ensure reagents with short shelf lives, and apparatus can be preparedIntroduction / pH / Activity / pH measurement / pKa / LogP / Partition Solvents / Use of LogP / Methods / Refs / Top 3.0 Log P/pKa measurement techniques:Method Measures Advantage Disadvantage Concrequired Sample sizeSirius Potentiometric pKa/Log P pKa, Log P,Log PappRapid, Convenient Insoluble or neutralsamples cannot bemeasured0.0001M(0.1mM)1-5 mgSirius Yesuda-Shedlovsky pKa pKa for insoluble samples Takes three or moretitrations0.0005M(0.5mM)5mgSirius Ion Pair Log P LogP, Log P(ip)Predict Log D moreaccurately Takes three or moretitrations0.0001M(0.1mM)3-15 mgManual potentiometric pKa pKa Simple, rapid Not for low oroverlapping pKa's>0.0025M(2.5mM)50 mgpKa by UV pKa pKa for poorly soluble orscarce compounds Slow0.000025M(25uM)6 mgpKa by Solubility pKa pKa for very insolublecompounds Slow, Low accuracy Below0.0005M(0.5mM)10 mgLogP by Filter Probe Log P Log P for poorly solublecompounds, Reliable > Log P of0.2.Messy, Slow to setup, requires care.Inaccurate below LogP of 0.20.000025M(25uM)6 mg。

Practice of EpidemiologyFamilial Relative Risk Estimates for Use in Epidemiologic AnalysesYutaka Yasui 1,Polly A.Newcomb 2,3,Amy Trentham-Dietz 3,and Kathleen M.Egan 41Department of Public Health Sciences,School of Public Health,University of Alberta,Edmonton,Alberta,Canada.2Cancer Prevention Program,Division of Public Health Sciences,Fred Hutchinson Cancer Research Center,Seattle,WA.3University of Wisconsin Comprehensive Cancer Center,Madison,WI.4Vanderbilt University School of Medicine and Vanderbilt-Ingram Cancer Center,Nashville,TN.Received for publication August 7,2005;accepted for publication March 21,2006.Commonly used crude measures of disease risk or relative risk in a family,such as the presence/absence of disease or the number of affected relatives,do not take into account family structures and ages at disease oc-currence.The Family History Score incorporates these factors and has been used widely in epidemiology.How-ever,the Family History Score is not an estimate of familial relative risk;rather,it corresponds to a measure of statistical significance against a null hypothesis that the family’s disease risk is equal to that expected from reference rates.In this paper,the authors consider an estimate of familial relative risk using the empirical Bayes framework.The approach uses a two-level hierarchical model in which the first level models familial relative risk and the second considers a Poisson count of the number of affected relatives given the familial relative risk from the first level.The authors illustrate the utility of this methodology in a large,population-based case-control study of breast cancer,showing that,compared with commonly used summaries of family history including the Family History Score,the new estimates are more strongly associated with case-control status and more clearly detect effect modification of an environmental risk factor by familial relative risk.Bayes theorem;family;Poisson distribution;regression analysis;riskAbbreviations:AFB,age at first birth;CBCS II,Collaborative Breast Cancer Study II;FSIR,Familial Standardized Incidence Ratio;MLE,maximum likelihood estimator.Estimates of disease relative risk in families have impor-tant utilities in investigations of disease etiology.They are used to examine whether the disease of interest clusters in certain families and whether its etiology has a familial component.They are also used to adjust for familial ag-gregations when evaluating the effects of other nonfamilial etiologic factors in epidemiologic studies.Furthermore,familial relative risk estimates are used to examine effect modification of an etiologic factor according to levels of disease relative risk in families.Finally,a valid assessment of familial relative risk may have important clinical utility in triaging persons for more involved genetic screening and informing family members about potential risks.In spite of the important utilities,family history informa-tion is often handled rather crudely in epidemiologic analy-ses.A commonly used summary of family history is a binary indicator (yes/no)of whether study participants have af-fected family members,often gender specific,in first-or second-degree relatives.Another summary that carries a little more information is the number of affected family members.These crude summaries have two critical deficien-cies in view of their use as familial relative risk estimates.First,they do not account for family size,structure,or ages of family rger families and families with older members are naturally more likely to have members who have developed chronic diseases such as cancer.Second,theCorrespondence to Dr.Yutaka Yasui,Department of Public Health Sciences,University of Alberta,13-106J Clinical Sciences Building,Edmonton,Alberta T6G 2G3,Canada (e-mail:yyasui@ualberta.ca).697Am J Epidemiol2006;164:697–705American Journal of EpidemiologyCopyright ª2006by the Johns Hopkins Bloomberg School of Public Health All rights reserved;printed in U.S.A.Vol.164,No.7DOI:10.1093/aje/kwj256Advance Access publication August 21,2006at :: on November 11, 2014/Downloaded fromcrude summaries do not take chance into account:families with identical familial relative risk levels,sizes,structures,and ages can yield different numbers of affected members by chance alone.Kerber (1)proposed the Familial Standardized Incidence Ratio (FSIR)as a measure of familial relative risk that ac-counts for family size,structure,or ages of family members.Boucher and Kerber (2)applied a linear empirical Bayes approach to log f 1þlog(1þFSIR)g with a normality as-sumption to its underlying true values.In this paper,we extend Kerber’s method for estimating familial relative risk levels,applying empirical Bayes estimation methods with a nonparametric discrete prior distribution to overcome the deficiencies of the crude summaries.Following a brief re-view of the Family History Score (3),which was proposed for the same reasons as described above,we explain why it is actually not an estimate of familial relative risk.The utility of the new method proposed here is shown in a large,population-based case-control study of breast cancer.Two main points are illustrated.First,the empirical Bayes esti-mates of familial relative risk are associated with case-control status more strongly than other summary measures of family history,including Family History Scores.Second,they detect an effect modification of an environmental risk factor according to the level of familial relative risk more clearly than do other summary measures.In the Discussion section of this paper,we outline the potential use of the empirical Bayes familial relative risk estimates in other areas of public health and clinical research.FAMILY HISTORY SCOREA method previously proposed to overcome the defi-ciencies of the crude summaries and used widely in epide-miologic analyses is the Family History Score (3).In thisapproach,an expected risk of the disease of interest is com-puted for each family member by using a set of external reference rates for the disease.For i th family’s j th member,the expected risk E ij is given by the cumulative risk of the disease under observation (4):E ij ¼1ÿexp ÿXkk k t ijk !;where k k is the external reference rate for the k th stratum(e.g.,age-sex-race–defined stratum)and t ijk is the length of time that i th family’s j th member spent under observation in the k th stratum.Ages of family members are accounted for in the computation of the expected risks.The Family His-tory Score Z i for i th family is defined byZ i ¼P j O ij ÿP j E ijPj E ij ð1ÿE ij Þn o ;where O ij is the disease indicator of i th family’s j th mem-ber.If the disease is rare,then E ij is approximately equal to Pk k k t ijk and E ij ð1ÿE ij Þ E ij ;resulting in a simpler formula:Z i ¼P j O ij ÿPj E ij Pj E ij1=2:The Family History Score Z i is in the form of a test sta-tistic,which suggests a measure of statistical significance against a null hypothesis that the disease risk for each family member is equal to the expected risk computed from the external reference rates.A Bernoulli random variable O ij has the ‘‘success probability’’E ij under the null hypothesis and,accordingly,we haveE XjO ij 2435¼X jE ij Var XjO ij 2435¼X jE ij ð1ÿE ij Þ;where the variance formula assumes that O ij ’s within each family are uncorrelated.The Family History Score Z i can then be seen as a test statistic in the form of ðX ÿE ½X Þ=ðVar ½X Þ1=2that usually leads to a standard normal large-sample distribution,where the large sample refers to the size of each family being large.A Family History Score is actually not an estimate of the familial relative risk level.It is a test statistic for a null hypothesis that the disease risk for each family member is equal to the expected risk computed from the external ref-erence rates.Statistical significance determined by the ob-served value of a test statistic is a function of a sample size (i.e.,family size,structure,and ages)as well as the degree of departure from the null hypothesis (i.e.,familial relative risk levels).Data for larger families tend to give higher statistical significance and therefore larger absolute values of Family History Scores given the same level of familial risk.Note also that the numeric values of Family History Scores cannot be interpreted directly.They suggest statis-tical significance levels determined according to a known probability distribution of the test statistic.In other words,Family History Scores order families by statistical signifi-cance against the null hypotheses,but their numeric values require a metric,the known probability distribution of the test statistic,in order to have interpretable numeric distances between them.These considerations have led us to a dif-ferent approach to estimating familial relative risk levels,which shares similarities with the methods of Kerber (1)and of Boucher and Kerber (2).EMPIRICAL BAYES ESTIMATES OF FAMILIAL RELATIVE RISKWe define the familial relative risk of the disease for i th family as the relative risk of the disease shared by the mem-bers of i th family relative to the external reference.Our model isE ½O ij ¼h i E ij ;698Yasui et al.Am J Epidemiol 2006;164:697–705at :: on November 11, 2014/Downloaded fromwhere O ij ’s are Bernoulli random variables conditionally independent given h i ’s.We may estimate h i by maximiz-ing the sum of the Bernoulli log-likelihood for i th family.The score equation that the maximum likelihood estimator(MLE)ˆhi satisfies is Pj ðO ij ÿˆh i E ij ÞP j ˆh ið1ÿˆh i E ij Þ¼0and the MLE can be simplified to ˆh i ¼P j O ij =P jE ij ;the standardized mortality (or incidence)ratio,under the rare disease assumption.The precision of the MLEs variesacross families,however,because ˆhi is based solely on i th family’s data,and family sizes,structures,and ages differ across families.Small families with Pj O ij 1could yieldextremely high values of ˆhi ’s just by chance alone.Similar difficulties with the MLEs can occur in other bio-statistical applications such as estimation of small-area dis-ease risks (5)and comparison of risk across hospitals for a given medical procedure (6).A common feature shared by these problems is that there are many parameters to be es-timated,each of which is indexed by one of the units of var-ious sizes (e.g.,families,small areas,and hospitals),and the data available from each unit are limited.As a consequence,extreme values of MLEs occur for small units corresponding to very large variances of MLEs.Such difficulties with MLEs can be alleviated by theuse of hierarchical models in which ˆhi ’s are considered random quantities and are modeled in an additional hier-archical layer.Specifically,the hierarchical model takes the formO ij ’s given h i ’s,are independent Bernoulli randomvariables with E ½O ij j h i ¼h i E ij h i ’s are independent following a common distribution G ;8<:where G denotes a probability distribution over positive real numbers.Let us call the layers for O ij j h i and h i the ‘‘observ-able level’’and the ‘‘latent level’’of the hierarchical model,respectively.The latent level assumes common stochastic features for h i ’s,which provide additional information on shared characteristics of h i ’s that are not used to compute MLEs.By adding the latent level,estimators of h i ’s can ‘‘borrow strength’’from other units (e.g.,families)by com-bining the information on each individual unit with that on the common characteristics of h i ’s.For the distribution G of h i ’s,we propose the use of a (nonparametric)discrete distribution with K levels of fa-milial relative risk f /k ;k ¼1;2;...;K g and their associ-ated probabilities f p k g .While G can be a (parametric)continuous distribution such as gamma or lognormal distri-butions,the nonparametric G has an advantage in its flex-ible shape,determined by the data.Maximum likelihood estimation of the nonparametric G has been discussed by a number of authors (7–9).To compute the MLE of G ,we used the C.A.MAN program (Computer Assisted Mixture ANalysis)of Bo ¨hning et al.(10)and their freeware (11).Once the MLE of G is computed,the empirical Bayes esti-mate of h i is given by the posterior mean of h i with the MLE f ˆ/kg ;f p ˆk g ;and K ˆ:ˆh i ¼P K ˆk ¼1ˆ/k p ˆk L ðo i ;ˆ/k ÞP K ˆk ¼1pˆk L ðo i ;ˆ/k Þ;where L ðo i ;ˆ/kÞis the probability of observing the realiza-tion vector o i ¼ðo i 1;o i 2;...Þgiven /k ¼ˆ/k :Note that ˆh i is of the form of a weighted average of f ˆ/kg :APPLICATION TO AN EPIDEMIOLOGICINVESTIGATION OF BREAST CANCER ETIOLOGYAs an example,we apply the proposed familial risk es-timates to a large,population-based case-control study ofbreast cancer.Two main points are illustrated.First,the empirical Bayes estimates of familial relative risk are asso-ciated with case-control status more strongly than other summary measures of family history,including Family His-tory Scores.Second,these estimates detect an effect modi-fication of an environmental risk factor according to the level of familial relative risk more clearly than do other summary measures.Collaborative Breast Cancer Study IIThe data used in this illustration were derived from the Collaborative Breast Cancer Study II (CBCS II);the CBCS II study protocol was approved by the institutional review boards of the participating institutions (12,13).Briefly,CBCS II was a case-control study of breast cancer in which cases were female residents of Wisconsin,Massachusetts (excluding metropolitan Boston),and New Hampshire with a new diagnosis of invasive breast cancer reported to each state’s cancer registry from January 1992through December 1994and aged 50–79years at the time of diagnosis.Of the 6,839eligible cases,5,685completed the standardized telephone interview (83percent).Community controls were randomly selected in each state by using two sampling frames:those 50–64years of age were selected from lists of licensed drivers,and those 65–79years of age were chosen from rosters of Medicare beneficiaries.The controls were selected at random within age strata to yield an age distri-bution similar to that of the cases within each state.Of the 7,655potential controls,5,951completed the telephone interview (78percent).A 40-minute telephone interview elicited information on the number of sisters and daughters for each participant,their current ages,and the age of their mother.If these fe-male relatives were deceased,the interview inquired about their age at death.Participants were asked whether these first-degree female relatives were ever diagnosed with can-cer (including breast cancer)and,if so,the type of cancer and age at diagnosis.The interview also covered reproduc-tive history,physical activity,selected dietary items,alcohol consumption and tobacco use,use of exogenous hormones,body height and weight,personal medical history,and de-mographic factors.Familial Relative Risk Estimates 699Am J Epidemiol 2006;164:697–705at :: on November 11, 2014/Downloaded fromEmpirical Bayes estimates of familial relative risk of breast cancerUsing the first-degree female family history data col-lected in CBCS II,we estimated familial relative risk lev-els of breast cancer by using the empirical Bayes method.For each first-degree female family member,we calculated her person-years at risk of breast cancer incidence stratify-ing by 5-year age segments from birth to the earlier occur-rence of death or the reference date of her family’s enrolled subject.Reference dates for study subjects were defined as the date of diagnosis for breast cancer cases and,for con-trols,the date randomly sampled from the dates of diagnosis among cases within the same 5-year age stratum (on aver-age,1year prior to interview).We then multiplied each person-time segment by the corresponding age-specific ref-erence rate of breast cancer incidence among White females taken from the data of the Surveillance,Epidemiology,and End Results Program registry (14).Summing the products of the above multiplication for each family member yielded each participant’s expected risk E ij of developing breast cancer.Since it is reasonable to assume the rare disease condition for breast cancer,we were able to approximate the model byO i ð¼Pj O ij Þ’s given h i ’s,are independent Poisson random variables with E ½O i j h i ¼h i P j E ijh i’s are independent following a common nonparametric discrete distribution G :8>><>>:We fitted this model by using the vertex exchange algo-rithm with the Newton-Raphson full-optimization step-length procedure in the C.A.MAN program (UNIX version)(10,11).The initial parameter grid was chosen as 10equally spaced points between a relative risk of 0.1and 5.0.The algorithm was stopped based on the maximum directional derivative with an accuracy level of 0.00001.The C.A.MANprogram identified seven grid points (Kˆ¼7)with positive support,which was then refined with the program’s EM algorithm.The resulting nonparametric MLE of G is shown in figure 1.Three of the seven points were very close to each other around a relative risk of 2.6because the EM algo-rithm was stopped by any practical convergence criterion (10):it stopped at the 806th step.However,this does not have any important consequences,as evident from several examples in the paper that described the C.A.MAN pro-gram in detail (10).Specifically,we can interpret figure 1as showing five relative risk clusters,instead of seven,andFIGURE 1.Nonparametric maximum likelihood estimates of the familial relative risk distribution of breast cancer in the Collaborative Breast Cancer Study II (Wisconsin;Massachusetts,excluding metropolitan Boston;and New Hampshire,1992–1994).700Yasui et al.Am J Epidemiol 2006;164:697–705at :: on November 11, 2014/Downloaded fromFIGURE 2.Empirical Bayes familial relative risk estimates of breast cancer for participants in the Collaborative Breast Cancer Study II (Wisconsin;Massachusetts,excluding metropolitan Boston;and New Hampshire,1992–1994)according to the expected number of affected familymembers.FIGURE 3.Family History Scores of breast cancer for participants in the Collaborative Breast Cancer Study II (Wisconsin;Massachusetts,excluding metropolitan Boston;and New Hampshire,1992–1994)according to the expected number of affected family members.Familial Relative Risk Estimates 701Am J Epidemiol 2006;164:697–705at :: on November 11, 2014/Downloaded fromthe numerical values of the empirical Bayes estimates f ˆhi g would have changed negligibly if the algorithm had run for a longer time.With this nonparametric MLE of G ,the empirical Bayesestimate ˆhi of the familial relative risk level for the i th participant was calculated by the posterior-mean equation.Figure 2displays the empirical Bayes familial relative risk estimates f ˆh i g according to the expected counts f P j E ij g of breast cancer cases in the families.The empirical Bayes familial relative risk estimates are lower for families with larger expected counts for a given observed count of affected family members,P j O ij :This is sensible because,for a given observed count of affected family members,P j O ij ;true familial relative risk should tend to be lower with a larger expected count of affected family members.For CBCS II participants with no family history of breast cancer ðP j O ij ¼0Þ;the empirical Bayes estimates are all less than 1.0.To contrast with the empirical Bayes estimates,the Family History Score values were plotted (figure 3).Recall that Family History Scores are indicators of statistical signifi-cance,not estimates of familial relative risk.Very small dif-ferences in the expected count of affected family members,Pj E ij ;can lead a range of observed counts of affected fam-ily members,P j O ij ;to the same Family History Score;for example,a Family History Score of 6can arise from fam-ilies with ðPj O ij ;P j E ij Þ¼(1,0.03),(2,0.10),(3,0.22),and (4,0.37).Extremely large Family History Score values were observed among the families with the smallest ex-pected counts.These features of Family History Scores are clearly unsuitable for use as estimates of familial relative risk levels.Main effects of family history on disease riskWe examined the degree of association between the case-control status of the CBCS II participants and their familial relative risk estimates to assess the strength of evidence for familial aggregation.We fitted a conditional logistic regres-sion model,conditioned on age group and US state (corre-sponding to the study design),to the case-control data of theTABLE 1.Model deviance and odds ratio estimates with 95%confidence intervals from conditional logistic regression analyses of Collaborative Breast Cancer Study II data (Wisconsin;Massachusetts,excluding metropolitan Boston;and New Hampshire,1992–1994)using various summary measures of familial risk of breast cancer as covariatesSummary measures of familial riskdfUnadjusted *Adjusted y Deviance explainedOdds ratio estimate95%confidenceintervalDeviance explainedOdds ratio estimate95%confidenceintervalFamily historyindicator 1111.5113.6No 1.00 1.00Yes1.731.56,1.92 1.791.60,1.99Observed count(continuous)1116.1 1.591.46,1.73119.8 1.631.49,1.78Observed count 4120.2122.60 1.00 1.001 1.67 1.50,1.87 1.71 1.53,1.922 1.99 1.49,2.66 2.18 1.61,2.963 5.40 2.09,13.93 5.34 2.05,13.9144.260.49,37.07 4.380.50,38.44Family History Score(continuous)187.8 1.141.11,1.1891.5 1.161.12,1.20Family History Score 4118.6118.7<0 1.00 1.00[0,1.305)z 1.42 1.17,1.72 1.54 1.26,1.87[1.305,1.938)z 1.78 1.47,2.16 1.87 1.53,2.28[1.938,2.910)z 1.81 1.49,2.19 1.75 1.43,2.15 2.910z 1.981.63,2.412.071.68,2.55Empirical Bayesestimates (continuous)1123.9 2.50 2.12,2.94122.0 2.58 2.18,3.06*Conditional logistic regression analysis conditional on age and state of residence.y Conditional logistic regression analysis conditional on age and state of residence,adjusting for age at menar-che,parity,age at first birth,age at menopause,body mass index,exogenous hormone use,alcohol consumption,and educational level.z Quartiles of positive Family History Scores.702Yasui et al.Am J Epidemiol 2006;164:697–705at :: on November 11, 2014/Downloaded fromCBCS II with their familial relative risk estimates as a sole covariate(unadjusted analysis)and with a set of adjustment variables(adjusted analysis).The adjustment variables in-cluded participants’age at menarche,parity,age atfirst birth (AFB),age at menopause,body mass index,exogenous hormone use,alcohol consumption,and educational level. Matching on age and the state of residence in the design of the CBCS II was accounted for in the analysis as strata of the conditional logistic regression.Table1presents the deviance explained and odds ratio estimates by each type of familial relative risk estimate in the unadjusted and adjusted condi-tional logistic regression analyses.The amount of deviance explained was used to measure the strength of association between disease status and familial relative risk estimates. Empirical Bayes estimates explained the largest amount of deviance in the unadjusted analysis and nearly the largest in the adjusted analysis using only1degree of freedom,close to the categorical observed counts that used4degrees of freedom.Family History Scores did not show as strong asso-ciations as empirical Bayes estimates,even when the scores were categorized intofive groups(negative and quartiles of positive scores).Thisfinding was consistent with our de-scription earlier that Family History Scores are not estimates of familial relative risk.The results shown in table1suggest that empirical Bayes estimates of familial relative risk pro-vide higher power in the assessment of the main effects of family history(familial aggregation)on disease risk than either the crude summaries or Family History Scores. Examination of an indication of gene-environmental interactionColditz et al.(15)and Egan et al.(16)reported that the effects of reproductive factors on breast cancer risk were modified by family history.Following this intriguingfind-ing,we assessed the effect modification of parity/AFB ef-fects according to familial relative risk levels.We created a covariate of parity and AFB by forming four categories of reproductive patterns:1)nulliparous,2)AFB before age 20years,3)AFB at age20–29years,and4)AFB at age 30years or ing the same conditional logistic re-gression models as those described above(unadjusted and adjusted analyses),we tested an interaction of the parity-AFB covariate with familial relative risk estimates.Three types of familial relative risk estimates were examined,and the results of the unadjusted analysis are shown in table2 (the adjusted analysis gave very similar odds ratio estimates, which are not shown in the tables).The top third of table2shows the odds ratio estimates and95percent confidence intervals for each category of the parity-AFB covariate by presence/absence of family history. The interaction of the parity-AFB covariate and family his-tory was not clear from the odds ratio estimates and was notstatistically significant:v2¼1.74with3degrees of freedom yielding p¼0.63in the unadjusted analysis(p¼0.78in the adjusted analysis).The middle third of this table shows the interaction of the parity-AFB covariate with whether the number of affectedfirst-degree female relatives was two or more.The odds ratio estimates suggest the presence of an effect modification,but the test for interaction was not statistically significant:v2¼4.60with3degrees of freedom yielding p¼0.20in the unadjusted analysis(p¼0.30in the adjusted analysis).The bottom third of table2shows the interaction of the parity-AFB covariate with whether the empirical Bayes es-timate of familial relative risk was1.75or more(i.e.,top 2percent).The odds ratio estimates suggest a pattern of the TABLE2.Odds ratio estimates with95%confidence intervals for parity/age atfirst birth according to various summary measures of familial risk or breast cancer from conditional logistic regression analyses of Collaborative Breast Cancer Study II data(Wisconsin;Massachusetts,excluding metropolitan Boston;and New Hampshire,1992–1994) Familial risk variable andage atfirst birth(years)Odds ratioestimate95%confidenceinterval Family history¼no<20 1.0020–29 1.51 1.26,1.8030 1.47 1.22,1.79Nulliparous 1.28 1.12,1.45 Family history¼yes<20 1.98 1.43,2.7420–29 2.01 1.42,2.8430 1.690.49,1.91Nulliparous 1.62 1.23,2.15Interaction test v2¼1.74(df¼3),p¼0.63<2affectedfirst-degreefemale relatives<20 1.0020–29 1.31 1.16,1.4730 1.58 1.22,1.88Nulliparous 1.57 1.12,1.842affectedfirst-degreefemale relatives<20 3.16 1.43,6.6220–29 1.80 1.42,2.4830 1.940.49,6.19Nulliparous 5.51 1.23,20.55Interaction test v2¼4.60(df¼3),p¼0.20 Empirical Bayesestimate<1.75<20 1.0020–29 1.31 1.17,1.4830 1.58 1.32,1.88Nulliparous 1.57 1.34,1.85 Empirical Bayesestimate 1.75<20 4.80 1.96,11.7220–29 1.59 1.12,2.2430 3.030.64,14.51Nulliparous 5.04 1.33,19.13Interaction test v2¼8.26(df¼3),p¼0.04Familial Relative Risk Estimates703Am J Epidemiol2006;164:697–705 at :: on November 11, 2014 / Downloaded from。