Tutorial in Biostatistics
Received20June2013,Accepted10February2014Published online in Wiley Online Library (https://www.doczj.com/doc/3a3544165.html,)DOI:10.1002/sim.6128
Instrumental variable methods for causal inference?
Michael Baiocchi,a Jing Cheng b and Dylan S.Small c*?
A goal of many health studies is to determine the causal effect of a treatment or intervention on health outcomes. Often,it is not ethically or practically possible to conduct a perfectly randomized experiment,and instead,an observational study must be used.A major challenge to the validity of observational studies is the possibility of unmeasured confounding(i.e.,unmeasured ways in which the treatment and control groups differ before treat-ment administration,which also affect the outcome).Instrumental variables analysis is a method for controlling for unmeasured confounding.This type of analysis requires the measurement of a valid instrumental variable, which is a variable that(i)is independent of the unmeasured confounding;(ii)affects the treatment;and(iii) affects the outcome only indirectly through its effect on the treatment.This tutorial discusses the types of causal effects that can be estimated by instrumental variables analysis;the assumptions needed for instrumental vari-ables analysis to provide valid estimates of causal effects and sensitivity analysis for those assumptions;methods of estimation of causal effects using instrumental variables;and sources of instrumental variables in health studies.Copyright?2014John Wiley&Sons,Ltd.
Keywords:instrumental variables;observational study;confounding;comparative effectiveness
1.Introduction
The goal of many medical studies is to estimate the causal effect of one treatment versus another,that is, to compare the effectiveness of giving patients one treatment versus another.To compare the effects of treatments,randomized controlled studies are the gold standard in medicine.Unfortunately,randomized controlled studies cannot answer many comparative effectiveness questions because of cost or ethical constraints.Observational studies offer an alternative source of data for developing evidence regarding the comparative effectiveness of different treatments.However,a major challenge for observational stud-ies is confounders—pretreatment variables that affect the outcome and differ in distribution between the group of patients who receive one treatment versus the group of patients who receive another treatment. The impact of confounders on the estimation of a causal treatment effect can be mitigated by meth-ods such as propensity scores,regression,and matching[1–3].However,these methods only control for measured confounders and do not control for unmeasured confounders.
The instrumental variable(IV)method was developed to control for unmeasured confounders.The basic idea of the IV method is(i)?nd a variable that in?uences which treatment subjects receive but is independent of unmeasured confounders and has no direct effect on the outcome except through its effect on treatment;(ii)use this variable to extract variation in the treatment that is free of the unmeasured con-founders;and(iii)use this confounder-free variation in the treatment to estimate the causal effect of the treatment.The IV method seeks to?nd a randomized experiment embedded in an observational study and use this embedded randomized experiment to estimate the treatment effect.
a Department of Statistics,Stanford University,Stanford,CA,U.S.A.
b Division of Oral Epidemiology and Dental Publi
c Health,School of Dentistry,University of California,San Francisco (UCSF),San Francisco,CA,U.S.A.
c Department of Statistics,The Wharton School,University of Pennsylvania,Philadelphia,PA,U.S.A.
*Correspondence to:Dylan S.Small,Department of Statistics,The Wharton School,University of Pennsylvania,400 Huntsman Hall,Philadelphia,PA19104,U.S.A.
?E-mail:dsmall@https://www.doczj.com/doc/3a3544165.html,
?The three authors contributed equally to this paper.
M.BAIOCCHI,J.CHENG AND D.S.SMALL
1.1.Tutorial aims and outline
IV methods have long been used in economics and are being increasingly used to compare treatments in health studies.There have been many important contributions to IV methods in recent years.The goal of this tutorial is to bring together this literature to provide a practical guide on how to use IV methods to compare treatments in a health study.We focus on several important practical issues in using IVs:(i) when is an IV analysis needed and when is it feasible;(ii)what are sources of IVs for health studies; (iii)how to use the IV method to estimate treatment effects,including how to use currently available software;(iv)for what population does the IV method estimate the treatment effect;(v)how to assess whether a proposed IV satis?es the assumptions for an IV to be valid;(vi)how to carry out sensitivity analysis for violations of IV assumptions;and(vii)how does the strength of a potential IV affect its usefulness for a study.
In the rest of this section,we will present an example of using the IV method that we will use through-out the paper.In Section2,we discuss situations when one should consider using the IV method.In Section3,we discuss common sources of IVs for health studies.In Section4,we discuss IV assump-tions and estimation for a binary IV and binary treatment.In Section5,we discuss the treatment effect that the IV method estimates.In Section6,we provide a framework for assessing IV assumptions and sensitivity analysis for violations of assumptions.In Section7,we demonstrate the consequences of weak instruments.In Section8,we discuss power and sample size calculations for IV studies.In Section9,we present techniques for analyzing outcomes that are not continuous outcomes,such as binary,survival, multinomial,and continuous outcomes.In Section10,we discuss multi-valued and continuous IVs.In Section11,we discuss using multiple IVs.In Section12,we present IV methods for multi-valued and continuously valued treatments.In Section13,we suggest a framework for reporting IV analyses.In Section14,we provide examples of using software for IV analysis.
If you are just beginning to familiarize yourself with IVs,we recommend focussing on Sections1–4, 5.1–5.2,6–8,and13–14,while skipping Sections5.3–5.5and9–12.Sections5.3–5.5and9–12contain interesting,cutting-edge,and more specialized applications of IVs that a beginner may want to return to at a later point.We include these sections for advanced readers,or those interested in more specialized applications.
Table I is a table of notation that will be used throughout the paper.
1.2.Example:Effectiveness of high-level neonatal intensive care units
As an example where the IV method is useful,consider comparing the effectiveness of premature babies being delivered in high volume,high technology neonatal intensive care units(high-level NICUs)versus local hospitals(low-level NICUs),where a high-level NICU is de?ned as a NICU that has the capac-ity for sustained mechanical assisted ventilation and delivers at least50premature infants per year. Lorch et al.[4]used data from birth and death certi?cates and the UB-92form that hospitals use for billing purposes to study premature babies delivered in Pennsylvania.The data set covered the years 1995–2005(192,078premature babies).For evaluating the effect of NICU level on baby outcomes,a baby’s health status before delivery is an important confounder.Table II shows that babies delivered at high-level NICUs tend to have smaller birthweight and be more premature,and the babies’mothers tend to have more problems during the pregnancy.Although the available confounders,which include those in Table II and several other variables that are given in[4],describe certain aspects of a baby’s
M.BAIOCCHI,J.CHENG AND D.S.SMALL
Table II.Imbalance of measured covariates between babies delivered at high-level NICUs versus low-level NICUs.
Characteristic X P.X j High-level NICU/P.X j Low-level NICU/Standardized difference Birthweight<1500g0.120.050.28 Gestational age632weeks0.180.070.34
Mother college graduate0.280.230.12
African-American0.220.090.36 Gestational diabetes0.050.050.03
Diabetes mellitus0.020.010.06 Pregnancy-induced hypertension0.120.080.13
Chronic hypertension0.020.010.07
The standardized difference is the difference in means between the two groups in units of the pooled within group standard deviation,that is,for a binary characteristic X,where D D1or0according to whether the baby was delivered at a high-level or low-level NICU,the standardized difference is P.X D1j D D1/ P.X D1j D D0/
.
p
f Var.X j D D1/C Var.X j D D0/g=2
Figure1.Directed acyclic graph for the relationship between an instrumental variable Z,a treatment D,
unmeasured confounders U,and an outcome Y.
health prior to delivery,the data set is missing several important confounding variables such as fetal heart tracing results,the severity of maternal problems during pregnancy(e.g.,we only know whether the mother had pregnancy-induced hypertension but not the severity),and the mother’s adherence to prenatal care guidelines.
Figure1,which is an example of a directed acyclic graph[5],illustrates the dif?culty with estimating a causal effect in this situation.The arrows denote causal relationships.Read the arrow between the treatment D and outcome Y like so:Changing the value of D causes Y to change.In our example,Y represents in-hospital mortality,and D indicates whether or not a baby attended a high-level NICU.Our goal is to understand the arrow connecting D to Y,that is,the effect of attending a high-level NICU on in-hospital mortality compared with attending a low-level NICU.Assume that Figure1shows relation-ships within a strata of the observed covariates X,for example,Figure1represents the relationships for only babies with gestational age of33weeks and mother had pregnancy-induced hypertension.The U variable causes concern as it represents the unobserved level of severity of the preemie,and it is causally linked to both mortality(sicker babies are more likely to die)and to which treatment the preemie receives (sicker babies are more likely to be delivered in high-level NICUs).Because U is not recorded in the data set,it cannot be precisely adjusted for using statistical methods such as propensity scores or regression. If the story stopped with just D,Y,and U,then the effect of D on Y could not be estimated.
IV estimation makes use of a form of variation in the system that is free of the unmeasured confound-ing.What is needed is a variable,called an IV(represented by Z in Figure1),which has very special
characteristics.In this example,we consider excess travel time as a possible IV.Excess travel time is de?ned as the time it takes to travel from the mother’s residence to the nearest high-level NICU minus the time it takes to travel to the nearest low-level NICU.We write Z D1if the excess travel time is less than or equal to10min(so that the mother is encouraged by the IV to go to a high-level NICU)
M.BAIOCCHI,J.CHENG AND D.S.SMALL and Z D0if the excess travel time is greater than10min.(We dichotomize the instrument here for simplicity of discussion.)
There are three key features a variable must have in order to qualify as an IV(see Section4for mathematical details on these features and additional assumptions for IV methods).The?rst feature (represented by the directed arrow from Z to D in Figure1)is that the IV causes a change in the treatment assignment.When a woman becomes pregnant,she has a high probability of establishing a relationship with the proximal NICU,regardless of the level,because she is not anticipating having a preemie.Proximity as a leading determinant in choosing a facility has been discussed in[6].By selecting where to live,mothers assign themselves to be more or less likely to deliver in a high-level NICU.The fact that changes in the IV are associated with changes in the treatment is veri?able from the data.
The second feature(represented by the crossed-out arrow from Z to U)is that the IV is not associated with variation in unobserved variables U that also affect the outcome.That is,Z is not connected to the unobserved confounding that was a worry to begin with.In our example,this would mean unobserved severity is not associated with variation in geography.As high-level NICUs tend to be in urban areas and low-level NICUs tend to be the only type in rural areas,this assumption would be dubious if there were a high level of pollutants in urban areas(think of Manchester,England,circa the Industrial Revolution) or if there were more pollutants in the drinking water in rural areas than in urban areas.These hypothet-ical pollutants may have an impact on the unobserved levels of severity.The assumption that the IV is not associated with variation in the unobserved variables,while certainly an assumption,can at least be corroborated by examining the values of variables that are perhaps related to the unobserved variables of concern(Section6.1).
The third feature(represented by the crossed-out line from Z to Y in Figure1)is that the IV does not cause the outcome variable to change directly.That is,it is only through its impact on the treatment that the IV affects the outcome.This is often referred to as the exclusion restriction(ER)assumption. In our case,the ER assumption seems reasonable as presumably a nearby hospital with a high-level NICU affects a baby’s mortality only if the baby receives care at that hospital.That is,proximity to a high-level NICU in and of itself does not change the probability of death for a preemie,except through the increased probability of the preemie being delivered at the high-level NICU.See Section6.2.2for further discussion about the ER in the NICU study.
2.Evaluating the need for and feasibility of an IV analysis
As discussed earlier,IV methods provide a way to control for unmeasured confounding in comparative effectiveness studies.Although this is a valuable feature of IV methods relative to regression,match-ing,and propensity score methods,which do not control for unmeasured confounding,IV methods have some less attractive features such as increased variance.When considering whether or not to include an IV analysis in an evaluation of a treatment effect,the?rst question one should ask is whether or not an IV analysis is needed.The second question one should ask is whether or not an IV analysis is feasible in the sense of there being an IV that is close enough to being valid and has a strong enough effect on the treatment to provide useful information about the treatment effect.In this section,we will discuss how to think about these two questions.
2.1.Is an IV analysis needed?
The key consideration in whether an IV analysis is needed is how much unmeasured confounding there is.It is useful to evaluate this using both scienti?c considerations and statistical considerations. Scienti?c consideration.Whether or not there is any unmeasured confounding should be?rst thought of from a scienti?c point of view.In the NICU example discussed in Section1.2,mothers(as advised by doctors)who choose to deliver in a far-away high-level NICU rather than a nearby low-level NICU often do so because they think their baby may be at a high risk of having a problem and that delivery at a high-level NICU will reduce this risk.Investigators know that many variables can be confounders (i.e.,associated with delivery at a high-level NICU and associated with in-hospital mortality)such as variables indicating a baby’s health prior to delivery.They know that the data set available for analy-
ses is missing several important confounding variables such as fetal heart tracing results,the severity of maternal problems during pregnancy,and the mother’s adherence to prenatal care guidelines.When unmeasured confounding is a big concern in a study like in the NICU study,analyses with IV methods are desired and helpful to better understand the treatment effect.
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Unmeasured confounders are particularly likely to be present when the treatment is intended to help the patient(as compared with unintended exposures)[7].When two patients who have the same measured covariates are given different treatments,there are often rational but unrecorded reasons.In particular,administrative data often do not contain measurements of important prognostic variables that affect both treatment decisions and outcomes such as lab values(e.g.,serum cholesterol levels),clinical variables(e.g.,blood pressure and fetal heart tracing results),aspects of lifestyle(e.g.,smoking status and eating habits),and measures of cognitive and physical functioning[8,9].
Common sources of IVs for health studies are discussed in Section3.When using IV analyses, the assumptions that are required for a variable to be a valid IV are usually at best plausible,but not certain.If the assumptions are merely plausible,but not certain,are IV analyses still useful?Imbens and Rosenbaum[10]provide a nice discussion of two settings in which IV analyses with plausible but not certain IVs are useful:(i)When one is concerned about unmeasured confounding in any way,it is helpful to replace the implausible assumption of no unmeasured confounding by a plausible assumption, although not a certain assumption,with IV methods;and(ii)when there is concern about unmeasured confounding,IV analyses play an important role in replicating an observational study.Consider two sequences of studies,the?rst sequence in which each study involves only adjusting for measured con-founders and the other sequence in which each study involves using a different IV(one of the studies in this second sequence could also involve only adjusting for measured confounders).Throughout the ?rst sequence of studies,the comparison is likely to be biased in the same way.For example,a repeated ?nding that people with more education are more healthy from different survey data sets that do not con-tain information about genetic endowments or early life experiences does little to address the concern of unmeasured confounding from these two variables.However,if different IVs are used for education,for example,a lottery that affects education[11],a regional discontinuity in educational policy[12],a tem-poral discontinuity in educational policy[13]and distance lived from a college when growing up[14], and if each IV is plausibly,but not certainly,valid,then there may be no reason why these different IVs should provide estimates that are biased in the same direction.If studies with these different IVs all pro-vide evidence that education affects health in the same direction,this would strengthen the evidence for this?nding[15](when different IVs are used,each IV identi?es the average treatment effect for a differ-ent subgroup,so that we would only expect that?ndings from the different IVs would agree in direction if the average treatment effects for the different subgroups have the same direction;see Sections5.5and 11for discussion).
In summary,when unmeasured confounding is a big concern in a study based on one’s understanding of the problem and data,investigators should consider IV methods in their analyses.At the same time, if investigators only expect a small amount of unmeasured confounding in their study,Brookhart et al.
[16]suggested that investigators may not want to use IV methods for the primary analysis but may want to consider IV methods for a secondary analysis.
Statistical tests.Under some situations in practice,especially for exploratory studies,investigators may not have enough scienti?c information to determine whether or not there is unmeasured confound-ing.Then statistical tests can be helpful to provide additional insight.The Durbin–Wu–Hausman test is widely used to test whether there is unmeasured confounding[17–19].The test requires the availability of a valid IV.The test compares the ordinary least squares(OLS)estimate and IV estimate of the treat-ment effect;a large difference between the two estimates indicates the potential presence of unmeasured confounding.
The Durbin–Wu—Hausman test assumes homogeneous treatment effects,meaning that the treatment effect is the same at different levels of covariates.The test cannot distinguish between unmeasured confounding and treatment effect heterogeneity[16,20].As an alternative approach,Guo et al.[20] developed a test that can detect unmeasured confounding as distinct from treatment effect heterogeneity in the context of the model described in Section4.1.
2.2.Valid IVs
As discussed in Section1,a variable must have three key features to qualify as an IV:(i)relevance:the IV causes a change in the treatment received;(ii)effective random assignment:the IV is independent of
unmeasured confounding conditional on covariates as if it was randomly assigned conditional on covari-ates;and(iii)ER:the IV does not have a direct effect on outcomes,that is,it only affects outcomes through the treatment.Section4includes mathematical details on these features and assumptions.To use IV methods in a real study,investigators need to evaluate if there is any variable that satis?es the
M.BAIOCCHI,J.CHENG AND D.S.SMALL three features and quali?es as a good IV based on both scienti?c understanding and statistical evidence. Please see Section3for sources of IVs in health studies.Note that not all of the features/assumptions can be completely tested,but methods have been proposed to test certain parts of the assumptions.Please see Section6for a discussion about how to evaluate if a variable satis?es those features/assumptions needed to be a valid IV.
We would also like to point out that even if there is no variable that is a perfectly valid IV,an IV anal-ysis may still provide helpful information about the treatment effect.As discussed earlier,when there is unmeasured confounding,a repeated?nding from a sequence of analyses with different IVs(even though none of the IVs are perfect)will provide very helpful evidence on the treatment effect[10].Also, sensitivity analyses can be performed to assess the evidence provided by an IV analysis allowing for the IV not being perfectly valid;see Section6.2.
2.3.Strength of IVs
An IV is considered to be a strong IV if it has a strong impact on the choice of different treatments and a weak IV if it only has a slight impact.When the IV is weak,even if it is a valid IV,treatment effect estimates based on IV methods have some limitations,such as large variance even with large samples. Then investigators face a trade-off between an IV estimate with a large variance and a conventional estimate with possible bias[16].Additionally,the estimate with a weak IV will be sensitive to a slight departure from being a valid IV.Please see Section7for more detailed discussion on the problems when only weak IVs are available in a study.
In summary,whether or not an IV analysis will be helpful for a study depends on if unmeasured con-founding is a major concern,if there is any plausibly close to valid IV,and if the IV is strong enough for a study.For studies with treatments that are intentionally chosen by physicians and patients,there is often substantial unmeasured confounding from unmeasured indications or severity[7,10,16].There-fore,an IV analysis can be most helpful for those studies.When an IV is available,even if it is not perfectly valid,an IV analysis or a sequence of IV analyses with different IVs can provide very help-ful information about the treatment effect.For studies in which unmeasured confounding is not a big concern and no strong IV is available,we suggest investigators to consider IV analyses as secondary or sensitivity analyses.
3.Sources of instruments in health studies
The biggest challenge in using IV methods is?nding a good IV.There are several common sources of IVs for health studies.
Randomized encouragement trials.One way to study the effect of a treatment when that treatment cannot be controlled is to conduct a randomized encouragement trial.In such a trial,some subjects are randomly chosen to obtain extra encouragement to take the treatment,and the rest of the subjects receive no extra encouragement[21].For example,Permutt and Hebel[22]studied the effect of mater-nal smoking during pregnancy on an infant’s birthweight using a randomized encouragement trial in which some mothers received extra encouragement to stop smoking through a master’s level staff per-son providing information,support,practical guidance,and behavioral strategies[23].For a randomized encouragement trial,the randomized encouragement assignment(1if encouraged,0if not encouraged) is a potential IV.The randomized encouragement is independent of unmeasured confounders because it is randomly assigned by the investigators and will be associated with the treatment if the encouragement is effective.The only potential concern with the randomized encouragement being a valid IV is that the randomized encouragement might have a direct effect on the outcome and not through the treatment.For example,in the aforementioned smoking example,the encouragement could have a direct effect if the staff person providing the encouragement also encouraged expectant mothers to stop drinking alcohol during pregnancy.To minimize a potential direct effect of the encouragement,Sexton and Hebel[23] asked the staff person providing encouragement to avoid recommendations or information concerning
other habits that might affect birthweight such as alcohol or caffeine consumption and also prohibited discussion of maternal nutrition or weight gain.A special case of a randomized encouragement trial is a usual randomized trial in which the intent is for everybody to take their assigned treatment,but in fact, some people do not adhere to their assigned treatment so that assignment to treatment is in fact just an
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encouragement to treatment.For such randomized trials with nonadherence,random assignment can be used as an IV to estimate the effect of receiving the treatment versus receiving the control provided that random assignment does not have a direct effect(not through the treatment);see Section4.7for further discussion and an example.
Distance to specialty care provider.When comparing two treatments,one of which is only provided by specialty care providers and one of which is provided by more general providers,the distance a per-son lives from the nearest specialty care provider has often been used as an IV.For emergent conditions, proximity to a specialty care provider particularly enhances the chance of being treated by the specialty care provider.For less acute conditions,patients/providers have more time to decide and plan where to be treated,and proximity may have less of an in?uence on treatment selection,while for treatments that are stigmatized(e.g.,substance abuse treatment),proximity could have a negative effect on the chance of being treated.A classic example of using distance as an IV in studying treatment of an emergent condition is the McClellan et al.study of the effect of cardiac catheterization for patients suffering a heart attack[24].The IV used in the study was the differential distance the patient lives from the near-est hospital that performs cardiac catheterization to the nearest hospital that does not perform cardiac catheterization.Another example is the study of the effect of high-level versus low-level NICUs[4] that was discussed in Section1.2.Because distance to a specialty care provider is often associated with socioeconomic characteristics,it will typically be necessary to control for socioeconomic characteristics in order for distance to potentially be independent of unmeasured confounders.The possibility that dis-tance might have a direct effect because the time it takes to receive treatment affects outcomes needs to be considered in assessing whether distance is a valid IV.
Preference-based IVs.A general strategy for?nding an IV for comparing two treatments A and B is to look for naturally occurring variation in medical practice patterns at the level of geographic region, hospital,or individual physician and then use whether the region/hospital/individual physician has a high or low use of treatment A(compared with treatment B)as the IV.Brookhart and Schneeweiss[9] termed these IVs‘preference-based instruments’because they assume that different providers or groups of providers have different preferences or treatment algorithms dictating how medications or medical procedures are used.Examples of studies using preference-based IVs are by Brooks et al.[25]who studied the effect of surgery plus irradiation versus mastectomy for breast cancer patients using geo-graphic region as the IV,Johnston[26]who studied the effect of surgery versus endovascular therapy for patients with a ruptured cerebral aneurysm using hospital as the IV,and Brookhart et al.[27]who studied the bene?ts and risks of selective cyclooxygenase2inhibitors versus nonselective nonsteroidal anti-in?ammatory drugs for treating gastrointestinal problems using individual physician as the IV.For proposed preference-based IVs,it is important to consider that the patient mix may differ between the different groups of providers with different preferences,which would make the preference-based IV invalid unless patient mix is fully controlled for.It is useful to look at whether measured patient risk factors differ between groups of providers with different preferences.If there are measured differences, there are likely to be unmeasured differences as well;see Section6.1for further discussion.Also,for pro-posed preference-based IVs,it is important to consider whether the IV has a direct effect(not through the treatment);a direct effect could arise if the group of providers that prefers treatment A treats patients dif-ferently in ways other than the treatment under study compared with the providers who prefer treatment B.For example,Newman et al.[28]studied the ef?cacy of phototherapy for newborns with hyper-bilirubinemia and considered the frequency of phototherapy use at the newborn’s birth hospital as an IV.However,chart reviews revealed that hospitals that use more phototherapy also have a greater use of infant formula;use of infant formula is also thought to be an effective treatment for hyperbilirubinemia. Consequently,the proposed preference-based IV has a direct effect(going to a hospital with higher use of phototherapy also means a newborn is more likely to receive infant formula even if the newborn does not receive phototherapy)and is not valid.The issue of whether a proposed preference-based IV has a direct effect can be studied by looking at whether the IV is associated with concomitant treatments such as use of infant formula[9].A related way in which a proposed preference-based IV can have a direct effect is that the group of providers who prefer treatment A may have more skill than the group of providers who prefer treatment B.Also,providers who prefer treatment A may deliver treatment A better than those providers who prefer treatment B because they have more practice with it,for exam-
ple,doctors who perform surgery more often may perform better surgeries.Korn and Baumrind[29] discussed a way to assess whether there are provider skill effects by collecting data from providers on whether or not they would have treated a different provider’s patient with treatment A or B based on the patient’s pretreatment records.
M.BAIOCCHI,J.CHENG AND D.S.SMALL Calendar time.Variations in the use of one treatment versus another over time could result from changes in guidelines;changes in formularies or reimbursement policies;changes in physician prefer-ence(e.g.,due to marketing activities by drug makers);release of new effectiveness or safety informa-tion;or the arrival of new treatments to the market[16].For example,Shetty et al.[30]studied the effect of hormone replacement therapy(HRT)on cardiovascular health among postmenopausal women using calendar time as an IV.HRT was widely used among postmenopausal women until2002;observational studies had suggested that HRT reduced cardiovascular risk,but the Women’s Health Initiative random-ized trial reported opposite results in2002,which caused HRT use to drop sharply.A proposed IV based on calendar time could violate the assumption of being independent of unmeasured confounders by being associated with unmeasured confounders that change in time such as the characteristics of patients who enter the cohort,changes in other medical practices,and changes in medical coding systems[16].The most compelling type of IV based on calendar time is one where a dramatic change in practice occurs in a relatively short period of time[16].
Genes as IVs.Another general source for potential IVs is genetic variants,which affect treatment vari-ables.For example,V oight et al.[31]studied the effect of high-density lipoprotein(HDL)cholesterol on myocardial infarction(MI)using as an IV the genetic variant LIPG396Ser allele for which carri-ers have higher levels of HDL cholesterol but similar levels of other lipid and non-lipid risk factors compared with noncarriers.Another example is that Wehby et al.[32]studied the effect of mater-nal smoking on orofacial clefts in babies using genetic variants that increase the probability that a mother smokes as IVs.The approach of using genetic variants as an IV is called Mendelian random-ization because it makes use of the random assignment of genetic variants conditional on parents’genes discovered by Mendel.Although genetic variants are randomly assigned conditional on a par-ent’s genes,genetic variants need to satisfy additional assumptions to be valid IVs that include the following:
Not associated with unmeasured confounders through population strati?cation.Most Mendelian randomization analyses do not condition on parents’genes,creating the potential of the proposed genetic variant IV being associated with unmeasured confounders through population strati?cation.
Population strati?cation is a condition where there are subpopulations,some of which are more likely to have the genetic variant,and some of which are more likely to have the outcome through mechanisms other than the treatment being studied.For example,consider studying the effect of alcohol consumption on hypertension.Consider using the ALDH2null variant,which is associated with alcohol consumption,as an IV(individuals who are homozygous for the ALDH2null variant have severe adverse reactions to alcohol consumption and tend to drink very little[33]).The ALDH2 null variant is much more common in people with Asian ancestry than other types of ancestry[34].
Suppose ancestry was not fully measured.If ancestry is associated with hypertension through mech-anisms other than differences in the ALDH2null variant(e.g.,through different ancestries tending to have different diets),then ALDH2would not be a valid IV because it would be associated with an unmeasured confounder.
Not associated with unmeasured confounders through genetic linkage.Genetic linkage is the ten-dency of genes that are located near to each other on a chromosome to be inherited together because the genes are unlikely to be separated during the crossing over of the mother’s and father’s DNA
[35].Consider using a gene A as an IV,where gene A is genetically linked to a gene B that has a
causal effect on the outcome through a pathway other than the treatment being studied.If gene B is not measured and controlled for,then gene A is not a valid IV because it is associated with the unmeasured confounder gene B.
No direct effect through pleiotropy.Pleiotropy refers to a gene having multiple functions.If the genetic variant being used as an IV affects the outcome through a function other than affecting the treatment being studied,this would mean the genetic variant has a direct effect.For exam-ple,consider the use of the APOE genotype as an IV for studying the causal effect of low-density lipoprotein cholesterol on MI risk.The 2variant of the APOE gene is associated with lower levels of low-density lipoprotein cholesterol and is also associated with higher levels of HDL cholesterol, less ef?cient transfer of very-low-density lipoproteins and chylomicrons from the blood to the liver,
greater postprandial lipaemia,and an increased risk of type III hyperlipoproteinaemia(the last three of which are thought to increase MI risk)[33].Thus,the gene APOE is pleiotropic,affecting MI risk through different pathways,making it unsuitable as an IV to examine the causal effect of any one of these pathways on MI risk.
M.BAIOCCHI,J.CHENG AND D.S.SMALL
Didelez and Sheehan[36]and Lawlor et al.[33]provided good reviews of Mendelian randomiza-tion methods.
Timing of admission.Another source of IVs for health studies is timing of admission variables.For example,Ho et al.[37]used day of the week of hospital admission as an IV for waiting time for surgery to study the effects of waiting time on length of stay and inpatient mortality among patients admitted to the hospital with a hip fracture.Day of the week of admission is associated with waiting time for surgery because many surgeons only do non-emergency operations on weekdays,and therefore,patients admit-ted on weekends may have to wait longer for surgery.In order for weekday versus weekend admission to be a valid IV,patients admitted on weekdays versus weekends must not differ on unmeasured character-istics(i.e.,the IV must be independent of unmeasured confounders),and other aspects of hospital care that affect the patients’outcomes besides surgery must be comparable on weekdays versus weekends (i.e.,the IV has no direct effect).Another example of a timing of admission variable used as an IV is hour of birth as an IV for a newborn’s length of stay in the hospital[38,39].
Insurance plan.Insurance plans vary in the amount of reimbursement they provide for different treat-ments.For example,Cole et al.[40]used drug co-payment amount as an IV to study the effect of “-blocker adherence on clinical outcomes and healthcare expenditures after a hospitalization for heart failure.In order for variations in insurance plan such as drug co-payment amount to be a valid IV,insur-ance plans must have comparable patients after controlling for measured confounders(i.e.,the IV is independent of unmeasured confounders),and insurance plans must not have an effect on the outcome of interest other than through in?uencing the treatment being studied(i.e.,the IV has no direct effect). We have discussed several common sources of IVs for health studies and considerations to think about in deciding whether potential IVs from these sources satisfy the assumptions to be a valid IV.A detailed understanding of how treatments are chosen in a particular setting may yield additional,creative ideas for potential IVs.In Section4,we will formally state the assumptions for an IV to be valid and discuss how to use a valid IV to estimate the causal effects of a treatment.
4.IV assumptions and estimation for binary IV and binary treatment
In this section,we consider the simplest setting for an IV design,when both the instrument and treatment are binary.The main ideas in IV methods are most easily understood in this setting,and the ideas will be expanded to more complicated settings in later sections.
4.1.Framework and notation
The Neyman–Rubin potential outcomes framework[41,42]will be used to describe causal effects and formulate IV assumptions.The classic econometric formulation of IVs is in terms of structural equations and assumptions about the IV being uncorrelated with structural error terms;the formulation in terms of potential outcomes that is described here provides clarity about what effects are being estimated when there are heterogeneous treatment effects and provides a?rm foundation for nonlinear as well as lin-ear outcome models[21,43].Suppose there are N subjects.Let Z denote the N-dimensional vector of IV assignments with individual elements Z i;i D1;:::;N,where Z i D0or1.Level1of the IV is assumed to mean the subject was encouraged to take level1of the treatment,where the treatment has levels0and1.Let D z be the N-dimensional vector of potential treatment under IV assignment z with
elements D z
i ,i D1;:::;N,D z
i
D1or0according to whether person i would receive treatment level
1or0under IV assignment z.Let Y z;d be the N-dimensional vector of potential outcomes under IV
assignment z and treatment assignment d,where Y z;d
i is the outcome subject i would have under IV
assignment z and treatment assignment d.The observed treatment for subject i is D iáD Z
i
,and the
observed outcome for subject i is Y iáY Z;D Z
i .Let X i denote observed covariates for subject i.When we
write expressions such as E.Y/,we mean the expected value of Y for a randomly sampled subject from the population.
Angrist et al.[43]considered an IV to be a variable satisfying?ve assumptions—the stable unit
treatment value assumption(SUTV A),the IV is positively correlated with treatment assumption,the IV is independent of unmeasured confounders assumption,the ER assumption,and the monotonicity assumption.We will describe the?rst four of these assumptions and then describe the need for the?fth assumption or some substitute to obtain point identi?cation.The?rst four assumptions are as follows:
M.BAIOCCHI,J.CHENG AND D.S.SMALL
IV-A1SUTVA .If z i D z 0i ,then D z i D D z 0i ,and if z i D z 0i and d i D d 0i ,then Y z ;d i D Y z 0;d 0
i .In other
words,this assumption says that the treatment affects only the subject taking the treatment and that there are no different versions of the treatment that have different effects (see [43,44]for details).The SUTV A allows us to write D z i as D ′i ,where ′here denotes subject i having IV assignment ′and Y z ;d i as Y ′;d i ,where ′and d here denote subject i having IV assignment ′and treatment d .
IV-A2IV is positively correlated with treatment received .E.D 1j X />E.D 0j X /(Note that we have
assumed that level 1of the IV means that the subject was encouraged to take level 1of the treatment).
IV-A3IV is independent of unmeasured confounders (conditional on covariates X ).
Z is independent of .D 1;D 0;Y 1;1;Y 1;0;Y 0;1;Y 0;0/j X .
IV-A4ER .This assumption says that the IV affects outcomes only through its effect on treatment received:Y ′;d i D Y ′0;d i for all i .Under the ER,we can write Y d i áY ′;d i for any ′,that is,Y 1
i is the potential outcome for subject i if she were to receive level 1of the treatment (regardless of her level of the IV)and Y 0i is the potential outcome if she were to receive level 0of the treatment.The ER assumption is also called the no direct effect assumption.
Assumptions (IV-A2)–(IV-A4)are the assumptions depicted in Figure 1.These assumptions are the ‘core’IV assumptions that basically all IV approaches make;assumption (IV-A1)is typically implicitly made as well.The core IV assumptions enable bounds on treatment effects to be identi?ed but do not point identify a treatment effect [45].
To see why the core IV assumptions alone do not point identify a treatment effect and to understand what additional assumptions would identify a treatment effect,it is helpful to introduce the idea of com-pliance classes [43].A subject in a study with binary IV and treatment can be classi?ed into one of four latent compliance classes based on the joint values of potential treatment received [43].The four compli-ance classes are referred to as never takers,always takers,de?ers,and compliers.We denote subject i ’s compliance class as C i ,which are de?ned like so:C i D never taker (nt)if D 0i ;D 1i D .0;0/;complier (co)if D 0i ;D 1i D .0;1/;always taker (at)if D 0i ;D 1i D .1;1/;and de?er (de)if D 0i ;D 1i D .1;0/.Note that there being four compliance classes is not an assumption but an exhaustive list of the possible types of compliance.Note also that a subject’s compliance class is relative to a particular IV ,for exam-ple,in studying the effect of regular exercise on the lung function of patients with chronic pulmonary obstructive disease,a person might be a complier if the IV is Z D 1means the person will receive $1000if she regularly exercises versus Z D 0means the person will receive no extra payment if she regularly exercises,but the person might be a never taker if Z D 1means the person will receive only $100if she regularly exercises.Table III shows the relationship between the latent compliance classes and the observed groups.
Suppose the outcome is binary so that the observed data .Y;D;Z/are a multinomial random variable with 2 2 2D 8categories.Under assumptions (IV-A1)–(IV-A4),there are ten free unknown param-eters:P.Z D 1/,P.Y 1D 1j C D at /,P.Y 1D 1j C D co /,P.Y 0D 1j C D co /,P.Y 0D 1j C D nt /,P.Y 1D 1j C D de /,P.Y 0D 1j C D de /,P.C D at /,P.C D co /,and P.C D nt /(note that P.C D de /is determined by P.C D co /C P.C D at /C P.C D nt /C P.C D de /D 1).As there are ten free parameters but the observed data multinomial random variable has only eight categories (so seven free probabilities),the model is not identi?ed.Two types of additional assumptions have been considered that reduce the number of free parameters:(i)an assumption about the process of selecting a Table III.The relation between observed
groups and latent compliance classes.
Z i
D i C i
1
1Complier or always taker 1
0Never taker or de?er 0
0Never taker or complier 01Always taker or de?er
treatment based on the IV that restricts the number of compliance classes by ruling out de?ers;and (ii)assumptions that restrict the heterogeneity of treatment effects among the different compliance classes.We ?rst consider approach (i)to point identi?cation of restricting the number of compliance classes.The assumption made by Angrist et al .[43]rules out de?ers:
IV-A5Monotonicity assumption .This assumption says that there are no subjects who are ‘de?ers’,
who would only take level 1of the treatment if not encouraged to do so,that is,there is no subject i with D 1i D 0;D 0i D 1.
Monotonicity is automatically satis?ed for single-consent randomized encouragement designs in which only the subjects encouraged to receive the treatment are able to receive it [46](for this design,there are only compliers and never takers).Monotonicity is also plausible in many applications in which the encouragement (Z D 1)provides a clear incentive and no disincentive to take the treatment.For the setting of a binary outcome,(IV-A5)reduces the number of free parameters to seven,enabling iden-ti?cation because there are seven free probabilities for the observed data.However,the model only identi?es the average treatment effect for compliers.The never takers and always takers do not change their treatment status when the instrument changes,so under the ER assumption,the potential treatment and potential outcome under either level of the IV (Z i D 1or 0)are the same.Consequently,the IV is not helpful for learning about the treatment effect for always takers or never https://www.doczj.com/doc/3a3544165.html,pliers are sub-jects who change their treatment status with the IV ,that is,the subjects would take the treatment if they were encouraged to take it by the IV but would not otherwise take the treatment.Because these subjects change their treatment with the level of the IV ,
the IV is helpful for
learning about their treatment effects.The average causal effect for this subgroup,E Y 1i Y 0i j C i D co ,is called the complier average causal
effect (CACE)or the local average treatment effect.It provides the information on the average causal effect of receiving the treatment for compliers.
Approach (ii)to making assumptions about IVs to enable point identi?cation of a treatment effect keeps assumptions (IV-A1)–(IV-A4)but does not make assumption (IV-A5)(monotonicity);instead,it makes an assumption that restricts the heterogeneity of treatment effects among the compliance classes.The strongest such assumption is that the average effect of the treatment is the same for all the compli-ance classes,E.Y 1 Y 0j C D co /D E.Y 1 Y 0j C D at /D E.Y 1 Y 0j C D nt /D E.Y 1 Y 0j C D de /.This assumption identi?es the average treatment effect for the whole population (this can be derived by using the same reasoning as in the derivation of (2)).A weaker restriction on the heterogene-ity of treatment effects among the compliance classes is the no current treatment value interaction assumption [47]:
E.Y 1 Y 0j D D 1;Z D 1;X /D E.Y 1 Y 0j D D 1;Z D 0;X /:(1)
Assumption (1)combined with (IV-A1)–(IV-A4)identi?es the average effect of treatment among the treated,E.Y 1 Y 0j D D 1/.Under assumptions (IV-A1)–(IV-A5),assumption (1)says that the average treatment effect is the same among always takers and compliers conditional on X ,as the left-hand side of (1)is the average effect of treatment among compliers and always takers,and the right-hand side is the average effect among always takers (all conditional on X ).For further information on approach (ii),see [48,49].
We are going to focus on approach (i)to the IV assumptions (i.e.,assumptions (IV-A1)–(IV-A5))for the rest of this tutorial.An attractive feature of this approach is that the monotonicity assumption (IV-A5)is reasonable in many applications (e.g.,when the encouragement level of the IV provides a clear incen-tive to take treatment and no disincentive);see also Section 5.3for discussion of a weaker assumption than monotonicity,which has similar consequences.Although the effect identi?ed by (IV-A1)–(IV-A5),the CACE,is only the effect for the subpopulation of compliers,the data are,in general,not informative about average effects for other subpopulations without extrapolation,just as a randomized experiment conducted on men is not informative about average effects for women without extrapolation [50].By focusing on estimating the CACE,the researcher sharply separates exploration of the information in the data from extrapolation to the (sub)-population of interest [50].See Sections 5.1–5.2for discussion of extrapolation of the CACE to other (sub)-populations.
Vytlacil [51]showed that assumptions (IV-A1)–(IV-A5)are equivalent to a version of common approach to IV assumptions in economics.In economics,selection of treatment A versus B is often modeled by a latent index crossing a threshold,where the latent index is interpreted as the expected net utility of choosing treatment A versus B .For example,
D i D?0C?1Z i C"i1 Y i Dˇ0Cˇ1D i C"i2
where
D i D 1if D
i
>0
0if D
i
60
Z i independent of"i1;"i2:
Vytlacil[51]showed that a nonparametric version of the latent index model is equivalent to the assumptions(IV-A1)–(IV-A5)above that Angrist et al.[43]used to de?ne an IV.
4.2.Two-stage least squares(Wald)estimator
Let us?rst consider IV estimation when there are no observed covariates X.For binary IV and treat-ment variable,Angrist et al.[43]showed that under assumptions(IV-A1)–(IV-A5),the CACE is nonparametrically identi?ed by
E.Y j Z D1/ E.Y j Z D0/
E.D j Z D1/ E.D j Z D0/
D
?P.C D at j Z D1/E.Y1;1j Z D1;C D at/C P.C D co j Z D1/E.Y1;1j Z D1;C D co/C P.C D nt j Z D1/E.Y1;0j Z D1;C D nt/C P.C D de j Z D1/E.Y1;0j Z D1;C D de/
?P.C D at j Z D0/E.Y0;1j Z D0;C D at/C P.C D co j Z D0/E.Y0;0j Z D1;C D co/C P.C D nt j Z D0/E.Y0;0j Z D0;C D nt/C P.C D de j Z D0/E.Y0;1j C D de/ ?P.C D at j Z D1/C P.C D co j Z D1/ ?P.C D at j Z D0/C P.C D de j Z D0/
D ?P.C D at j Z D1/E.Y1;1j Z D1;C D at/C P.C D co j Z D1/E.Y1;1j Z D1;C D co/C P.C D nt j Z D1/E.Y1;0j Z D1;C D nt/ ?P.C D at j Z D0/E.Y0;1j Z D0;C D at/C P.C D co j Z D0/E.Y0;0j Z D0;C D co/C P.C D nt j Z D0/E.Y0;0j Z D0;C D nt/ ?P.C D at j Z D1/C P.C D co j Z D1/ ?P.C D at j Z D0/
D ?P.C D at/E.Y1;1j C D at/C P.C D co/E.Y1;1j C D co/C P.C D nt/E.Y1;0j C D nt/ ?P.C D at/E.Y0;1j C D at/C P.C D co/E.Y0;0j C D co/C P.C D nt/E.Y0;0j C D nt/
?P.C D at/C P.C D co/ ?P.C D at/
D ?P.C D at/E.Y1j C D at/C P.C D co/E.Y1j C D co/C P.C D nt/E.Y0j C D nt/ ?P.C D at/E.Y1j C D at/C P.C D co/E.Y0j C D co/C P.C D nt/E.Y0j C D nt/
?P.C D at/C P.C D co/ ?P.C D at/
D
P.C D co/?E.Y1 Y0j C D co/
P.C D co/
D
E.Y1 Y0j C D co/;(2)
where the second equality follows from the monotonicity assumption(assumption(IV-A5)),the third equality follows from the IV is independent of unmeasured confounders assumption(assumption(IV-A3)),the fourth equality follows from the ER assumption(assumption(IV-A4)),and the?fth equality follows from the IV is correlated with treatment received assumption(assumption(IV-A2)).
The standard IV estimator for a binary IV and a binary treatment is the sample analogue of the?rst expression in(2),
O CACE D
O E.Y
i
j Z i D1/ O E.Y i j Z i D0/
O E.D
i
j Z i D1/ O E.D i j Z i D0/
;(3)
where O E denotes the sample mean.The standard IV estimator is called the Wald estimator after Wald[52].
The standard IV estimator is also called the two-stage least squares(2SLS)estimator because it can be obtained from the following2SLS procedure:(i)regress D on Z by least square to obtain O E.D j Z/;
and(ii)regress Y on O E.D j Z/.The coef?cient on O E.D j Z/from regression(ii)equals(3).As(3)can be obtained by the2SLS procedures,we denote(3)by O
CACE2SLS,
O
CACE2SLS D
O E.Y
i
j Z i D1/ O E.Y i j Z i D0/
O E.D
i
j Z i D1/ O E.D i j Z i D0/
:(4)
To see why2SLS provides a consistent estimate of the CACE,write Y D?C CACE D C u,where ?is chosen so that E.u/D0.Then,under the monotonicity and ER assumption,
?C u i D 8
?<
?:
Y1
i
CACE C i D at
Y0
i
C
Y1
i
Y0
i
CACE
Z i C i D co
Y0
i
C i
D nt
:
Thus,under the IV independent of unmeasured confounders assumption,E.Y j Z/D?C CACE E.D j Z/and an unbiased estimate of the CACE can be obtained from regressing Y on E.D j Z/.We do not know E.D j Z/but can replace it by the consistent estimate O E.D j Z/from regressing D on Z and then regress Y on O E.D j Z/;this is the2SLS procedure.The standard error for O
CACE2SLS is not the standard error from the second stage regression but needs to account for the sampling uncertainty in using O E.D j Z/as an estimate of E.D j Z/;see[53–55]and[56,Chapter9.8].Speci?cally,the asymp-totic standard error for O
CACE2SLS is given in[55,Theorem3].The2SLS estimator O
CACE2SLS can also
be written as O Cov.Y;Z/
O Cov.D;Z/
[54].
The2SLS estimator does not take into full account the structure in Table III that the observed out-comes are mixtures of outcomes from different compliance classes.Imbens and Rubin[57,58]and Cheng et al.[59,60]developed approaches to estimating the CACE that use the mixture structure to improve ef?ciency.For example,Cheng et al.[59]developed an empirical likelihood approach that is consistent under the same assumptions as2SLS but that provides substantial ef?ciency gains in some ?nite sample settings.
4.3.Estimation with observed covariates
As discussed earlier,various methods have been proposed to use IVs to overcome the problem of unmea-sured confounders in estimating the effect of a treatment on outcomes without covariates.However,in practice,IVs may be valid only after conditioning on covariates.For example,in the NICU study of Section1.2,race is associated with the proposed IV excess travel time,and race is also thought to be associated with infant complications through mechanisms other than level of NICU delivery such as maternal age,previous cesarean section,inadequate prenatal care,and chronic maternal medical condi-tions[61].Consequently,in order for excess travel time to be independent of unmeasured confounders conditional on measured covariates,it is important that race be included as a measured covariate.To incorporate covariates into the2SLS estimator,regress D i on X i and Z i in the?rst stage to obtain O D i and then regress Y i on O D i and X i in the second stage.Denote the coef?cient on O D i in the second stage regression by O 2SLS.The estimator O 2SLS estimates a covariate-averaged CACE as we shall discuss[62]. Let. ; /be the minimum mean squared error linear approximation to the average response function for compliers E.Y j X;D;C D co/,that is,. ; /D arg min ; E?.Y T X D/2j C D co (where X is assumed to contain the intercept).Speci?cally,if the CACE given X is the same for all X and the effect of X on the outcomes for compliers is linear(i.e.,E.Y j X;D;C D co/D T X C D), then equals the CACE.The estimator O 2SLS is a consistent(i.e.,asymptotically unbiased)estimator of .Thus,if the CACE given X is the same for all X and the effect of X on the outcomes for com-pliers is linear,O 2SLS is a consistent estimator of the CACE.As discussed in Section4.2,the standard error for O 2SLS is not the standard error from the second stage regression but needs to account for the sampling uncertainty in using O D i as an estimate of E.D i j X i;Z i/;see[53–55]and[56,Chapter9.8].
Other methods besides2SLS for incorporating measured covariates into the IV model are discussed in[59,63–69],among others.Little and Yau[63]and Hirano et al.[64]introduced covariates in the IV model of Imbens and Angrist[55]with distributional assumptions and functional form restrictions. Angrist and Imbens[65]considered settings under fully saturated
speci?cations with discrete covari-ates.Without distributional assumptions or functional form restrictions,Abadie[66]developed closed
forms for average potential outcomes for compliers under treatment and control with covariates.Cheng et al.[59]discussed incorporating covariates with an empirical likelihood approach.
4.4.Robust standard errors for2SLS
When there is clustering in the data,standard errors that are robust to clustering should be computed. For2SLS,this can be performed by using robust Huber–White standard errors[70].Code for computing robust Huber–White standard errors for IV analysis with clustering in R is given in Section14.For the NICU study,there is clustering by hospital.
Even when there is no clustering,we recommend always using the robust Huber–White standard errors for2SLS as the non-robust standard error’s correctness requires additional strong assumptions about the relationships between the different compliance classes’outcome distributions and homoskedasticity, while the robust standard error’s correctness does not require these assumptions;see[55,Theorem3] and[62,Section4.2.1].Code for computing robust Huber–White standard errors without clustering in R is given in Section14.
4.5.Two-sample IV
The2SLS estimator(4)can be used when information on Y,Z,D,and X are not available in a single data set,but one data set has Y,Z,and X,and the other data set has D,Z,and X.One can estimate the regression function O E.D j Z;X/from the?rst data set and then compute O E.D j Z i;X i/for the subjects i in the second data set and regress Y i on O E.D j Z i;X i/and X i for the second data set.This is called two-sample2SLS[71,72];see[72]on how to compute standard errors.An example of using two-sample 2SLS is by Kaushal[73]who studied the effect of food stamps on body mass index(BMI)in immigrant families using differences in state responses to a change in federal laws on immigrant eligibility for the food stamp program as an IV.The National Health Interview Study was used to estimate the effect of state lived in on BMI,and the Current Population Survey was used to estimate the effect of state lived in on food stamp program participation because neither data set contained all three variables.
4.6.Example1:Analysis of NICU study
For the NICU study,Table IV shows the2SLS estimate for the effect of high-level NICUs using excess travel time as an IV and compares the2SLS estimate to the estimate that does not adjust for any con-founders and the multiple regression estimate that only adjusts for the measured confounders(those in Table IV plus several other variables described in[4]).The unadjusted estimate is that high-level NICUs increase the death rate,causing10.9more deaths per1000deliveries;this estimate is probably strongly biased by the selection bias that doctors and mothers are more likely to insist on babies being delivered at a high-level NICU if the baby is at high risk of mortality.The regression estimate that adjusts for measured confounders is that high-level NICUs save4.2babies per1000deliveries.The2SLS estimate that adjusts for measured and unmeasured confounders is that high-level NICUs save even more babies, 5.9babies per1000deliveries.
As illustrated in Table IV,the multiple regression estimate of the causal effect will generally have a smaller con?dence interval(CI)than the2SLS estimate.However,when the IV is valid and there is unmeasured confounding,the multiple regression estimate will be asymptotically biased,whereas the 2SLS estimate will be asymptotically unbiased.Thus,there is a bias–variance trade-off between mul-tiple regression versus2SLS(IV estimation).When the IV is not perfectly valid,the2SLS estimator will be asymptotically biased,but the bias–variance trade-off may still favor2SLS.Basu and Chan[74] developed a diagnostic tool for deciding whether to use multiple regression versus2SLS.
Table IV.Risk difference estimates for mortality per1000premature births in high-level NICUs versus low-level NICUs.
Estimator Risk difference Con?dence interval
Unadjusted10.9(6.6,15.3) Multiple regression,adjusted for measured confounders 4.2( 6.8, 1.5) Two-stage least squares,adjusted for measured and unmeasured confounders 5.9( 9.6, 2.2) The con?dence intervals account for clustering by hospital through the use of Huber–White robust standard errors.
4.7.Example2:The effect of receiving treatment in a randomized trial with nonadherence
An important application of IV methods is to estimate the effect of receiving treatment in randomized
trials with nonadherence.When some subjects do not adhere to their assigned treatments in a random-ized trial,the intention-to-treat(ITT)effect is often estimated,O ITT D O E.Y j Z D1/ O E.Y j Z D0/;ITT
is estimating the effect of being assigned the active treatment compared with being assigned the control
(e.g.,a placebo or usual care).When there is nonadherence,the ITT effect is different from the effect
of receiving the treatment versus the control.Both of these effects are valuable to know.One situation
when knowing the effect of receiving the treatment versus the control is particularly valuable is when
the treatment nonadherence pattern is expected to differ between the study sample and the target pop-
ulation[75–77].In this situation,the ITT estimate may be biased for estimating the effect of offering
the treatment to the target population[75,76],and a key quantity that needs to be known to accurately
predict the effect of offering the treatment to the target population is the effect of actually receiving the
treatment[76,77].For example,Sommer and Zeger[75]discussed a trial of vitamin A supplementa-
tion to reduce child mortality.In the trial,the vitamin A supplementation was implemented by having
children take pills,and some children who were randomized to treatment did not take the pills.The ITT
effect is the effect of making vitamin A pills available to children.However,if the trial showed that tak-
ing the pills was ef?cacious,vitamin A supplementation would not likely be implemented by providing
pills but instead by fortifying a daily food item such as monosodium glutamate or salt[75].By knowing
the effect of receiving vitamin A supplementation(the biologic ef?cacy)and the rate at which vitamin
A supplementation would be successfully delivered under a forti?cation program,we can estimate the
effectiveness of a forti?cation program.A second situation in which knowing the effect of receiving
treatment versus control is particularly valuable is when patients who are interested in fully adhering to
a treatment are making decisions about whether to take the treatment[76,78].For example,Hernán and
Hernández-Díaz[78]mentioned the setting that to decide whether to use a certain contraception method,
a couple may want to know the failure rate if they use the method as indicated,rather than the failure
rate in a population that included a substantial proportion of nonadherers.
A standard estimate of the effect of receiving the treatment versus the control is the as-treated estimate,O E.Y j D D1/ O E.Y j D D0/,which compares the outcomes of subjects who received
the treatment versus the control regardless of the subjects’assigned treatment.The as-treated esti-
mate may be biased for estimating the effect of receiving the treatment because of unmeasured con-
founding,for example,individuals with better diet may be more likely to adhere to treatment and to
have better outcomes regardless of treatment.Another standard estimate is the per-protocol estimate, O E.Y j Z D1;D D1/ O E.Y j Z D0;D D0/,which compares the outcomes of subjects who were assigned to the treatment and followed the treatment protocol to subjects who were assigned the con-
trol and followed the control protocol;similar to the as-treated estimate,the per-protocol estimate may
be biased for estimating the effect of receiving the treatment because of unmeasured confounding,for
example,an individual with better diet may be more likely to adhere to treatment,but all subjects may
adhere with the control if the control is usual care.The IV method has the potential of overcoming bias
from unmeasured confounding in estimating the effect of receiving the treatment.Consider as a possible
IV,the randomly assigned treatment Z.The randomly assigned treatment satis?es that the IV is indepen-
dent of unmeasured confounders assumption(IV-A3)because of the randomization,and the randomly
assigned treatment will usually make receiving treatment more likely,thus satisfying(IV-A2)that the IV
is positively correlated with treatment received.It needs to be considered whether the randomly assigned
treatment satis?es the ER(IV-A4)and monotonicity assumptions(IV-A5)for speci?c trials.In the vita-
min A pill trial mentioned earlier,the treatment was only available to those assigned to treatment so
that monotonicity was automatically satis?ed.Sommer and Zeger[75]argued that the ER is also likely
satis?ed for the vitamin A trial because for never takers,being assigned to the treatment group versus the
control group is unlikely to affect mortality(there was no placebo in the trial).In contrast,Ten Have et
al.[79]raised concern about the ER holding in certain mental health randomized trials.If the randomly assigned treatment does satisfy all IV assumptions(IV-A1)–(IV-A5)for a trial,then the2SLS(Wald) estimator(4)is a consistent estimate of the effect of actually receiving treatment for compliers.The numerator of(4)is equal to the ITT estimate,and the denominator of(4)is an estimate of the proportion
of compliers.
Table V shows the mortality rates in the vitamin A trial,strati?ed by assigned treatment and received
treatment[75].The ITT estimate for the effect on the mortality rate per1000children is3:8 6:4D 2:6,
the as-treated estimate is1:2 7:7D 6:5,the per-protocol estimate is1:2 6:4D 5:2,and the IV
Table V.Mortality rates in vitamin A trial,strati?ed by assigned treatment and received treatment. Randomization Treatment Deaths Mortality rate assignment received#of children(per1000) Control Control11,58874 6.4 Treatment Control2,4193414.1 Treatment Treatment9,67512 1.2 Treatment Control or treatment2;419C9;675D12;09434+12 3.8 Control or treatment Control11;588C74C7.7
2,41934
The top part of the table shows all three strata,and the bottom part shows certain collapsed strata.
estimate is3:8 6:4
9675=12;094D 3:3.As discussed earlier,the assumptions for randomization assignment to
be a valid IV are plausible for the vitamin A trial,and the IV estimate says that taking the vitamin A pills saves an estimated3.3per1000children among those children who would take the vitamin A pills if offered to them(the compliers in this trial—note that there are no always takers in this trial).
5.Understanding the treatment effect that IV estimates
As discussed in Section4,the IV method estimates the CACE,the average treatment effect for the com-pliers(i.e.,E?Y1 Y0j C D co ),which might not equal the average treatment effect for the whole population.Although we might ideally want to know the average treatment effect for the whole popu-lation,the average treatment effect for compliers often provides useful information about the average treatment for the whole population,and the average treatment effect for compliers may be of interest in its own right.In Section5.1,we discuss how to relate the average treatment for compliers to the average treatment effect for the whole population,and in Section5.2,we discuss how to understand more about who the compliers are,which is helpful for interpreting the average treatment effect for compliers in its own right.In Sections5.3–5.5,we discuss additional issues related to understanding the treatment effect that IV estimates.In particular,in Section5.3,we discuss interpreting the treatment effect when the compliance class is not deterministic;in Section5.4,we discuss on interpreting the treatment effect when there are different versions of the treatment;and in Section5.5,we discuss the interpretation issues when there is heterogeneity in response.
5.1.Relationship between average treatment effect for compliers and average treatment effect for the whole population
As discussed in Section4,the IV method estimates the CACE,the average treatment effect for the compliers(i.e.,E?Y1 Y0j C D co ).The average treatment effect in the population is,under the mono-tonicity assumption,a weighted average of the average treatment effect for the compliers,the average treatment effect for the never takers,and the average treatment effect for the always takers:
E?Y1 Y0 D P.C D co/E?Y1 Y0j C D co C P.C D at/E?Y1 Y0j C D at C P.C D nt/E?Y1 Y0j C D nt :
The IV method provides no direct information on the average treatment effect for always takers(i.e., E?Y1 Y0j C D at )or the average treatment effect for never takers(i.e.,E?Y1 Y0j C D nt ).How-ever,the IV method can provide useful bounds on the average treatment effect for the whole population if a researcher is able to put bounds on the difference between the average treatment effect for compliers and the average treatment effects for never takers and always takers based on subject matter knowledge. For example,suppose a researcher is willing to assume that this difference is no more than b.Then
E?Y1 Y0j C D co b?1 P.C D co/ 6E?Y1 Y0 6E?Y1 Y0j C D co C b?1 P.C D co/ ;(5)
where the quantities on the left-hand and right-hand sides of(5)other than b can be estimated as dis-
cussed in Section4and[58,60,64].For binary or other bounded outcomes,the boundedness of the outcomes can be used to tighten bounds on the average treatment effect for the whole population or other treatment effects[45,80].Qualitative assumptions,such as that the average treatment effect is larger for always takers than compliers,can also be used to tighten the bounds,for example,[80–82].
In thinking about extrapolating the CACE to the full population,it is useful to think about how com-pliers’outcomes compare to always takers’and never takers’outcomes[50].The data provide some information about this.Speci?cally,we can compare
E.Y0j C D nt/vs.E.Y0j C D co/and(6)
E.Y1j C D at/vs.E.Y1j C D co/:
Under(IV-A1)–(IV-A5),Abadie[83]showed that the following are consistent estimates of the quan-tities in(1)when there are no covariates:O E.Y0j C D nt/D O E.Y j D D0;Z D1/,O E.Y0j C D co/D O E.Y.1 D/j Z D1/ O E.Y.1 D/j Z D0/
O E.1 D j Z D1/ O E.1 D j Z D0/
,O E.Y1j C D at/D O E.Y j D D1;Z D0/and O E.Y1j C D co/D O E.YD j Z D1/ O E.YD j Z D0/
O E.D j Z D1/ O E.D j Z D0/
;when there are covariates,the methods in[66]or[64]can be used to estimate the quantities in(1).If compliers,never takers,and always takers are found to be substantially different in levels by evidence of a substantial difference between E.Y0j C D nt/and E.Y0j C D co/and/or between E.Y1j C D at/and E.Y1j C D co/,then it appears much less plausible that the average effect for compliers is indicative of average effects for other compliance types.On the other hand,if one?nds that potential outcomes given the control for never takers and compliers are similar,and potential out-comes given the treatment are similar for compliers and always takers,it is more plausible that average treatment effects for the groups are also comparable[50].For example,in the vitamin A trial described in Table V,the mortality rate for never takers is estimated to be14.1(per1000children)and for com-pliers under control is estimated to be4.8(note that there are no always takers in the vitamin A trial). This substantial difference in estimated mortality rates between the compliance classes suggests that we should be cautious in extrapolating the CACE to the full population.
5.2.Characterizing the compliers
The IV method estimates the average treatment effect for the subpopulation of compliers.In most situa-tions,it is impossible to identify which subjects in the data set are‘compliers’because we only observe a subject’s treatment selection under either Z D1or Z D0,which means we cannot identify if the subject would have complied under the unobserved level of the instrument.So who are these compliers and how do they compare to noncompliers?To understand this better,it is useful to characterize the compliers in terms of their distribution of observed covariates[9,62].The mean of a covariate X i among the com-pliers is the following under IV assumptions1–5from Section4.1,where f represents the probability mass function or probability density function,
E?X j C D co D Z
x
f.x j C D co/
f.x/
f.x/dx D E
?
X
f.X j C D co/
f.X/
;(7)
where
f.x j C D co/
f.x/D
P.C D co j x/f.x/
P.C D co/
f.x/
D
P.C D co j x/
P.C D co/
D
E.D j Z D1;X D x/ E.D j Z D0;X D x/
E.D j Z D1/ E.D j Z D0/
:
(8)
We estimate E.X j C D co/by estimating?i D f.X i j C D co/
i for i D1;:::;N based on(8)(e.g.,using
logistic regression to estimate E.D j Z;X/and then plugging into(8))and then taking the sample aver-age of X i?i.See[66]for an alternate representation of E.X j C D co/.For a binary characteristic X,(7) simpli?es to
P.X D1/?E.D j Z D1;X D1/ E.D j Z D0;X D1/
E.D j Z D1/ E.D j Z D0/
:
The prevalence ratio of a binary characteristic X among compliers compared with the full population is
Prevalence ratio D P.X D1j C D co/
P.X D1/
:
Table VI shows the mean of various characteristics X among compliers versus the full population and also shows the prevalence ratio.Babies whose mothers are
college graduates are slightly under-represented(prevalence ratio=0:87)and African-Americans are slightly over-represented(prevalence
Table https://www.doczj.com/doc/3a3544165.html,plier characteristics for NICU study.
Prevalence of X Prevalence of X Prevalence ratio of X Characteristic X among compliers in full population among compliers to full population Birthweight<1500g0.030.090.33
Gestational age632weeks0.040.130.34
Mother college graduate0.230.260.87
African-American0.170.15 1.14
Gestational diabetes0.050.050.91
Diabetes mellitus0.020.020.77
Pregnancy-induced hypertension0.080.100.82
Chronic hypertension0.020.020.89
The second column shows the estimated proportion of compliers with a characteristic X,the third column shows the estimated proportion of the full population with the characteristic X,and the fourth column shows the estimated ratio of compliers with X compared with the full population with X.
ratio=1:14)among compliers.Very low birthweight(<1500g)and very premature babies(gestational age632weeks)are substantially under-represented among compliers,with prevalence ratios around one-third;these babies are more likely to be always takers,that is,delivered at high-level NICUs regard-less of mother’s travel time.Babies whose mothers’have comorbidities such as diabetes or hypertension are slightly under-represented among compliers.Overall,Table VI suggests that higher-risk babies are under-represented among the compliers.If the effect of high-level NICUs is greater for higher-risk babies,then the IV estimate will underestimate the average effect of high-level NICUs for the whole population.
5.3.Understanding the IV estimate when compliance status is not deterministic
For an encouragement that is uniformly delivered,such as patients who made an appointment at a psychi-atric outpatient clinic are sent a letter encouraging them to attend the appointment[84],it is clear that a subject is a complier,an always taker,a never taker,or a de?er with respect to the encouragement.How-ever,sometimes encouragements that are not uniformly delivered are used as IVs.For example,in the NICU study,consider the IV of whether the mother’s excess travel time to the nearest high-level NICU is more than10min.If a mother whose excess travel time to the nearest high-level NICU was more than10min moved to a new home with an excess travel time of less than10min,whether the mother would deliver her baby at a high-level NICU might depend on additional aspects of the move,such as the location and availability of public transportation at her new home[85]and the exact travel time to the nearest high-level NICU at her new home.Consequently,a mother may not be able to be deterministi-cally classi?ed as a complier or not a complier—she may be a complier with respect to certain moves but not others.Another example of nondeterministic compliance is that when physician preference for one drug versus another is used as the IV(e.g.,Z D1if a patient’s physician prescribes drug A more often than drug B),whether a patient receives drug A may depend on how strongly the physician prefers drug A[9,86].Another situation in which nondeterministic compliance status can arise is that the IV may not itself be an encouragement intervention but a proxy for an encouragement intervention.Consider the case of Mendelian randomization,in which the IV is often a single nucleotide polymorphism(SNP). Changes in the SNP itself may not affect the exposure D.Instead,genetic variation at another location on the same chromosome as the SNP,call it L,might affect D.The SNP might just be a marker for the subject’s genetic code at location L.The encouragement intervention is having a certain genetic code at L,and the SNP is just a proxy for this encouragement.Consequently,even if a subject’s exposure level would change as a result of a change in the genetic code at location L,whether the subject is a complier with respect to a change in the SNP depends on whether the change in the SNP leads to a change in the genetic code at location L,which is randomly determined through the process of recombination[85].
Brookhart and Schneeweiss[9]provided a framework for understanding how to interpret the IV esti-mate when compliance status is not deterministic.Suppose that the study population can be decomposed
into a set of?C1mutually exclusive groups of patients based on clinical,lifestyle,and other charac-teristics such that within each group of patients,whether a subject receives treatment is independent of the effect of the treatment.All of the common causes of the potential treatment received D1;D0and the potential outcomes Y1;Y0should be included in the characteristics used to de?ne these groups.
For example,if there are L binary common causes of.D1;D0;Y1;Y0/,then the subgroups can be the ?C1D2L possible values of these common causes.Denote patient membership in these groups by the set of indicators S D f S1;S2;:::;S?g.Consider the following model for the expected potential outcome:
E.Y d j S/D?0C?1d C?T2S C?T3S d:
The average effect of treatment in the population is?1C?T
3E?S ,and the average effect of treat-
ment in subgroup j is?1C?3;j.Under IV assumptions(IV-A1)–(IV-A4)in Section4.1,that is,all the assumptions except monotonicity,the2SLS estimator(4)converges in probability to the following quantity:
E.Y j Z D1/ E.Y j Z D0/ E.D j Z D1/ E.D j Z D0/D?1C
?
X
j D1
?3;j E?S j w j;(9)
where
w j D E.D j Z D1;S j D1/ E.D j Z D0;S j D1/
E.D j Z D1/ E.D j Z D0/
:
The IV estimator(9)is a‘weighted average’of treatment effects in different subgroups,where the sub-groups in which the instrument has a stronger effect on the treatment obtain more weight.Note that when the compliance class is deterministic,the subgroups can be de?ned as the compliance classes, and(9)just says that the IV estimator is the average treatment effect for compliers.In the NICU study, where compliance class may not be deterministic,Table VI suggests that babies in lower-risk groups,for example,not very low birthweight or not very low gestational age,are weighted more heavily in the IV estimator.If there are subgroups for which the instrument has no effect on their treatment level,then that subgroup obtains zero weight.For example,mothers or babies with severe preexisting conditions may virtually always be delivered at a high-level NICU,so that the IV of excess travel time has no effect on their treatment level[4].If there are subgroups for which the encouraging level of the instrument makes them less likely to receive the treatment,then this subgroup would obtain‘negative weight’,and(9)is not a true weighted average,potentially leading the IV estimator to have the opposite sign of the effect of the treatment.For example,Brookhart and Schneeweiss[9]discussed studying the safety of metformin for treating type II diabetes versus other antihyperglycemic drugs among patients with liver disease using physician preference as the IV(Z D1if a physician is more likely to prescribe metformin than other antihyperglycemic drugs).Metformin is contraindicated in patients with decreased renal function or liver disease,as it can cause lactic acidosis,a potentially fatal side effect.Brookhart and Schneeweiss [9]speculated that physicians who infrequently use metformin(Z D0)will be less likely to understand its contraindications and would therefore be more likely to misuse it.If this hypothesis is true,then for estimating the effect of metformin on lactic acidosis,the IV estimator could mistakenly make metformin appear to prevent lactic acidosis because the subgroup(s)of patients with decreased renal function or liver disease,for which metformin causes lactic acidosis,would have a negative weight w j.When the compliance class is deterministic,a subgroup obtaining negative weight means that there are de?ers, violating the monotonicity assumption.
5.4.Understanding the treatment effect estimated by IV when SUTVA is violated
Consider the(IV-A1)assumption from Section4.1,SUTV A.Two ways in which SUTV A could be vio-lated are as follows:(i)there are different versions of the treatment that have different effects,that is,Y1
i depends on which version of the treatment was received;or(ii)there is interference between units,that
is,Y1
i depends on whether unit i0received the treatment or control[87].When one of these violations
occur,the IV estimate(4)may still be interpretable as long as(IV-A2)–(IV-A5)hold.
Consider?rst the no different versions of the treatment part of SUTV A.This would be violated if there are different ways of implementing the treatment that have different effects.For example,consider the effect of lowering one’s BMI on one’s mental health.There are different ways that a lower BMI might be
achieved,that is,by eating less or by exercising more,and these different ways of lowering BMI might have different effects on mental health.The version of the treatment effect estimated by IV is the one that implements the treatment in the same way as the IV.For example,consider estimating the effect of BMI on mental health using the FTO gene as an IV for BMI[88].It has been hypothesized that FTO affects
BMI through affecting appetite,and there is some support for this hypothesis[89].If this hypothesis is correct,then the treatment effect of lowering BMI on mental health that is estimated by using the FTO gene as an IV is the version that involves lowering BMI by reducing food intake.An intervention that lowered BMI by increasing exercise might have different effects on mental health than an analysis that uses FTO as an IV suggests[90].
Consider next the no-interference assumption part of SUTV A that subject A receiving the treatment affects only subject A and not other subjects.In the NICU study,the no-interference assumption is reasonable—if preemie A is treated at a high-level NICU,this does not affect preemie B’s outcome. However,if there were crowding effects(e.g.,treating additional babies at a hospital decreases the quality of care for babies already under care at that hospital),this assumption might not be true.The no-interference assumption is also not appropriate for situations such as estimating the effect of a vac-cine on an individual because a non-vaccinated individual A may bene?t from individual B receiving the vaccine because A can no longer become infected from contact with person B[91].When no interfer-ence fails to hold,the IV method is roughly estimating the difference between the effect of the treatment and the spillover effect of some units being treated on those units left untreated(see[92]for a precise formulation and details).
5.5.Interpreting the treatment effect estimated by IV when there are heterogeneous responses
As discussed in Section4.1,the treatment effect estimated by the IV applies to only a subset of the subjects,namely the subjects whose treatment level is modi?ed by the level of the IV.In a binary setting, we refer to the subjects that respond to the IV as the compliers,in contrast to the never takers and always
takers.If there is heterogeneity in the response to the treatment(i.e.,Y1
i Y0
i
¤Y1
i0
Y0
i0
for some i;i0),
then the IV estimate is only valid for the compliers and may not generalize to the entire population.In fact,in many medical situations,it is almost certain that there is heterogeneity in response to treatment. Further,it is often the case that the always takers always take the treatment because it is believed their response to the treatment is quite large,whereas the never takers have either minimal response or even a negative response to the treatment.If only one instrument is available,the treatment effect is not iden-ti?able for the never takers and always takers.Careful thought is needed to state for which populations the IV estimate is valid.
In the NICU example,the compliers are those preemies whose NICU level would change because of travel time to the different facilities.The‘always-taker’preemies tended to be more dif?cult to treat (e.g.,younger and lower birthweight;see Table IV)and thus more obviously in need of care at a high-level NICU.It is quite possible that the treatment effect for the always-takers subgroup is larger than the effect estimated by the IV analysis.
Continuing with this logic,if the compliance groups are determined by how their treatment level changes because of the IV,then it follows that different IVs may estimate different treatment effects because the effects are being estimated on different subgroups.That is,if two different analyses are run on the same population,using two different but completely valid IVs,it is entirely possible for the effect estimates to differ because the composition of the compliers changes.For example,the preemies who have their NICU level changed by relative proximity to treatment facilities may have a different risk pro-?le than preemies who would have their NICU level changed by a modi?cation to hospital contracts with insurance providers,wherein a large percentage of the population would have to pay‘out-of-network’fees in order to receive care at a high-level facility.
The issue of multiple IVs is discussed in more detail in Section11.
6.Assessing the IV assumptions and sensitivity analysis for violations
of assumptions
For most proposed IVs,there is some uncertainty about whether the proposed IV actually satis?es the IV assumptions.Consequently,it is important to empirically assess whether a proposed IV satis?es the IV assumptions.Although not all of the assumptions can be completely tested,there are methods that test certain parts of the assumptions;we discuss these methods in Section6.1.Even if a proposed IV is
not perfectly valid,it may still provide useful inferences about treatment effects as long as it does not violate the assumptions for being a valid IV too badly.In Section6.2,we discuss sensitivity analysis methods that characterize how much inferences are affected by a proposed IV violating the assumptions by speci?ed magnitudes.
信息技术《有趣的绘画工具》说课稿 一、教材分析 《有趣的绘画工具》是省小学信息技术教材第一册（下）的内容，教学对象是小学四年级学生。它是教材关于金山画王2002画图知识的初步认识，并且贯穿着以后整个的画图知识教学，是学生能够顺利、快捷操作使用画图的基础之一，也是形成学生“了解熟悉——基本技能——综合运用”这一合理知识链的必要环节。教材目的是让学生学会金山画王中一些基本操作工具的运用，重点是掌握利用金山画王2002画板下的9种工具的基础操作及利用工具画图。新的工具的学习与使用，对学生充满着挑战，能够让学生在现有的基础上，产生一种求知与创作的冲动。正是这种冲动，也导致了学生内心理想与实际技能的不平衡。因此，探究学习的过程中，学生学习和创作的欲望极其强烈。学生的需要与兴趣就是学生探究的动力和起点。基于此点，从信息课本身的学科特点出发，结合学科课程整合理念，我设计了这一课时，目的在于让学生掌握各种工具的同时，着重培养学生的动手操作,思维能力,自我创新能力，进而唤起学生的生活体验，提高学生的信息素养。拓展信息技术课，只教电脑操作狭隘的课程局面。争取把更多的信息纳入到我们信息课程体系中来。培养学生的综合能力，从而使学生发现美，感觉美，创造美。让他们在无数的失败中寻找成功，感受成功的快乐。 从内容层面出发，对具备一定抽象思维能力和动手操作能力的四年级学生来说并不难，而且也是学生非常感兴趣的东西，因此在课堂上只需坚持精讲多练的原则，重难点知识让学生通过自己探究和小组合作学习等主要学习方式完成，同时结束教师适当个别指导。 二、教学目标 认知目标：让学生熟悉和掌握画板下工具的操作。掌握对工具的综合运用的方法。 能力目标：培养学生如何获取信息、处理信息和应用信息的能力。 培养学生自我探索、自主学习的能力和自我创新、团体协作的能力。 情感目标：让学生在无数的失败中，寻找并且体验成功。 三、教学重点与难点 重点：熟悉和掌握画板下9种工具的操作。 难点：对油漆桶的正确用法。 四、教法阐述 本课采用的主要教学方法有“任务驱动法”、“创设情境法”等。 信息技术课程本身的特点，要求我们知识及技能的传授应以完成典型"任务"为主。因此本课采用建构主义理论指导下的主体式教学模式。通过学生已经受过的美术教育和信息技术教育，利用创设情境教学法创设情境。设置一个任务，让学生在学习的过程中，自己动手，有机结合画图的各种工具，以任务驱动的方式发展能力。使教学内容合理流动，水到渠成。教学中，启发、诱导贯穿始终，创造学生自主探究学习的平台，使学生变被动学习为主动愉快的学习，提高课堂40分钟的战斗力与生命力。 五、学法指导 本课教给学生的学法是“分析体验---接受任务——合作探究——综合运用”。
有趣的测量说课设计与反思 有趣的测量说课设计与反思 设计理念： 《数学课程标准》中强调，数学教学活动必须建立在学生的认知发展水平和已有的知识经验基础之上。教师应向学生提供充分从事数学活动的机会，帮助他们在自主探索和合作交流的过程中真正理解和掌握基本的数学知识与技能、数学思想和方法，获得广泛的数学活动经验。培养学生发现问题、提出问题、解决问题的能力，感受数学与生活的联系。 教学内容： 《义务教育课程标准实验教科书》（北师大版）五年级下册第54—55页 学情与教材分析： 本节课主要是研究不规则物体体积的测量方法，是学生在掌握长方体和正方体的体积计算的基础上进行拓展延伸的。让学生通过实践操作，综合运用所学的知识和方法解决实际问题。而测量不规则形状物体的体积，采取的主要方法是将物体放入水中，通过计算水上升的体积，从而得到物体的体积。从显性方面来说，这是“等积变形”，从隐性方面来说，是将未知转化为已知。学生把握这一数学的转化思想，不仅可以解决一两个实际问题，也能以此类推，解决一大批这样的问题。所以，在教学时，不应仅仅停留在知识的显性联系上，更应
把这种隐性的数学思想渗透在其中，从而让学生真正把握数学知识之间的联系。 教学目标： 1、结合具体的活动情境，经历测量石块体积的实验过程，探索不规则物体体积的测量方法。 2、在实践与探究过程中，尝试用多种方法解决实际问题。 教学重难点： 探索不规则物体体积的测量方法。 教具准备： 石块、量杯、水槽、黄豆、课件等。 教学过程： 一、创设情境，生成问题 1、师：同学们，你们听过《乌鸦喝水》的故事吗？乌鸦是怎样喝到水的，请大家注意看。（课件演示：《乌鸦喝水》） 问：你看到了什么？水为什么会上升？上升部分水的体积和石块有着什么样的关系？ 【设计意图：问题是开展科学研究的动力和源泉，问题是数学实践活动的核心。在此环节中，通过学生熟悉的《乌鸦喝水》的情境引入，让学生产生疑问：水为什么上升？上升部分水的体积和石块有着什么样的关系？学生强烈的求知欲望被激发出来，这样用数学自身的思考力度来唤起学生学习的欲望。】 2、观察石块的形状
《有趣绘画工具》说课稿 《有趣绘画工具》说课稿 一、教材分析 《有趣的绘画工具》是省小学信息技术教材第一册（下）的内容，教学对象是小学四年级学生。它是教材关于金山画王xxxx画图知识的初步认识，并且贯穿着以后整个的画图知识教学，是学生能够顺利、快捷操作使用画图的基础之一，也是形成学生“了解熟悉——基本技能——综合运用”这一合理知识链的必要环节。教材目的是让学生学会金山画王中一些基本操作工具的运用，重点是掌握利用金山画王xxxx画板下的9种工具的基础操作及利用工具画图。新的工具的学习与使用，对学生充满着挑战，能够让学生在现有的基础上，产生一种求知与创作的冲动。正是这种冲动，也导致了学生内心理想与实际技能的不平衡。因此，探究学习的过程中，学生学习和创作的欲望极其强烈。学生的需要与兴趣就是学生探究的动力和起点。基于此点，从信息课本身的学科特点出发，结合学科课程整合理念，我设计了这一课时，目的在于让学生掌握各种工具的同时，着重培养学生的动手操作,思维能力,自我创新能力，进而唤起学生的生活体验，提高学生的信息素养。拓展信息技术课，只教电脑操作狭隘的课程局面。争取把更多的信息纳入到我们信息课程体系中来。培养学生的综合能力，从而使学生发现美，感觉美，创造美。让他们在无数的失败中寻找成功，感受成功的快乐。 从内容层面出发，对具备一定抽象思维能力和动手操作能力的四年级学生来说并不难，而且也是学生非常感兴趣的东西，因此在课堂上只需坚持精讲多练的原则，重难点知识让学生通过自己探究和小组合作学习等主要学习方式完成，同时结束教师适当个别指导。 二、教学目标 认知目标：让学生熟悉和掌握画板下工具的操作。掌握对工具的综合运用的方法。能力目标：培养学生如何获取信息、处理信息和应用信息的能力。 培养学生自我探索、自主学习的能力和自我创新、团体协作的能力。 情感目标：让学生在无数的失败中，寻找并且体验成功。 三、教学重点与难点
大班数学公开课教案《有趣的测量》 【活动目标】 1．感受并体验远近的含义，激发幼儿的求知欲望和探究精神。 2．学习用工具测量远近，并能将测量结果记录在表格中。 3．初步感知同样的距离，使用的测量工具不同，测得的次数也不 同以及同样的距离，使用的工具不同，测量的次数也不同，越长的工 具所用的测量次数越少。 【活动重难点】 1．重点：按照正确的步骤用工具测量 2．难点： （1）理解不同的距离，用同一种工具测量，测量的次数越多越远，测量的次数越少越近 （2）同样的距离，使用的工具不同，测量的次数也不同，越长的 工具所用的测量次数越少 活动准备： 铅笔，表格、路线图每人一份、水彩笔盖、短水彩笔、没削过得 铅笔。 【活动过程】 一、故事导入 师：今天，动物学校要举行一场盛大的运动会，小兔、小熊、小 猫都报名参加了比赛。你们看，小动物们马上就要从自己家里出发到 学校去了，究竟是哪个小动物会最先到达体育馆呢？ 二、学习用工具测量的方法比较路线的远近。 1．（引导幼儿观察路线图）请幼儿观察比较，哪个小动物去体育 馆的路最近？哪个小动物去体育馆的路最远？你是怎么知道的？这种 方法准确吗？ 2．师：用眼睛看的方法叫做目测法，但是目测法比一定准确，我 们还能用什么方法来判断路线的远近呢？（请幼儿讲讲自己的想法， 如工具：尺子、棍子、绳子、积木等）老师今天也给小朋友们带来了 一种测量工具，你们看看老师带来了什么工具？（水彩笔盖）3．师：你们觉得这样工具能测量小动物家到学校的距离么？（能）那咱们就先量一量小猫家到学校要几个水彩笔盖，你会量吗？（会），请你来试一试。
在幼儿尝试过程中教授测量方法，，边演示边引导幼儿一起讲述测量的正确步骤（找起点，沿着线，接着量）将测量结果记录在表格中（小猫家到学校量了5个水彩笔盖） 4.师：请你们也量一量小猫家到学校用了几个水彩笔盖。并将结果记录在表格里。 幼儿操作，教师巡回指导。 请你再量量其他两个小动物家到学校用了几个水彩笔盖，把结果记录在表格里。 5、请幼儿坐好，检验幼儿测量的结果，教师小结不同的距离，用同一种工具测量，测量的次数越多越远，测量的次数越少越近 6、师：郑老师还给你们准备了两种测量工具呢，我们就用这两种工具来量一量咱们的小椅子好不好。 请幼儿示范测量方法，及时纠正不对的测量步骤。 7、请幼儿坐好，检验幼儿测量结果，教师小结同样的距离，使用的工具不同，测量的次数也不同，越长的工具所用的测量次数越少。 三、教师小结 生活中还有很多东西都能被当做测量工具呢，我们的教室里就有很多，待会请你选一样你喜欢的东西作为测量工具，来量一量咱们的桌子、黑板，还能比比小朋友的身高呢……
北师大版小学数学教学大纲
一年级上册 第一单元生活中的数 一、数数 二、识数，认识阿拉伯数字 三、写阿拉伯数字 第二单元比较 一、介绍等号，大于符号，小于符号，以及其表示的意义 二、比较数的大小 三、从数的大小到生活中各类事物的大小，多少，高矮，轻重的比较 第三单元加与减（一） 一、介绍加法符号，以及十以内的无进位的加法。加法交换律的初步认识 二、介绍减法符号，减法的意义，十以内数字的减法 三、加法与减法的内在联系，进一步理解减法的意义 第四单元分类 一、对事物进行简单的归类，根据归类进行分类。 第五单元位置与顺序 一、前后顺序，位置的前后给事物排序 二、大小顺序，数的大小排序 三、上下顺序 四、左右顺序 五、将各种顺序与生活中的实际情况相联系 第六单元认识图形 一、从实际出发认识几何物体 二、从直观上认识正方体，长方体，圆柱体，球体
第七单元加与减（二） 一、十以上的数的认识，数位的初步的认识 二、加数有十以上，和为二十以下无进位的加法 三、二十以内无借位的减法 四、二十以内有进位的加法 五、二十以内有借位的减法 第八单元认识钟表 一、认识钟表的各组成部分以及其代表的意义 二、从时针，分针分布的位置大致的判断时间 一年级下册 第一单元加减法（一） 一、整十数的加减 二、一百以内两位数与一位数的加减，无进、借位 三、一百以内两位数与一位数列竖式计算，无进、借位 第二单元观察物体 一、认识物体的正面，侧面，认识正面侧面的区别 二、测量工具的认识，长度单位厘米，米的认识。厘米，米之间的单位互换 三、米，厘米所表示长度在实际生活中的体现 第三单元生活中的数 一、数一百以内的数 二、数位的认识，个位，十位，及其代表的意义 三、十以上数的大小比较，利用数位比较数的大小 第四单元有趣的图形
幼儿园大班数学游戏活动教案《有趣的测量》 活动目标： 1．感受并体验远近的含义，激发幼儿的求知欲望和探究精神。 2．学习用工具测量远近，并能将测量结果记录在表格中。 3．初步感知同样的距离，使用的测量工具不同，测得的次数也不 同以及同样的距离，使用的工具不同，测量的次数也不同，越长的工 具所用的测量次数越少。 活动重难点： 1．重点：按照正确的步骤用工具测量 2．难点： （1）理解不同的距离，用同一种工具测量，测量的次数越多越远，测量的次数越少越近 （2）同样的距离，使用的工具不同，测量的次数也不同，越长的 工具所用的测量次数越少 活动准备： 铅笔，表格、路线图每人一份、水彩笔盖、短水彩笔、没削过得 铅笔。 活动过程： 一、故事导入
师：今天，动物学校要举行一场盛大的运动会，小兔、小熊、小 猫都报名参加了比赛。你们看，小动物们马上就要从自己家里出发到 学校去了，究竟是哪个小动物会最先到达体育馆呢？ 二、学习用工具测量的方法比较路线的远近。 1．（引导幼儿观察路线图）请幼儿观察比较，哪个小动物去体育 馆的路最近？哪个小动物去体育馆的路最远？你是怎么知道的？这种 方法准确吗？ 2．师：用眼睛看的方法叫做目测法，但是目测法比一定准确，我 们还能用什么方法来判断路线的远近呢？（请幼儿讲讲自己的想法， 如工具：尺子、棍子、绳子、积木等）老师今天也给小朋友们带来了 一种测量工具，你们看看老师带来了什么工具？（水彩笔盖）3．师：你们觉得这样工具能测量小动物家到学校的距离么？（能）那咱们就先量一量小猫家到学校要几个水彩笔盖，你会量吗？（会），请你来试一试。 在幼儿尝试过程中教授测量方法，，边演示边引导幼儿一起讲述 测量的正确步骤（找起点，沿着线，接着量）将测量结果记录在表格 中（小猫家到学校量了5个水彩笔盖） 4.师：请你们也量一量小猫家到学校用了几个水彩笔盖。并将结 果记录在表格里。 幼儿操作，教师巡回指导。 请你再量量其他两个小动物家到学校用了几个水彩笔盖，把结果 记录在表格里。 5、请幼儿坐好，检验幼儿测量的结果，教师小结不同的距离，用 同一种工具测量，测量的次数越多越远，测量的次数越少越近6、师：
第1章 两阶段最小二乘法 在模型的基本假定中，解释变量与误差项正交保证了参数估计量的无偏性和一致性。当这一假定被违背时，称解释变量是内生的。常见的几种情况会导致内生问题：忽略重要的解释变量、变量的测量误差、变量的联立性。工具变量估计是解决解释变量内生问题的基本方法。本章介绍工具变量法和两阶段最小二乘法，以及模型内生性检验和过度识别约束检验等问题。 1.1 变量的内生性 如果模型中的解释变量与误差项出现相关，即(')E =X u 0，称解释变量是内生的。导致 解释变量内生性的原因有很多，主要的几个原因包括：模型中忽略了重要的解释变量、变量因果关系的双向性、变量的测量误差等。 模型中出现内生解释变量时，OLS 估计量是不一致的。根据OLS 估计量： 11111?(')(')(')(')(')(')N N -----==+=+βX X X y βX X X u βX X X u (1.1) 由假定Rank(X)=K 和大数定律，样本均值的概率极限等于总体均值，可得： 1Plim(')E(')N -=≡X X X X A ， 1Plim(')E(')N -=≠X u X u 0。 (1.2) 又由Slustky 定理， 111Plim(')N ---=X X A 1?Plim E(')-=+≠β βA X u β (1.3) 1.2 工具变量估计 1.2.1 工具变量 在如下模型中， y = X β+ u 第i 个解释变量x i 为内生解释变量。如果存在变量z ，z 满足如下两个条件： 正交条件：与u 不相关，即cor(z, u) = 0 相关条件：与x 相关，即cor(z, x i ) ≠ 0，也称为识别约束条件。 那么，z 被称作x i 的工具变量。
WINDOWS系列工具--画图详细教程 目录 一.如何使用画图工具 二.《画图》工具系列-妙用曲线工具 三. 《画图》工具系列-巧用圆形工具 四. 《画图》工具系列妙用文字工具 五. 用“画图”进行屏幕拷贝 六. “画图”程序的放大修改功能 七. “画图”中的工具与颜色配置 八. 灵活使用编辑功能 九. Windows画图程序操作技巧 十. Windows画图程序操作技巧 十一. 用画图程序检测LCD的暗点
一.如何使用画图工具 想在电脑上画画吗？很简单，Windows 已经给你设计了一个简洁好用的画图工具，它在开始菜单的程序项里的附件中，名字就叫做“画图”。 启动它后，屏幕右边的这一大块白色就是你的画布了。左边是工具箱，下面是颜色板。 现在的画布已经超过了屏幕的可显示范围，如果你觉得它太大了，那么可以用鼠标拖曳角落的小方块，就可以改变大小了。 首先在工具箱中选中铅笔，然后在画布上拖曳鼠标，就可以画出线条了，还可以在颜色板上选择其它颜色画图，鼠标左键选择的是前景色，右键选择的是背景色，在画图的时候，左键拖曳画出的就是前景色，右键画的是背景色。 选择刷子工具，它不像铅笔只有一种粗细，而是可以选择笔尖的大小和形状，在这里单击任意一种笔尖，画出的线条就和原来不一样了。
图画错了就需要修改，这时可以使用橡皮工具。橡皮工具选定后，可以用左键或右键进行擦除，这两种擦除方法适用于不同的情况。左键擦除是把画面上的图像擦除，并用背景色填充经过的区域。试验一下就知道了，我们先用蓝色画上一些线条，再用红色画一些，然后选择橡皮，让前景色是黑色，背景色是白色，然后在线条上用左键拖曳，可以看见经过的区域变成了白色。现在把背景色变成绿色，再用左键擦除，可以看到擦过的区域变成绿色了。 现在我们看看右键擦除：将前景色变成蓝色，背景色还是绿色，在画面的蓝色线条和红色线条上用鼠标右键拖曳，可以看见蓝色的线条被替换成了绿色，而红色线条没有变化。这表示，右键擦除可以只擦除指定的颜色－－就是所选定的前景色，而对其它的颜色没有影响。这就是橡皮的分色擦除功能。 再来看看其它画图工具。 是“用颜料填充”，就是把一个封闭区域内都填上颜色。 是喷枪，它画出的是一些烟雾状的细点，可以用来画云或烟等。 是文字工具，在画面上拖曳出写字的范围，就可以输入文字了，而且还可以选择字体和字号。 是直线工具，用鼠标拖曳可以画出直线。 是曲线工具，它的用法是先拖曳画出一条线段，然后再在线段上拖曳，可以把线段上从拖曳的起点向一个方向弯曲，然后再拖曳另一处，可以反向弯曲，两次弯曲后曲线就确定了。 是矩形工具，是多边形工具，是椭圆工具，是圆角矩形，多边形工具的用法是先拖曳一条线段，然后就可以在画面任意处单击，画笔会自动将单击点连接起来，直到你回到第一个点单击，就形成了一个封闭的多边形了。另外，这四种工具都有三种模式，就是线框、线框填色、和只有填色。
五年级下册数学《有趣的测量》教案 北师大版五年级下册数学《有趣的测量》教案范文 教学内容： 本节内容属北师大版小学数学五年级下册第四单元“长方体（二）”最后一节的内容：有趣的测量（求不规则物体的体积）。 教材分析： 本节课是在学生已经掌握了长方体和正方体的认识，长方体和正方体的表面积、体积的知识，了解了容积的内容的基础上呈现的。要使学生通过观察、比较，掌握不规则物体的体积的求法，拓展了学生的知识面，渗透了转化的思想。 学情分析： 本班级学生，大部分学习认真、踏实、自觉，基础扎实，好学上进，部分男生活泼好动，爱思考。对于探索数学问题有着极其浓厚的兴趣，喜欢自己动手解决问题。在他们身上还明显地存在着儿童的天性，好动、好奇等。对于本单元的知识，大部分学生掌握得比较扎实。 教学目标： 1、经历测量芒果、石头、水瓶的体积的实验过程，探索不规则物体体积的测量方法，渗透转化的思想。 2、掌握不规则物体的测量方法，并能测量不规则物体的体积。 3、在实践与探索过程中，尝试用多种方法解决实际问题，提高灵活解决实际问题的能力。 教学重点：
让学生掌握不规则物体体积的测量方法。 教学难点： 灵活运用“排水法”和“溢出法”解决实际问题。 教具准备： 魔方、芒果、圆柱体量杯、长方体水槽、石块、苹果醋若干瓶 教学过程： 一、导入 1、同学们，周末老师在整理房间的时候，从柜子里发现了一个魔方，我特别喜欢。 从数学的角度来讲，魔方是一个什么样的物体？（正方体） 怎样求出这个正方体的体积呢？（板书：V正=a） 它的棱长是10cm，体积是多少呢？（1000cm） 2、除了正方体，你还会求哪些立体图形的体积？（板书：V长=abh） 3、像长方体和正方体这样，都能够直接通过公式求出它们的体积，这样的物体，我们把它们叫做“规则物体”。（板书：规则物体） 4、现在请同学们再观察老师手中的魔方，它还是正方体吗？（旋转一下）那它是什么形状的物体呢？ 像这样，无法用语言准确地说出具体形状的一类物体，在我们的生活中随处可见，我们称它们为“不规则物体”。（板书：不） 5、现在这个魔方的体积是多少呢？（还是1000cm）你是怎么想的？（板书：转化）
第1课初识画笔 教学目标：认识“画图板”窗口。 教学时间：1课时 教学过程： 同学们，喜欢画画吗？在我们的电脑中有一个强大的工具软件叫“画图板”，在这个软件里面有用不完的“颜料”和“画布”，使用它可以绘制美丽的风景画、人物画、想象画，还可以用它制作名片、明信片和贺卡。 上图所示就是使用“画图板”程序画的画，怎么样，心动了吗？下面我们一起来学习使用这个软件吧。 一、启动“画图” 1、画图程序是电脑中一个非常有趣实用的小程序，启动方法如下： 步骤1：启动电脑后，使用鼠标左键单击“开始”按钮； 步骤2：在弹出的菜单里选择“娱乐”； 步骤3：使用鼠标左键单击“画图”即可启动程序。 2、也可以使用画图程序的快捷图标起动程序：点击桌面“娱乐（4）”按钮，双击“画图”图标启动程序。 二、认识“画图” 1、画图的窗口 “画图”窗口主要有3个区域，左边是工具栏，下面是颜料盒，中间的大块区域就是绘图区（画布）等。 2、练一练 将下面的工具和它们对应的名称连接起来。 曲线画笔 文本选择（椭圆的） 颜色提取器连接线 填充颜色橡皮擦 喷雾罐直线 选择（自由形式）多边形
3、想一想 尝试使用工具箱中的不同工具，并注意观察工具箱下方“工具状态选择器”的变化。 4、看一看 使用“图像（Ｉ）”菜单中的“改变大小／缩放（Ｅ）……”命令可以调整画图区的大小。 三、退出“画图” 使用完“画图”程序后，要正确地退出“画图”程序。 单击“关闭”按钮后，出现对话框，分别点击“保存（Ｓ）”、“放弃（Ｄ）”、“取消（Ｃ）”，看看它们分别有什么作用？ 四、讨论坊： 还有哪些计算机软件能帮助我们画图？ 五、成果篮：
大班数学游戏活动教案《有趣的测量》活动目标： 1．感受并体验远近的含义，激发幼儿的求知欲望和探究精神。 2．学习用工具测量远近，并能将测量结果记录在表格中。 3．初步感知同样的距离，使用的测量工具不同，测得的次数也不同以及同样的距离，使用的工具不同，测量的次数也不同，越长的工具所用的测量次数越少。 活动重难点： 1．重点：按照正确的步骤用工具测量 2．难点： （1）理解不同的距离，用同一种工具测量，测量的次数越多越远，测量的次数越少越近 （2）同样的距离，使用的工具不同，测量的次数也不同，越长的工具所用的测量次数越少 活动准备： 铅笔，表格、路线图每人一份、水彩笔盖、短水彩笔、没削过得铅笔。 活动过程： 一、故事导入 师：今天，动物学校要举行一场盛大的运动会，小兔、
小熊、小猫都报名参加了比赛。你们看，小动物们马上就要从自己家里出发到学校去了，究竟是哪个小动物会最先到达体育馆呢？ 二、学习用工具测量的方法比较路线的远近。 1．（引导幼儿观察路线图）请幼儿观察比较，哪个小动物去体育馆的路最近？哪个小动物去体育馆的路最远？你是怎么知道的？这种方法准确吗？ 2．师：用眼睛看的方法叫做目测法，但是目测法比一定准确，我们还能用什么方法来判断路线的远近呢？（请幼儿讲讲自己的想法，如工具：尺子、棍子、绳子、积木等）老师今天也给小朋友们带来了一种测量工具，你们看看老师带来了什么工具？（水彩笔盖） 3．师：你们觉得这样工具能测量小动物家到学校的距离么？（能）那咱们就先量一量小猫家到学校要几个水彩笔盖，你会量吗？（会），请你来试一试。 在幼儿尝试过程中教授测量方法，，边演示边引导幼儿一起讲述测量的正确步骤（找起点，沿着线，接着量）将测量结果记录在表格中（小猫家到学校量了5个水彩笔盖） 4.师：请你们也量一量小猫家到学校用了几个水彩笔盖。并将结果记录在表格里。 幼儿操作，教师巡回指导。
工具变量法 一、工具变量法的主要思想 在无限分布滞后模型中，为了估计回归系数，通常的做法是对回归系数作一些限制，从而对受限的无限分布滞后模型进行估计。在这里，考伊克模型、适应性期望模型与部分调整模型给出了很好的解决此类问题的思路。经过变换，新的模型中，随机扰动项的表达式为： 考伊克模型：1t t t v u u λ-=- （01λ<< ，λ为衰减率） （1.1）； 适应性期望模型：1（1）t t t v u u λ-=--（01λ<< ，λ为期望系数）（1.2）； 部分调整模型：（1）t t v u γ=-（01γ≤< ， 1γ-为调整系数） （1.3）。 t u 为原无限分布滞后模型中的扰动项，t v 为变换后的扰动项。 在原模型中的随机扰动项满足经典假设的前提下，部分调整模型也满足经典假设，但是考伊克模型与适应性期望模型的随机扰动项由于存在原随机扰动项的滞后项，也就是说考伊克模型与适应性期望模型的解释变量1t Y - 势必与误差项t v 相关，因此，可能会出现上述两个模型的最小二乘估计甚至是有偏的这样严重的问题。那么，我们是否可以找到一个与1t Y -高度相关但与t v 不相关的变量来替代 1t Y -？在这里，一个可行的估计方法就是工具变量法。 在讨论工具变量法之前，我们先来了解一下外生变量和内生变量。 一般来说：一个回归模型中的解释变量有的与随机扰动项无关，我们称这样的解释变量为外生变量；而模型中有的解释变量与随机扰动项相关，我们可称这样的解释变量为内生解释变量。内生解释变量的典型情况之一就是滞后应变量为解释变量的情形，如上述考伊克模型与适应性期望模型中的1t Y -。 外生解释变量：回归模型中的解释变量与随机扰动项无关； 内生解释变量：回归模型中的解释变量与随机扰动项无关； 了解了内生变量和外生变量的概念，我们接着讨论工具变量法的主要思想：工具变量法和普通最小二乘法是模型参数估计的两类重要方法，在多元线性回归模型中，如果出现解释变量与随机误差项相关（即出现内生变量）时，其回归系数的普通最小二乘估计是非一致的，这时就需要引入工具变量。 工具变量，顾名思义是在模型估计过程中被作为工具使用，以替代模型中与随机误差性相关的随机解释变量（即内生变量）。 满足条件：1）总体无关：工具变量与随机扰动项无关； 2）样本相关：工具变量必须与被它所代替的内生变量高度相关； 3）与模型中其他解释变量不相关，以避免出现多重共线性。 做了替代后，用普通最小二乘法即可得到原回归系数的一致估计量。 二、工具变量法的基本原理
第九课有趣的画图工具 教学目的和要求 1. 掌握画图软件的启动与退出，并熟悉画图软件窗口的组成。 2. 学会设置画纸的大小。 3. 学会铅笔、刷子、直线、曲线、圆形等绘图工具的使用。 4. 通过运用画笔软件绘制公共汽车，使学生进一步熟练掌握画笔软件各部分的操作方法，同时激发学生对学习电脑的兴趣。 教学重点：绘图软件的操作与应用。 教学难点：曲线工具的运用。 教学准备：计算机及辅助教学软件。 教学过程 一、新课导入 谈话：“画图”软件是windows98操作系统中所附的绘图软件，利用它可以绘制简笔画、水彩画、插图或贺年片等。也可以绘制比较复杂的艺术图案；既可以在空白的画稿上作画，也可以修改其他已有的画稿。这节课我们就来学习win98画图软件的操作与运用。 二、新课教学 1、启动“画图”软件:讲解并演示启动“画图”软件的方法与操作步骤。 A.单击“开始”按钮，打开“开始”菜单； B.将鼠标指向“开始”菜单下的“程序”选项，打开“程序”菜单。 C.将鼠标指向“程序”菜单中的附件选项，打开“附件”菜单。 D.用鼠标单击“附件”菜单下的“画图”选项，启动画图程序。 启动后的屏幕窗口如图1所示： 2.讲解并演示画图软件的窗口组成: (1)标题栏:它包含了画笔的标题和图画的命名。 (2)菜单栏:有六个下拉式菜单。 (3)工具箱:有许多绘图工具，绘画时任选一项工具。
(4)线宽框:改变每个工具的线条宽度。 (5)调色板:左面是绘画时的前景色和背景色的显示框，右边有28种颜色供选择。 (6)滚动条:上、下、左、右移动绘图区域。 (7)绘图区:在该区作图、绘画。 3.讲解绘画工具的选择和应用:（边讲解边演示） (1)剪切工具:裁剪工具:它可以定义形状自由的剪切块。 (2)选定工具:它可以定义一个矩形剪切块。 (3)橡皮：可以擦除图面中不想要的部分。 (4)涂色工具:用前景色对封闭区填充。 (5)取色工具:它是用一个图形的颜色填另外的封闭图形区域。 (6)铅笔:可以在绘图区内任意画线， (7)刷子:与铅笔工具相似，只是刷子工具状态有12种，使绘图更为丰富。 (8)喷枪:该工具与前两种工具的功能类似，它们留下的痕迹的不同是由鼠标的拖动速度决定的，速度越们慢，斑点越密。 (9)文字:利用文字工具可以在图画上写字。 (10)直线:利用它可以画直线、水平线、垂直线。 (11)曲线:利用它可以画单弯头曲线、双弯头曲线。 (12)矩形:可以画空心方框或空心矩形。 (13)多边形:可以画一些多边形图形。 (14)椭圆:可以画一些垂直或水平的椭圆环。 (15)圆角矩形:可以画一些圆角方框。 5.作品存盘退出:（讲解并演示） 讲解：选择"文件"菜单下的"保存"命令，将所绘制的图画保存磁盘上。 退出画图程序：a.单击画图窗口右侧的关闭按钮； b.单击菜单中“文件”选项中的退出命令； c.单击【是（Y）选项，保存当前窗口中的图形并退出画图程序；
活动目标： 1．感受并体验远近的含义，激发幼儿的求知欲望和探究精神。 2．学习用工具测量远近，并能将测量结果记录在表格中。 3．初步感知同样的距离，使用的测量工具不同，测得的次数也不同以及同样的距离，使用的工具不同，测量的次数也不同，越长的工具所用的测量次数越少。 活动重难点： 1．重点：按照正确的步骤用工具测量2．难点：（1）理解不同的距离，用同一种工具测量，测量的次数越多越远，测量的次数越少越近（2）同样的距离，使用的工具不同，测量的次数也不同，越长的工具所用的测量次数越少活动准备： 铅笔，表格、路线图每人一份、水彩笔盖、短水彩笔、没削过得铅笔。 活动过程： 一、故事导入师：今天，动物学校要举行一场盛大的运动会，小兔、小熊、小猫都报名参加了比赛。你们看，小动
物们马上就要从自己家里出发到学校去了，究竟是哪个小动物会最先到达体育馆呢？ 二、学习用工具测量的方法比较路线的远近。 1．（引导幼儿观察路线图）请幼儿观察比较，哪个小动物去体育馆的路最近？哪个小动物去体育馆的路最远？你是怎么知道的？这种方法准确吗？ 2．师：用眼睛看的方法叫做目测法，但是目测法比一定准确，我们还能用什么方法来判断路线的远近呢？（请幼儿讲讲自己的想法，如工具：尺子、棍子、绳子、积木等）老师今天也给小朋友们带来了一种测量工具，你们看看老师带来了什么工具？（水彩笔盖）3．师：你们觉得这样工具能测量小动物家到学校的距离么？（能）那咱们就先量一量小猫家到学校要几个水彩笔盖，你会量吗？（会），请你来试一试。 在幼儿尝试过程中教授测量方法，，边演示边引导幼儿一起讲述测量的正确步骤（找起点，沿着线，接着量）将测量结果记录在表格中（小猫家到学校量了5个水彩笔盖）4. 师：请你们也量一量小猫家到学校用了几个水彩笔盖。并将结果记录在表格里。 幼儿操作，教师巡回指导。
工具变量法 一、工具变量法得主要思想 在无限分布滞后模型中,为了估计回归系数,通常得做法就是对回归系数作一些限制,从而对受限得无限分布滞后模型进行估计。在这里,考伊克模型、适应性期望模型与部分调整模型给出了很好得解决此类问题得思路。经过变换,新得模型中,随机扰动项得表达式为: 考伊克模型: ( ，为衰减率) （1、1); 适应性期望模型:（,为期望系数)(1、2）; 部分调整模型:( ，为调整系数） (1、3)。 为原无限分布滞后模型中得扰动项,为变换后得扰动项。 在原模型中得随机扰动项满足经典假设得前提下,部分调整模型也满足经典假设,但就是考伊克模型与适应性期望模型得随机扰动项由于存在原随机扰动项得滞后项,也就就是说考伊克模型与适应性期望模型得解释变量势必与误差项相关,因此,可能会出现上述两个模型得最小二乘估计甚至就是有偏得这样严重得问题。那么，我们就是否可以找到一个与高度相关但与不相关得变量来替代？在这里，一个可行得估计方法就就是工具变量法。 在讨论工具变量法之前，我们先来了解一下外生变量与内生变量。 一般来说:一个回归模型中得解释变量有得与随机扰动项无关,我们称这样得解释变量为外生变量;而模型中有得解释变量与随机扰动项相关,我们可称这样得解释变量为内生解释变量。内生解释变量得典型情况之一就就是滞后应变量为解释变量得情形，如上述考伊克模型与适应性期望模型中得。 外生解释变量:回归模型中得解释变量与随机扰动项无关； 内生解释变量:回归模型中得解释变量与随机扰动项无关; 了解了内生变量与外生变量得概念,我们接着讨论工具变量法得主要思想：工具变量法与普通最小二乘法就是模型参数估计得两类重要方法,在多元线性回归模型中,如果出现解释变量与随机误差项相关（即出现内生变量）时,其回归系数得普通最小二乘估计就是非一致得,这时就需要引入工具变量。 工具变量，顾名思义就是在模型估计过程中被作为工具使用,以替代模型中与随机误差性相关得随机解释变量（即内生变量）。 满足条件:１)总体无关：工具变量与随机扰动项无关; 2)样本相关:工具变量必须与被它所代替得内生变量高度相关; 3)与模型中其她解释变量不相关,以避免出现多重共线性。 做了替代后，用普通最小二乘法即可得到原回归系数得一致估计量。 二、工具变量法得基本原理 我们分别从简单线性回归模型与多元线性回归模型两方面来具体分析工具变量法得基本原理： 简单线性回归模型 考虑简单线性回归模型(2、1)其中为内生变量。 则其正规方程为：(2、2) 设回归模型中得解释变量与随机扰动项相关,则如前所述，普通最小二乘估计量就是非一致得。现用一个工具变量来代替正规方程中得解释变量,其残差表达式不变。
奇妙的Word画图工具 教学内容 小学四年级下册（川版）信息技术课中第六课奇妙的Word画图工具 教材分析 本节课是小学信息技术四年级下册第六课，是在学生初步掌握了计算机的基本知识，操作技能以及word的基础知识上进行学习的。本节课内容的设计形象直观，灵活有趣，可以充分调动学生的手和脑，培养学生学习计算机的兴趣，使学生掌握一种简单有趣的绘图方法，熟悉word里进行绘图的操作方法，并在画图的过程中，把知识的教学和思维能力的培养结合起来，有利于促进学生创造性思维的发展，是进行创造性教育的好助手，为今后的学习奠定良好的基础。 学生分析 四年级的学生因年龄小，组织教学时，难以使每一个学生的注意力都很集中，因此在备课和设计练习与问题时，应尽量照顾到每一位学生，调动起每一位学生积极性，尽量满足学生的表现欲，尊重学生的个体差异。在教学中尽量营造不同的气氛，如：教学长方形时，设置长方形的线条和颜色及培养学生的综合应用知识的能力和动手的能力。 教学目的 1、认识word绘图工具，基本掌握绘图工具条的简单使用。 2、学会制作简单的图形。 3、培养学生逐渐养成自主探索学习的习惯。 重点、难点 本节课的重难点是使学生掌握画图中各种工具的使用并培养学生的创新能力。 所用教具：多媒体教室、教学广播系统。 所用教法：演示法、练习法、讲述对比法。 教学准备： 制作如教材P30的三个图形。 长方形斜坡上的小车科技之光一、教学流程 为了突破教学重难点，本课教学设计是以“学生练”为本，把学习的主动权交给学生，让学生主动参与学习及其自由的发挥，从而使学生学得生动活泼，并且妙趣横生。如果学生出现偏差，不恰当之处，教师适当点拨一下，本节课力求在教师帮助指导下，让学生自己领悟，自己画图，使学生养成独立思考勇于发现创新的思维习惯。 我设计的教学过程有这样几个环节。
大班数学《有趣的测量》活动设计及 反思 大班数学《有趣的测量》活动设计及反思 设计意图《纲要》提出的：“引导幼儿体会数学与人们生活的密切关系，初步尝试解决生活中的实际问题。培养幼儿参加数学活动的兴趣，激发幼儿探索数学规律的愿望。让幼儿在生活和游戏活动中感受事物的数 量关系并体验到数学的重要和有趣。测量是认识量的手段，幼儿的测量最早是“目测”，即通过感知比较量的差异。大班幼儿的测量活动是自然测量。自然测量是指利用自然物（如筷子，小棍，脚步，小碗等）作为量具（器）进行直接测量。即仅局限于简单工具的测量，而不是标准工具的测量。 学习自然测量，可以加深幼儿对各种物体量的认识；有助于幼儿对不同量的测量工具的初步认识；加深幼儿对10以内数的理解；培养幼儿动手操作能力以及对测量活动
的兴趣。 什么东西可以用来测量？这个有趣的 问题会引起孩子的好奇，促使他们开动脑筋，有步骤去探索，去发现，在动手操作中不仅获得知识经验，而且还获得了学习知识的方法和能力的提高。 一、活动目标： 1．学习用自然测量的方法测量物体的 长短，并会用表格的形式进行记录。 2．初步感知同样的距离，使用的测量 工具不同，测得的数据也不同，训练思维的相对性。 二、活动准备： 1．每两人一张桌子。 2．各种自然测量的工具（铅笔、积木、布条、纸条等）。 3．记录表、笔。 三、活动过程： 1．导入，引出主题 导入语：我们马上要搬新的幼儿园了，需要定做一批新的桌子，现在请小朋友帮一个忙，测一下我们桌子长的边到底有多长。
可是我们没有尺，你们说怎么办呢？ 2．学习正确自然测量的方法 过渡语：对，我们可以用好多材料来进行测量，在你们凳子底下有一支铅笔，现在就请你用这只铅笔先来测一测自己桌子的长边，记住自己测到的数字？ （1）集体测量，并讨论出正确的测量方法 师：谁来说说你用铅笔侧到了几段？是怎么测量的？（个别幼儿边讲解边示范）（2）教师总结 师：我们测量时，使用的工具头要和起点对齐，然后测下一段时工具的头和上次的尾要紧接住，就是首尾相接，这样能测得比较准确些。 过渡语：刚才我们用铅笔测量了桌子的长度。老师又为小朋友准备了一些其它的测量工具，而且还准备了每人一张记录单，把每种工具侧到的结果用笔记录下来。 3．运用正确的测量方法进行测量，体验测量工具的长短与测量结果的关系。 （1）出示记录表
幼儿园大班数学活动：风趣的测量 活动目标： 1、理解长度测量的意义，体验测量的欢乐。 2、尝试探索及学习例外的长度测量方法，并能用语言表述自己的想法。 3、知道例外的测量工具会带来例外的测量结果，引发进一步探究的欲望。 活动准备： 1、一寸虫图片1张，集体记录图表1张，投影仪。 2、幼儿测量用图（知更鸟、苍鹭、老鹰、巨嘴鸟、大雁操作纸）、1寸和2寸吸管若干，黑色记号笔若干支。 活动过程： 一、引出测量我明白了，你们是看出来的，确凿地说，你们使用目光测量出来的。 二、故事引导，理解测量 1、导入情景，初步测量。 2、提出测量要求：一寸虫会做的事情你会做吗？那么，听清撤我的要求：不搬小凳子到桌子上，用小碗里的一寸虫去测量一下知更鸟的尾巴，看看你用了几条一寸虫长？ 3、简单测量，操作后引导孩子表述操作结果，提问：谁能告诉我，你的测量结果是多少？你是怎们测量的？追问：3条一寸虫的长度就是——3寸。（强调一条紧挨着一条测量，用投影仪展示测量方法，首尾相接。） 三、探究方法，表达见解。1、引导孩子交流操作情况。逐个统计测量结果，并提问：你测量的是什么鸟？测出来的长度是多少？你是用什么方法测量的？（出示各种鸟的测量结果，并将幼儿用到的方法用图标列出来。）
2、引导幼儿探究最确凿的一种测量方法。请幼儿解放表达自己的想法，辅助提问：用什么方法测量最确凿。 四、运用方法，再次测量。引导幼儿交流测量结果。辅助提问：你测出来的结果是用到了几次？大雁的身体是一样长的，为什么有些孩子测出来是6？有些孩子测出来是3？——哦，测量工具长短例外，测出来的次数也会例外，如果我有一条“三寸虫”呢？教师小结：的确，测量工具的例外，会造成测量次数的例外，测量工具越短，测量的次数越多，测量工具越长，测量的次数就越少。 活动分析： 一、《纲要》强调幼儿科学是科学启蒙教育，旨在培养幼儿的认识兴趣和探究欲望，教幼儿尝试运用数学知识去解决生活中简单的问题。因此，我重构增设了一下环节，旨在引领幼儿将经验迁移，升华本次数学活动：【第五环节、认知冲突，激发欲望。】 1、抛出问题，形成冲突：如果请你来测量一下我们的教室有多长，你会选择一寸虫吗？为什么？你觉得用什么工具则两比较适合？（活动目标：将经验胜利迁移，能根据实际情况选择正确的根据进行测量） 2、幼儿解放讨论，留下尾巴，引发欲望。（保证活动的可持续发展） 二、记录表使用得较为胜利，较好地呈现了本次活动的主要重难点的内容，在知识点的展现、归纳上比较清撤的。作为科学活动的常规模式来说，列表归纳的方法应该推广使用，用着十分方便的作用。
工具变量法的Stata命令及实例 ●本实例使用数据集“grilic.dta”。 ●先看一下数据集的统计特征： . sum Variable Obs Mean Std. Dev. Min Max rns 758 .2691293 .4438001 0 1 rns80 758 .292876 .4553825 0 1 mrt 758 .5145119 .5001194 0 1 mrt80 758 .8984169 .3022988 0 1 smsa 758 .7044855 .456575 0 1 smsa80 758 .7124011 .452942 0 1 med 758 10.91029 2.74112 0 18 iq 758 103.8562 13.61867 54 145 kww 758 36.57388 7.302247 12 56 year 758 69.03166 2.631794 66 73 age 758 21.83509 2.981756 16 30 age80 758 33.01187 3.085504 28 38 s 758 13.40501 2.231828 9 18 s80 758 13.70712 2.214693 9 18 expr 758 1.735429 2.105542 0 11.444 expr80 758 11.39426 4.210745 .692 22.045 tenure 758 1.831135 1.67363 0 10 tenure80 758 7.362797 5.05024 0 22 lw 758 5.686739 .4289494 4.605 7.051 lw80 758 6.826555 .4099268 4.749 8.032 ●考察智商与受教育年限的相关关系： . corr iq s (obs=758) iq s iq 1.0000 s 0.5131 1.0000 上表显示，智商（在一定程度上可以视为能力的代理变量）与受教育年限具有强烈的正相关关系（相关系数为0.51）。 ●作为一个参考系，先进行OLS回归，并使用稳健标准差：