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Accelerated Titration Designs for Phase I Clinical Trials in Oncology

Richard Simon,Boris Freidlin,Larry Rubinstein,Susan G.Arbuck, Jerry Collins,Michaele C.Christian*

Background:Many cancer patients in phase I clinical trials are treated at doses of chemotherapeutic agents that are below the biologically active level,thus reducing their chances for therapeutic benefit.Current phase I trials often take a long time to complete and provide little information about interpatient variability or cumulative toxicity.Pur-pose:Our objective was to develop alternative designs for phase I trials so that fewer patients are treated at subthera-peutic dose levels,trials are of reduced duration,and impor-tant information(i.e.,cumulative toxicity and maximum tol-erated dose)needed to plan phase II trials is obtained. Methods:We fit a stochastic model to data from20phase I trials involving the study of nine different drugs.We then simulated new data from the model with the parameters estimated from the actual trials and evaluated the perfor-mance of alternative phase I designs on this simulated data. Four designs were evaluated.Design1was a conventional design(similar to the commonly used modified Fibonacci method)using cohorts of three to six patients,with40% dose-step increments and no intrapatient dose escalation. Designs2through4included only one patient per cohort until one patient experienced dose-limiting toxic effects or two patients experienced grade2toxic effects(during their first course of treatment for designs2and3or during any course of treatment for design4).Designs3and4used100% dose steps during this initial accelerated phase.After the initial accelerated phase,designs2through4resorted to standard cohorts of three to six patients,with40%dose-step increments.Designs2through4used intrapatient dose es-calation if the worst toxicity is grade0-1in the previous course for that patient.Results:Only three of the actual trials demonstrated cumulative toxic effects of the chemo-therapeutic agents in patients.The average number of pa-tients required for a phase I trial was reduced from39.9for design1to24.4,20.7,and21.2for designs2,3,and4,re-spectively.The average number of patients who would be expected to have grade0-1toxicity as their worst toxicity over three cycles of treatment is23.3for design1,but only

7.9,3.9,and4.8for designs2,3,and4,respectively.The average number of patients with grade3toxicity as their worst toxicity increases from5.5for design1to6.2,6.8,and

6.2for designs2,3,and4,respectively.The average number

of patients with grade4toxicity as their worst toxicity in-creases from1.9for design1to3.0,4.3,and3.2for designs

2,3,and4,respectively.Conclusion:Accelerated titration (i.e.,rapid intrapatient drug dose escalation)designs appear

to effectively reduce the number of patients who are under-treated,speed the completion of phase I trials,and provide a substantial increase in the information obtained.[J Natl Cancer Inst1997;89:1138-47]

There has been considerable recent interest in new designs for phase I clinical trials.With currently used designs,many pa-tients are treated at doses below the biologically active level, minimizing the opportunity for antitumor response(1).Although most patients who participate in phase I trials hope to obtain

*Affiliations of authors:R.Simon,L.Rubinstein,S.G.Arbuck,M.C.Chris-tian,Cancer Therapy Evaluation Program,Division of Cancer Treatment,Diag-nosis,and Centers,National Cancer Institute,Bethesda,MD;B.Freidlin,The Emmes Corporation,Potomac,MD;J.Collins,U.S.Food and Drug Adminis-tration,Rockville,MD.

Correspondence to:Richard Simon,D.Sc.,National Institutes of Health,Ex-ecutive Plaza North,Rm.739,Bethesda,MD20892.

See‘‘Notes’’following‘‘References.’’

?Oxford University Press

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therapeutic benefit from promising new experimental treat-ments,few achieve this objective(2).Whereas most patients would not have derived benefit from drugs studied in phase I trials,even if treated at the maximum tolerated dose(MTD), treating patients at substantially lower doses is likely to further reduce whatever chance for benefit might exist.

A second problem with current designs is that phase I trials may take a long time to complete,especially when the starting dose is far below the MTD(3).Current phase I trials also pro-vide almost no information about variability among patients in the dose that can be tolerated without dose-limiting toxicity (DLT)or about whether there is evidence of cumulative toxicity.

In phase I trials of new drugs,the starting dose is usually one tenth of the LD10(i.e.,the dose that is lethal to10%of animals) in the most sensitive animal species in which toxicology studies have been performed.Dose steps are defined by a modified Fibonacci series in which the increments of dose for succeeding levels are100%,67%,50%,and40%,followed by33%for all subsequent levels.Three patients are usually treated at a dose level and observed for acute toxicity for one course of treatment before any more patients are entered.If none of the three patients experience DLT,then the next cohort of three patients is treated at the next higher dose.If two or more of the three patients experience DLT,then three more patients are treated at the next lower dose unless six patients have already been treated at that dose.If one of three patients treated at a dose experiences DLT, then three more patients are treated at that same level.If the incidence of DLT among those six patients is one in six,then the next cohort is treated at the next higher dose.In general,if two or more of the six patients treated at a dose level experience DLT,then the MTD is considered to have been exceeded,and three more patients are treated at the next lower dose as de-scribed above.The MTD is defined as the highest dose studied for which the incidence of DLT was less than33%.Usually dose escalation for subsequent courses in the same patient,intrapa-tient dose escalation,is not permitted.

In this article we will describe alternative phase I designs that attempt to overcome some of the problems described above.We will then report the results of a computer simulation study con-ducted to evaluate the performance of alternative designs.The designs will be evaluated with regard to safety,the extent to which they provide patients the opportunity to be treated at higher doses more likely to provide antitumor response,the number of patients and time required to complete the trial,and the amount of information obtained.

Several alternative approaches to the design of phase I trials have been discussed in previous years.Collins et al.(3)recom-mended accelerating the dose escalations in humans by using the plasma drug C×T(i.e.,the area under the concentration versus time curve)value at the LD10in the mouse as the target expo-sure.This provides a pharmacokinetic basis for dose escalation, but is limited to clinical situations where a sensitive assay for the active drug moieties is available and where interspecies phar-macodynamic differences do not exist for the drug.

Storer(4)introduced the concept that the objective of a phase I trial is to estimate the dose that causes DLT in a specified proportion(e.g.,25%of the patients),and that this MTD should be estimated by fitting a logistic model to the dose versus DLT data.Storer also proposed using a single patient per dose level

until the first DLT is observed.

Several investigators(5-10)have considered Bayesian de-signs.This approach makes use of a model relating dose admin-istered to the probability of DLT.The parameters of the model

are unknown initially,but some prior probability distribution for their values is assumed to be available based on preclinical data

or experience with other drugs.As patients are treated,the prob-ability estimates of the unknown parameters are updated based

on the actual toxicity experience observed.Each patient is as-signed the dose predicted to result in DLT for a target percentage (e.g.,25%)of the population.

Mick and Ratain(11)used a linear model relating white blood cell(WBC)count nadir to dose and pretreatment WBC count.They sequentially estimated the regression parameters of

the model as data accumulated and individualized the dose based

on pretreatment WBC count in an attempt to achieve a specified optimal WBC count nadir.Their approach predicts the optimal dose for each patient is based on pretreatment patient character-istics.

None of the designs described above considers how patients should be treated after the first course,nor do they use informa-

tion obtained from subsequent courses.Except for the approach

of Mick and Ratain(11),they do not consider interpatient vari-ability or use information about toxic effects less than DLT.

Sheiner et al.(12,13)have argued for the use of titration(or intrapatient dose-escalation designs)for evaluating drug efficacy

for diseases where the condition of a patient remains stable over

a period of time.Titration designs involve dose escalation within patients until the desired biologic effect is obtained.If analyzed properly,they can provide information about interpatient vari-ability in dose–response effects.The analysis of titration designs

has been studied(14,15),but this approach has not been dis-cussed in the context of phase I trials in oncology.

Methods

Phase I Designs Studied

The designs we evaluated differ with regard to the escalation/de-escalation

rules for the first-course treatment of subsequent cohorts of patients as indicated

in the‘‘Appendix’’section.Design1is the standard design described above.The

other dose-escalation methods are based on a four-grade scale for defining the highest level of overall toxicity during each course of therapy.This scale can be defined differently to accommodate different clinical situations.For the purposes

of this article,we have related the toxicity experience to grading scales com-monly used in oncology,such as the National Cancer Institute Common Toxicity Criteria,and have described the levels as follows:none-mild(grades0-1),mod-

erate(grade2),dose limiting(grade3),and unacceptable(grades4-5).Consis-

tent with recent practice,we have not considered grade3neutropenia unaccom-panied by either fever or infection to be dose limiting.We have grouped no toxicity with grade1toxicity because of the difficulty of determining whether

mild abnormalities are drug or illness related in patients with cancer.

Design2treats one patient per dose level until one patient exhibits DLT or two patients exhibit grade2toxicity during their first course of treatment.At that time,the escalation plan switches to design1.That is,two additional patients are accrued at the dose that triggered the switch,and three to six patients are treated

in that and each subsequent cohort.This approach offers the possibility of speeding up the trial and reducing the number of patients assigned to low doses.

It uses the first instance of first-course DLT to trigger the switch as proposed by Storer(4).It also uses first-course grade2toxicity to provide an added element

of caution.We use the second instance of grade2toxicity for practical reasons,

since it is often difficult to determine whether a grade2toxicity is drug related

in a heterogeneous population of very ill patients.

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Designs3and4also use only one patient per cohort during the early stage of

the trial,but they incorporate more rapid dose escalation by using double-dose steps during this stage.With design3,the single-patient-cohort stage of the trial also terminates when one patient experiences first-course DLT or two patients experience first-course grade2toxicity.With design4,this accelerated stage terminates when the first instance of DLT or the second instance of grade2 toxicity is observed in any course of treatment.In either case,after the rapid escalation stage terminates,subsequent cohort sizes are three to six patients and single-dose escalation steps are used as in design1.

The Appendix also describes two approaches to individualizing dose through intrapatient dose modification.Intrapatient modification option A is the one most commonly used.There is no intrapatient dose escalation,only de-escalation.If the toxicity is dose limiting or worse in a course of chemotherapy,then the dose is reduced one level for the next course.Otherwise,the dose stays the same for the next course.Intrapatient modification option B permits escalation for each patient if the toxicity is grade0-1in the previous course for that patient.If the toxicity is moderate(grade2),the dose remains unchanged.However,if the toxicity is DLT or worse,the dose is reduced.Designs3and4use two-dose-step (100%)intrapatient escalations during the initial accelerated phase of the trial, although de-escalations are always by single-dose steps.We have combined the standard cohort escalation design with the standard intrapatient dose modifica-tion option(A)as design1and have combined accelerated cohort escalations with the intrapatient dose escalation option(B)as designs2through4.We will also provide results,however,for the mixed designs such as escalation option A with designs2through4.

The accelerated designs are intended for use in phase I trials of drugs that have not been used previously in humans,where only preclinical information will be available for selecting a starting dose.Starting doses in these cases are often quite low,and designs that limit the number of patients treated at very low doses may be particularly useful.

Methodologic Approach

To evaluate alternative phase I designs,we wished to use data from actual phase I trials as much as possible.This could not be done directly because past trials were conducted with a particular escalation plan and we wished to evaluate new plans.Instead,we fit a stochastic model to data from past phase I trials.We then simulated new data from the model with the parameters estimated from the actual trials and evaluated the performance of alternative escalation designs on these simulated data.For any particular phase I trial,we generated1000simu-lated sets of data to reliably estimate the relative performance of the alternative designs.We repeated this for20different actual phase I trials of nine different drugs.

We required that the model we used be able to represent different levels of worst toxicity,not just presence or absence of DLT,and that the toxicity level experienced in a particular course would be determined by the dose administered in that course and the total dose administered in previous courses.We required that both interpatient and intrapatient variability be represented.We used the following model.Suppose that the i th patient receives dose d

during course j

and has received a total dose of D

for courses previous to j.We let the coef-ficient?represent the influence of prior total dose(??0indicates no cumu-lative toxicity)and let the magnitude of toxicity increase logarithmically with

dose.We introduced a random number?

,normally distributed with mean??and variance?2?.This variable represents the interpatient variability in sensitivity

to the toxic effects of the drug.We also introduced a random number?

, normally distributed with mean zero and variance??2,to represent the intrapa-tient variability in toxic response for a given patient receiving a given dose. These terms and random variables determine the magnitude of worst toxicity represented by

y ij=log?d ij??D ij)+?i+?ij.[1]

If this value y

ij was less than a specified constant K

,then patient i was consid-

ered to have experienced less than grade2toxicity during course j with dose d

If the value of y

ij was greater than K

but less than K

,then the toxicity level was

taken to be grade2;if the value was greater than K

2but less than K

,then the

toxicity was considered to be dose limiting;and if y

ij was greater than K

,then

the toxicity was considered unacceptable.The values of the random numbers?

i vary across patients,but the same?

was used for all treatment courses of the i th

patient,while the within patient variability values?

change from patient to patient as well as across courses.

This model can be viewed as a generalization of the K max model used by

Sheiner et al.(12,13).The above expression is equivalent to

e y ij

1+e y ij

?d ij+?D ij?

e???i+?ij?+?d ij+?D ij?

.[2]

The right-hand side of this equation is similar to the K

max

model.The stimulus

is of the form d

+?D

and the level giving50%maximum response(exclusive

of cumulative toxicity)is taken as a random variable,with mean approximately

e???and with a component identified with interpatient variability and a compo-

nent associated with intrapatient variability.Our model measures toxicity in a

categorical rather than continuous manner.Since the scale of the constants K

,and K

is arbitrary,the fact that the left side of the equation involves a

transformation of the originally defined y

does not matter.In fact,it can be shown that our model can be viewed as a generalization of the model of Chou

and Talalay(16)in which the stimulus d

+?D

and50%value are raised to a power p.With a categorical response in which the K’s may be fit from the data, however,the power p is not identifiable,and the model is equivalent to that shown in equation1.

The value??2represents the amount of intrapatient variability unexplained by current and previous doses.Setting??2?0means that the toxicity experienced

by a patient is determined entirely by the doses and by patient characteristics that

do not change from day to day.The value of?2?represents the amount of interpatient variability.Setting?2??0means that patients entered in the clinical

trial do not differ in their ability to tolerate the drug under study.

For these simulations,we used40%increments between dose levels.With

40%increments,two-dose levels represent approximately a doubling of the dose because1.42?1.96.A40%increment is close to the33%increment that is used

after the first few dose levels of trials based on the modified Fibonacci approach

with which phase I investigators are familiar.Because interpatient variability in patient pharmacokinetic parameters and intrapatient variability in day-to-day susceptibility to toxicity are often substantial,it is usually not realistic to expect

that one can estimate more precisely than to within40%the dose that will give

a desired level of biologic effect(17).

For all the simulations,we used???0,although the results are independent

of this parameter.Table1shows the maximum likelihood estimates of the model parameters for the20actual phase I clinical trials studied.These trials were selected for a related study of nonstandard dose-escalation procedures.Although

they were selected initially because they were planned to use nonstandard dose-escalation methods,only9.5%of the patients received intrapatient dose escala-tion.Detailed information about the characteristics of these trials will be ad-dressed in a separate report.

Only three of the20trials showed any evidence of substantial cumulative

toxic effects as seen from the column labeled?in Table1.Two of these studies involved the drug pyrazine diazohydroxide(PZDH)administered as a bolus every3weeks initially,but the interval between courses was eventually length-

ened to4-6weeks because of delayed recovery from myelosuppression.Trial

T90-156administered PZDH daily for5days every4-6weeks,and no evidence

of cumulative toxicity was obtained from our model parameters for that trial.The

third trial showing evidence of cumulative toxicity involved flavone acetic acid (FAA).This latter trial was the only phase I trial with FAA that demonstrated cumulative toxicity.It differed from the other four FAA trials in that it used a weekly schedule of administration.

The standard deviations for intrapatient(??)and interpatient(??)variability varied substantially.The larger values of??seen could represent true biologic variability or may reflect the difficulty of distinguishing drug-related toxicity

from manifestations of illness for very sick patients.We used the original treat-

ing physician’s assessment as to whether toxicity was drug related.Many of these patients were taking concomitant medications(not anticancer drugs)that

may have influenced the toxicity experienced,and,in some cases,there may also

have been nonstandardized treatment delays as a result of previous toxicity.With prospective use of titration designs,we expect that there will be more attention

to these issues than could be the case in a retrospective analysis of a database.

The K

value is given in terms of(K

?log starting dose)/log1.4because this value represents approximately the number of40%dose steps between the starting dose and the dose at which the average patient has a50%chance of experiencing grade2or worse toxicity(since???0).The distance between

other K values is similarly presented.Seven of the actual trials did not have any

patients who experienced grade4toxicity.For these cases,the estimate of K

very large by default,but the specific value is not meaningful.

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It may be noted in Table1that the parameter estimates for different trials of the same drug sometimes vary substantially.This is due to a variety of causes, but the estimates provide a wide range of conditions for generating simulated data with which to compare alternative escalation designs.

Results

Comparison of Designs

The distribution of the highest dose level at which fewer than two instances of DLT occurred was very similar for the four designs for all of the20sets of parameters studied(Fig.1).The true MTD was defined as the largest dose level for which the probability of first-course DLT or worse was less than.25,com-puted from the model using each set of parameters in Table1. For simulations with each set of parameters,we tabulated the accuracy of the highest dose level with fewer than two instances of first-course DLT as a predictor of the true MTD.Fig.1shows that the four designs performed similarly in this regard.Al-though designs2through4use many fewer patients than design 1,in the dose range of interest,they have similar sample sizes. As will be seen later,fitting the model to data from a phase I trial provides a much richer set of information with which to plan phase II development.Fig.1demonstrates,however,that even with regard to the traditional estimate of phase II dose,accuracy is not sacrificed by the accelerated designs.

Fig.2shows histograms of the average number of patients required in the simulated trials for each design.In each graph, the sum of the heights of the bars is20,the number of sets of parameters that is simulated.The x axis represents the average number of patients accrued in the1000simulated trials with each of the20sets of parameters.The standard design has a very broad distribution of sample size.For six of the sets of param-eters,design1required more than55patients.For the20sets of parameters,design1required an average of39.9patients(me-dian,36.7patients).Design1required substantially more pa-tients than did the other designs.Design2,which uses single 40%dose steps,required an average of only24.4patients(me-dian,21.8patients).As seen in Fig.2,the distribution of the number of patients is much narrower for design2than for design 1.Designs3and4also compare very favorably with design1 with mean numbers of patients of20.7and21.2,respectively, and median numbers of patients of19.3and19.1,respectively. Design2does not require many more patients than the acceler-ated designs that use double dose steps.As will be seen below,

Table1.Estimates of model parameters for20phase I clinical trials

Drug Trial?(K

1?ln d

)/ln1.4*(K

)/ln1.4(K

)/ln1.4????

Flavone acetic acid85-168016.2 6.935?.26 1.9 Flavone acetic acid85-244016.18.429? 2.9.85 Flavone acetic acid86-0040 4.4 2.40.95.47.59 Flavone acetic acid86-017.248.0 2.9 2.20.83 Flavone acetic acid86-060018.5 6.420?.006 2.8 Piroxantrone86-227.088.4 2.7 2.3 1.03.42 Piroxantrone86-268016.413.3?9.5?0 1.8 Chloroquinoxaline

sulfonamide

88-114.0417.3 2.6 1.6.88.87

Chloroquinoxaline

sulfonamide

88-127013.7 4.6 2.9.62.90 Pyrazine diazohydroxide89-053.56 6.7 1.3 2.0.37.50 Pyrazine diazohydroxide89-175.24 6.6 1.30.53.002.65 Pyrazine diazohydroxide90-156.02 4.6.53.56.001.18 Pyrazoloacridine90-073.048.9 1.0 1.3.24.32 Cyclopentenylcytosine91-0180 4.4.830.18.19.26 Fostriecin91-106.04 3.5 3.6 4.5 1.06.54 Fostriecin91-1960 6.37.218?.58 1.6 9-Aminocamptothecin92-1080 6.4.480.39.24.11 9-Aminocamptothecin92-1860 6.0.51 1.1.35.27 Penclomedine93-087.05 6.0 3.715?.68.81 Penclomedine93-1250 5.8 2.017?.43.53

?starting dose.

?No grade4toxicity.

?No grade3+

toxicity.

Fig.1.Distribution of the maximum tolerated dose(MTD)chosen in simulated

phase I trials averaged over the20sets of model parameters and1000replica-

tions for each set of parameters.In simulations,MTD is chosen in the traditional

way as the largest dose level at which six patients are started and fewer than two

experience first-course dose-limiting toxicity(DLT)or worse.True MTD is

defined as the highest dose level for which the probability of first-course DLT

or worse is less than.25,computed from the model with the use of each set of

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the important difference between design 1and the others is largely due to a reduction in patients treated early at subthera-peutic doses,where designs 2through 4accrue only one patient per level.Another question of some importance is whether a reduction in the number of patients translates into a reduction in the du-ration of the trial.When eligible patients are very limited,the number of patients is closely associated with the duration of the trial.But if eligible patients are readily available,then it would take little more time to place three patients on a dose level than to place a single patient.Therefore,we also tabulated the number of cohorts required for each design,as shown in Fig.3.The advantage of design 2over design 1with regard to the average number of patients does not translate into an advantage in the number of cohorts required.In fact,design 1requires slightly fewer cohorts because design 2sometimes overshoots its target and requires more cohorts at de-escalated levels.Designs 3and 4,however,show substantial savings over designs 1and 2be-cause of their use of double dose steps during the initial stage of the trials.Fig.4shows the toxicity experience in the application of these designs to the phase I trials.In these simulations,we have assumed that all patients stay in the study for three courses of treatment and have tabulated the distribution of worst toxicity over these courses for each patient.For each set of parameters and each design,we have calculated the average number of patients whose worst toxicity was grade 0-1,grade 2,grade 3,or grade 4.This average was computed based on 1000simulations for each of the 20sets of design parameters.With the standard design 1,the average number of patients who have grades 0-1toxicity as their worst toxicity over three cycles of treatment is 23.3.This number is substantially reduced for all of the newer designs;7.9for design 2,3.9for design 3,and 4.8for design 4.Therefore,the number of undertreated patients is substantially reduced.This reduction is achieved with some increase in the

number of patients with worst toxicity grade 3or 4.The average number of patients with worst toxicity grade 3increases from 5.5with design 1to 6.2,6.8,and 6.2for designs 2,3,and 4,respectively.

Fig.4shows that the average number of patients with grade 4toxicity increased from 1.9with design 1to 3.0,4.3,and 3.2for designs 2,3,and 4,respectively.Hence,in comparing design 2to design 1,on average,there is a reduction of about 15patients per trial whose highest level of toxicity is grade 0-1and an average increase of 1.8patients per trial whose highest level of toxicity is grade 3-4.Design 4provides a reduction of about 18undertreated patients per trial and an average increase of about 2.1overtreated patients.Design 3provides a reduction of about 19undertreated patients per trial,for an average increase of 3.7overtreated patients.Hence,design 3appears to have no real advantage over design 4.Although the average number of

patients with worst toxicity grade 3-4is not substantially in-creased using designs 2through 4compared with design 1,the proportion of patients with grades 3-4toxicity is substantially increased.This is because designs 2through 4substantially re-duce the expected number of patients with worst toxicity grade 0-1and the total number of patients on trial compared with design 1.With design 1,a weighted average (taken over the 20parameter sets,weighted by average sample size)of about 18%of patients experience grade 3-4toxicity during some course of treatment.For designs 2,3,and 4,the percentages are about 38%,53%,and 45%,respectively.For grade 4toxicity alone,

the Fig.2.Histograms of the av-

erage numbers of patients for

simulated phase I trials with

each of the 20sets of model

parameters.Averages are

based on 1000replications for

each set of parameters.Total

height of bars in each panel

equals 20,the number of sets

of model parameters.

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percentages are5%,12%,20%,and15%for designs1through 4,respectively.

There are six sets of parameters by use of design1for which three or more patients are expected to experience grade4tox-icity.The trial with the largest number of such patients was T89-175.This is a PZDH trial with??.24.The PZDH trial with??.56(T89-053)and the FAA trial with??.24are also included in this set of six trials.It is not surprising that trials with a substantial amount of cumulative toxicity should result in pa-tients experiencing grade4toxicity,even without using intrapa-tient dose escalation.The other three trials for which there were three or more patients expected to experience grade4toxicity using design1were T86-004,T88-114,and T91-018.These three trials are characterized by a combination of very steep dose–toxicity curves[as indicated by small values of(K3-K2)/ln(1.4)]and relatively large amounts of intrapatient variabil-ity.With designs2or4,the increase in the expected number of grade4toxic effects compared with design1is one patient or fewer in12of the20trials.The increase is greater than three patients in the three trials(T90-156,T91-018,and T92-108) characterized by very steep dose–toxicity curves.The increase in incidence of grade4toxicity was greater for design3than for designs2or4.

The results presented above combined the conventional co-hort escalation design1with the conventional intrapatient dose-modification option https://www.doczj.com/doc/f48678162.html,bining design1with intrapatient option B has no effect on the number of patients or number of cohorts compared with1A.It reduces the average number of patients with grade0-1as their highest level of toxicity from 23.3to19.3,but this is still not competitive with the numbers for designs2through4using option B.

Combining designs2through4with option A also has little or no effect on the number of patients or cohorts required com-pared with the same design using option B.In each case,about one fewer patient on average experiences grade3toxicity using option A than the same design with option B(5.2,5.7,and5.4 for2A,3A,and4A,respectively).The expected number of patients with grade4toxicity is reduced on average by0.4-1.1 patient(3.0,4.3,and3.2for designs2B,3B,and4B to2.2,3.2, and2.8,respectively,for designs2A,3A,and4A).The average number of patients with grade0-1toxicity is increased by about

2.4-

3.0patients on average(10.3,6.5,and7.0for2A,3A,and 4A,respectively,compared with7.9,3.9,and

4.8).Much of the reduction in numbers of undertreated patients is achieved with designs2A,3A,and4A compared with the standard design1A, and they result in somewhat less grade3-4toxicity than the designs using dose titration.They are particularly attractive when there is preclinical concern about cumulative toxicity. They do not,however,provide patients accrued early in the trial a full opportunity to be treated at a dose that provides the great-est opportunity for benefit.Also,in situations where interpatient variability is substantial relative to(K2?K1)/ln1.4and intra-patient variability is small,designs without intrapatient dose escalation will not give each patient as much opportunity to be treated at a dose level appropriate to her particular level of drug tolerance and thus will be much less effective than designs with dose titration.Such combinations of parameters are not frequent in Table1,but smaller values of??may be more prevalent with prospective use of accelerated designs.

Example

We generated one set of data for a clinical trial with the use of design4and the parameter values estimated from the actual data for trial T88-127of chloroquinoxaline sulfonamide.Table2 shows the data generated using these parameters.The first col-umn lists patient sequence numbers.Each row of the table cor-responds to a single patient.The numbers in a row represent the grades of toxicity experienced by that patient during her three courses of therapy.The columns correspond to dose levels,and the levels are labeled at the top of the columns.

The first patient received dose level1in her first course,and this resulted in toxicity grade0or1.The table records this as a 0because our simulations and analysis do not distinguish be-tween grades0and1.Since design4is used in this example,the first patient had her dose escalated by two steps for her second course,and she again showed grade0-1toxicity.Consequently, she received dose level5for her third course.She again showed no toxicity.

Since patient1had no toxicity in her first course,patient2 started at dose level3.Our simulations assumed that the time between patient entries was the same as the length of a single treatment course.Patient2also did not show any toxicity in her first course,and her dose was escalated two steps to level5for her second course.At that same time,patient3started at dose level5.

The first toxicity observed was grade2,which occurred in the second course of therapy for patient4at dose level9.Hence,her dose was not escalated for her third course.

Patient6had grade2toxicity during her first course that was at dose level11.She was kept at dose level11for her second course,but it resulted in no toxicity.Consequently,her dose was escalated to level12for her third course.It was escalated only a single dose step because the grade2toxicity she experienced during her first course was the second instance of grade2tox-icity during the trial.This ended the rapid escalation phase of the design.Consequently,the cohort started at dose level11was expanded to three new patients started at that dose.The single dose escalations of three patients per cohort continued until the second patient started at dose level15,patient19,experienced grade3toxicity.That cohort is therefore expanded to six pa-tients.Patient22experienced grade4toxicity in her first course at dose level15,and hence the escalation of starting dose for new cohorts of patients stops.Three additional patients started

Table2.Sequence of dose escalations and toxicity grades for patients treated in simulated phase I trial using design4*

Dose step?

Patient No.1234567891011121314151617 1000

2000

3000

2 /0

5000

1/0

7000 8000

100

11000

122

1/2

13000

142

1/2

15000

160

170

2 /2

180

190

1 /2

202

1/2

212

1/2

222

2/2

232

1/2

24000

250

1/2

260

*Subscript?treatment course.

?Units are just the sequentially numbered dose steps.Level1?starting dose.Level2corresponds to a dose40%greater than the starting dose. by guest on June 4, 2014 https://www.doczj.com/doc/f48678162.html,/ Downloaded from

on the next lower dose level,level 14.No patients experienced DLT at that level,and hence accrual to the trial was completed.The traditional recommended phase II dose would be level 14.We fit the model to the data of Table 2obtaining the follow-ing maximum likelihood estimates with 90%confidence inter-vals (CIs):K 1is estimated as 7.4(90%CI ?6.8-7.9)instead of the true value of 7.5;(K 2?K 1)/.34is estimated as 4.1(90%CI ?1.3-7.0)instead of the true value of 4.6;(K 3?K 2)/0.34is estimated as 1.4(90%CI ?0-2.9)instead of 2.9;?is estimated as 0(90%CI ?0-0.67)with the true value of 0;??is estimated

as 0.71(90%CI ?0.40-1.25),with a true value of 0.62;and ??is estimated as 0.83(90%CI ?0.37-1.84),with a true value of 0.90.In this example,there is good agreement between the es-timates obtained from fitting the model and the true values used to generate the data example.The CIs are based on the usual normal approximations to the maximum likelihood estimates of the K ’s,log ??,and log ??and on the approximate chi-squared distribution of the logarithm of the likelihood ratio statistic as a function of ?.There is no evidence of cumulative toxicity because the alpha parameter is estimated as zero.There appears to be a substantial amount of both interpatient variability and intrapatient variabil-ity.The standard deviations are large,relative to the logarithm of the dose step ln(1.4)that is about 0.34.The K 1and K 2values appear to be well separated,but the K 2and K 3values are close.Fig.5shows the probability of grade 2or worse toxicity as a function of dose level and similar functions for the probability of grade 3or worse toxicity and of grade 4toxicity.These func-tions were computed by use of the model parameters estimated from the simulated data.From these graphs,one can estimate the dose level associated with any target level of any grade of tox-icity.If one were to recommend a single dose level,the recom-mendation should reflect the distance between the grade 3+curve and grade 4+curve in Fig.5.At dose level 17,the model estimates that 19%of the patients will experience grade 4tox-icity.At dose level 16,the probability of grade 4toxicity is reduced to 12%,the probability of grade 3+toxicity is 22%,and the probability of grade 2+toxicity is 70%.

The functions in Fig.5do not give a clear picture of inter-patient differences.Fig.6shows curves of the probability of grade 2+,3+,and 4+toxicity for three representative patients.The middle graph is for a patient whose ?value equals the mean ??.The upper graph is for a patient whose ?value is one

standard deviation below the mean;i.e.,?

????.The lower

graph is for a patient with ?

???+?

?.Dose levels 16or 17

may be reasonable for the patient represented by the middle

graph.For the patient represented by the upper graph,dose level

19would be more appropriate.For the patient represented by the

lower graph,dose level 14or 15would be more appropriate.

This graph illustrates the substantial interpatient variability in

the toxic response to this drug in this patient population.The

separation between the grade 2+and grade 3+curves here and in

Fig.5indicates the ability to effectively titrate patients to grade

2toxicity.The closeness of the grade 3+and grade 4+curves

indicates that doses that give grade 3toxicity overlap substan-

tially with those that give grade https://www.doczj.com/doc/f48678162.html,e of any fixed dose

for all patients is problematic,since any dose both overtreats and

undertreats some patients.This is the principal conclusion of the

data analysis.

Discussion

The new designs described here appear to accomplish several

objectives.They reduce the number of patients potentially un-

dertreated.Some of these designs also reduce the duration of

trials by doubling the dose until toxicity develops.These ap-

proaches also improve the information yield of phase I trials.

They provide for estimation of the population distribution of the

MTD and may also provide a statistical estimate of the degree of

cumulative toxicity.

We have addressed phase I trials in which patients may re-

ceive more than one course of treatment.Not all phase I trials are

of this type.Even in trials of this type,many patients remain in

the study for only one or two courses of treatment because of tumor progression.This limits the information available for analysis.Patients may be able to remain in the study longer with

accelerated titration designs because use of intrapatient dose

escalation provides greater opportunity for therapeutic benefit.

The reduced risk of design 4compared with design 3was based

on using information from the second and third courses in de-

termining when to stop the initial accelerated stage.This addi-

tional protection can be assured with fewer courses of treatment

per patient by requiring that when the first instance of grade

2Fig.5.Probability of toxicity of each grade level in a single course of treatment as a function of dose level.Probabilities are averaged over the population of patients.Probability curves are computed from model 1using maximum likeli-

hood estimates of model parameters.Specifically,the probability of grade 2+toxicity with dose d and cumulative dose for previous courses of D is ??log ?d +?D ?+???K 1

??2

?+?2

??,where ?denotes the cumulative standard normal distribution function.For com-puting probability of grade 3+or grade 4toxicity,replace K 1by K 2and K 3,

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toxicity occurs,two other patients be treated at that same dose without grade 2toxicity before the dose is doubled.This may be satisfied by later courses at escalated doses in previous patients or may require starting a new patient at the same dose as the one who experienced grade 2toxicity.This modification is not needed for design 2,since it uses only first-course toxicity for determining when to terminate the accelerated stage and uses smaller dose steps.For designs without intrapatient dose esca-lation,this modification would increase the number of patients treated at lower doses and may extend the time to completion.In these simulations,we used the conventional stopping rule with all designs for consistency.The study stopped when two patients experienced DLT at a dose level,and six patients were treated at the next lower dose level with no more than one patient experiencing DLT.For the new designs,the population distri-bution of MTDs is estimated,and there is nothing special about the highest dose at which fewer than two patients experienced DLT.One might,therefore,continue entering patients beyond the usual stopping point to refine the estimates of the population distributions.In fact,the entire second stage of sampling could use a model-based or Bayesian approach to selecting the first-course dose for each patient.Simple up-down phase I designs with cohort sizes other than three to six patients are also some-times used when the amount of DLT that is to be tolerated is much less than 33%.We have analyzed the results of 20actual phase I trials by use of the model described above for the generation of simulated trial data.Other models could be used in place of the expression shown in equation 1and,in particular,other approaches to the modeling of cumulative toxicity may be more appropriate in specific trials.

Use of an accelerated titration design requires careful defini-tion of the level of toxicity considered dose limiting and the level considered sufficiently low (e.g.,none-mild)that intrapatient dose escalation is acceptable.These definitions must be made for each organ system.In the simulations,we tabulated the in-cidence of unacceptable or grade 4toxicity,but this is not nec-essary in using an accelerated titration design.The dose escala-tion and de-escalation decisions that must be made during the

trial depend on distinguishing none-mild toxicity from moderate toxicity and on distinguishing moderate toxicity from DLT.These definitions may be protocol specific.The tracking of tox-icity over multiple treatment courses and the use of intrapatient titrations require careful patient management.However,the re-sult will enhance the likelihood that patients receive therapeutic dosing and increase the useful information obtained from each treated patient.

The approach to design and analysis of phase I trials de-scribed in this article will help identify when there is large interpatient variability in sensitivity to the toxic effects of a drug.If interpatient variability is small,a fixed-dose regimen can be used in phase II trials,and few patients will be either overdosed or underdosed.Mick et al.(18)have described important sources of interpatient and intrapatient variability that might be usefully

incorporated into the model.Further improvement might result from modeling toxicity separately by organ system.

Pharmacokinetic differences are sometimes an important source of interpatient variability.In such cases,it may be

advis-Fig.6.Probability toxicity of each grade level in a

single course of treatment as a function of dose

level for individual patients.Probabilities are not

averaged over the population of patients but are

computed separately for the average patient

(middle panel with ?i ???),the patient with re-

duced sensitivity to the toxic effects of the com-

pound (upper panel with ?i ??????),and the

patient with increased sensitivity to the toxic effects

of the compound (lower panel with ?i ???+??).

Probability curves are computed from model 1us-

ing maximum likelihood estimates of model param-

eters.Specifically,the probability of grade 2+tox-

icity with dose d and cumulative dose for previous

courses of D for a patient with value ?

i is

??log ?d +?D ?+?i ?K 1

???

where ?denotes the cumulative standard normal

distribution function.For computing probability of

grade 3+or grade 4toxicity,replace K 1by K 2and

K 3,respectively.

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able to attempt to control systemic exposure rather than dose.If drug clearance can be predicted by use of baseline patient char-acteristics such as liver or renal function,then the dose needed to achieve the targeted concentration can be estimated.Other-wise,an adaptive dosing scheme may be needed to achieve a target exposure.If the drug is delivered by a prolonged infusion, one may adapt the infusion rate based on estimates of pharma-cokinetic parameters to target systemic exposure levels.The accelerated titration designs described here then may be applied with the only change being the use of exposure levels rather than dose levels.When prolonged infusions are not used,it may not be feasible to deliver a target exposure level during the same course of treatment in which pharmacokinetic parameters are estimated.It still may be possible,however,to use parameters estimated in the first course of treatment for the titration of exposure in subsequent courses.

Accelerated titration designs are more aggressive than stan-dard approaches and,therefore,may be associated with more risk.The simulations were performed with a very wide range of model parameters and suggest that the risks appear acceptable for designs2and4.We believe that these designs are appropri-ate for clinical testing.For drugs that exhibit preclinical evi-dence of cumulative toxicity,special caution in the conduct of any type of phase I trial is needed.Accelerated designs without intrapatient dose escalations achieve most of the advantages of accelerated titration designs,with little or no increase in risk compared with the standard design1A.However,they do not provide as great a reduction in the number of undertreated pa-tients and,in particular,do not provide patients accrued early in the trial or those who have an especially high individual toler-ance for the drug as much opportunity as do titration designs to be treated at a dose that provides the greatest opportunity for benefit.We hope to sponsor phase I clinical trials to provide prospective evaluation of these new approaches. Appendix

Four designs were evaluated as follows.Design1:cohorts of three new patients per dose level.If one of three patients expe-riences DLT in the first course,expand the cohort to six patients. Intrapatient escalation option A.Design2:cohorts of one new patient per dose level.When the first instance of first course DLT is observed,or the second instance of first course grade2 toxicity of any type,expand the cohort for current dose level and revert to use of design1for all further cohorts.Intrapatient escalation option B.Design3:same as design2,except that double dose steps are used during the initial accelerated stage of the trial(both for between-patient and within-patient escala-tions).Intrapatient escalation option B.Design4:cohorts of one new patient per dose level and double dose steps are used during the initial accelerated stage of the trial.When the first instance of DLT is observed at any course or the second instance of any course grade2toxicity of any type,expand the cohort for current dose level and revert to use of design1for all further cohorts. Intrapatient escalation option B.

The intrapatient dose modification options are defined as fol-lows:

Option A:no within-patient dose escalation.De-escalate if grade3or worse toxicity at previous course.

Option B:Escalate if grade0-1toxicity at previous course.

De-escalate if grade3or worse toxicity at previous course. References

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in the design and conduct of phase I and II clinical trials of new anticancer

agents.J Natl Cancer Inst1993;85:1637-43.

(2)Estey E,Hoth D,Simon R,Marsoni S,Leyland-Jones B,Wittes R.Thera-

peutic response in phase I trials of antineoplastic agents.Cancer Treat Rep

1986;70:1105-15.

(3)Collins JM,Zaharko DS,Dedrick RL,Chabner BA.Potential roles for

preclinical pharmacology in phase I clinical trials.Cancer Treat Rep1986;

70:73-80.

(4)Storer BE.Design and analysis of phase I clinical trials.Biometrics1989;

45:925-37.

(5)Eichhorn BH,Zacks S.Sequential search for an optimal dosage.J Am Stat

Assoc1973;68:594-8.

(6)O’Quigley J,Pepe M,Fisher L.Continual reassessment method:a practical

design for phase I clinical trials in cancer.Biometrics1990;46:33-48.

(7)Faries D.The modified continual reassessment method for phase I cancer

clinical trials.American Statistical Association1991Proceedings of the

Biopharmaceutical Section.Alexandria(VA):American Statistical Asso-

ciation,1991:269-73.

(8)Goodman SN,Zahurak ML,Piantadosi S.Some practical improvements in

the continual reassessment method for phase I studies.Stat Med1995;14:

1149-61.

(9)Moller S.An extension of the continual reassessment methods using a

preliminary up-and-down design in a dose finding study in cancer patients,

in order to investigate a greater range of doses.Stat Med1995;14:

911-22.

(10)Piantadosi S,Liu G.Improved designs for dose escalation studies using

pharmacokinetic measurements.Stat Med1996;15:1605-18.

(11)Mick R,Ratain MJ.Model-guided determination of maximum tolerated

dose in phase I clinical trials:evidence for increased precision.J Natl

Cancer Inst1993;85:217-23.

(12)Sheiner LB,Beal SL,Sambol NC.Study designs for dose-ranging.Clin

Pharmacol Ther1989;46:63-77.

(13)Sheiner LB,Hashimoto Y,Beal SL.A simulation study comparing designs

for dose ranging.Stat Med1991;10:303-21.

(14)Chuang C.The analysis of a titration study.Stat Med1987;6:583-90.

(15)Shih WJ,Gould AL,Hwang IK.The analysis of titration studies in phase

III clinical trials.Stat Med1989;8:583-91.

(16)Chou TC,Talalay P.Generalized equations for the analysis of inhibitions

of Michaelis-Menten and higher-order kinetic systems with two or more

mutually exclusive and nonexclusive inhibitors.Eur J Biochem1981;115:

207-16.

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The pharmacological basis of therapeutics.New York:McGraw-Hill,1996:

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risk of toxic effects:impact on enrollment and decision making in phase I

cancer trials.J Natl Cancer Inst1994;86:1685-93.

Notes

We thank Michelle Gossard and Sally Lopes of The Emmes Corporation for

their assistance in the management of the phase I trial database used for this study.We also thank the reviewers for suggestions on improvement of an earlier

draft of the manuscript.

Manuscript received January27,1997;revised May16,1997;accepted May

30,1997.

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to与for的用法和区别

to与for的用法和区别一般情况下, to后面常接对象; for后面表示原因与目的为多。 Thank you for helping me. Thanks to all of you. to sb.表示对某人有直接影响比如，食物对某人好或者不好就用to; for表示从意义、价值等间接角度来说，例如对某人而言是重要的，就用for. for和to这两个介词，意义丰富，用法复杂。这里仅就它们主要用法进行比较。 1. 表示各种“目的” 1. What do you study English for? 你为什么要学英语？ 2. She went to france for holiday. 她到法国度假去了。 3. These books are written for pupils. 这些书是为学生些的。 4. hope for the best, prepare for the worst. 作最好的打算，作最坏的准备。 2．对于 1．She has a liking for painting. 她爱好绘画。 2．She had a natural gift for teaching. 她对教学有天赋/ 3．表示赞成同情，用for不用to. 1. Are you for the idea or against it? 你是支持还是反对这个想法？ 2. He expresses sympathy for the common people.. 他表现了对普通老百姓的同情。 3. I felt deeply sorry for my friend who was very ill. 4 for表示因为，由于（常有较活译法） 1 Thank you for coming. 谢谢你来。 2. France is famous for its wines. 法国因酒而出名。 5．当事人对某事的主观看法，对于（某人），对…来说（多和形容词连用）用介词to，不用for.. He said that money was not important to him. 他说钱对他并不重要。 To her it was rather unusual. 对她来说这是相当不寻常的。 They are cruel to animals. 他们对动物很残忍。 6．for和fit, good, bad, useful, suitable 等形容词连用，表示适宜，适合。 Some training will make them fit for the job. 经过一段训练，他们会胜任这项工作的。 Exercises are good for health. 锻炼有益于健康。 Smoking and drinking are bad for health. 抽烟喝酒对健康有害。 You are not suited for the kind of work you are doing. 7. for表示不定式逻辑上的主语，可以用在主语、表语、状语、定语中。 1．It would be best for you to write to him. 2．The simple thing is for him to resign at once. 3．There was nowhere else for me to go. 4．He opened a door and stood aside for her to pass.

延时子程序计算方法

学习MCS-51单片机，如果用软件延时实现时钟，会接触到如下形式的延时子程序：delay:mov R5,#data1 d1:mov R6,#data2 d2:mov R7,#data3 d3:djnz R7,d3 djnz R6,d2 djnz R5,d1 Ret 其精确延时时间公式：t=（2*R5*R6*R7+3*R5*R6+3*R5+3）*T （“*”表示乘法，T表示一个机器周期的时间）近似延时时间公式：t=2*R5*R6*R7 *T 假如data1,data2,data3分别为50，40，248，并假定单片机晶振为12M，一个机器周期为10-6S，则10分钟后，时钟超前量超过1.11秒，24小时后时钟超前159.876秒（约2分40秒）。这都是data1,data2,data3三个数字造成的，精度比较差，建议C描述。

上表中e=-1的行（共11行）满足（2*R5*R6*R7+3*R5*R6+3*R5+3）=999，999 e=1的行（共2行）满足（2*R5*R6*R7+3*R5*R6+3*R5+3）=1，000，001 假如单片机晶振为12M，一个机器周期为10-6S，若要得到精确的延时一秒的子程序，则可以在之程序的Ret返回指令之前加一个机器周期为1的指令（比如nop指令）， data1,data2,data3选择e=-1的行。比如选择第一个e=-1行，则精确的延时一秒的子程序可以写成： delay:mov R5,#167 d1:mov R6,#171 d2:mov R7,#16 d3:djnz R7,d3 djnz R6,d2

djnz R5,d1 nop ；注意不要遗漏这一句 Ret 附： #include"iostReam.h" #include"math.h" int x=1,y=1,z=1,a,b,c,d,e(999989),f(0),g(0),i,j,k; void main() { foR(i=1;i<255;i++) { foR(j=1;j<255;j++) { foR(k=1;k<255;k++) { d=x*y*z*2+3*x*y+3*x+3-1000000; if(d==-1) { e=d;a=x;b=y;c=z; f++; cout<<"e="<

常用介词用法(for to with of)

For的用法 1. 表示“当作、作为”。如: I like some bread and milk for breakfast. 我喜欢把面包和牛奶作为早餐。 What will we have for supper? 我们晚餐吃什么? 2. 表示理由或原因,意为“因为、由于”。如: Thank you for helping me with my English. 谢谢你帮我学习英语。 3. 表示动作的对象或接受者,意为“给……”、“对…… (而言)”。如: Let me pick it up for you. 让我为你捡起来。 Watching TV too much is bad for your health. 看电视太多有害于你的健康。 4. 表示时间、距离,意为“计、达”。如: I usually do the running for an hour in the morning. 我早晨通常跑步一小时。 We will stay there for two days. 我们将在那里逗留两天。 5. 表示去向、目的,意为“向、往、取、买”等。如: Let’s go for a walk. 我们出去散步吧。 I came here for my schoolbag.我来这儿取书包。 I paid twenty yuan for the dictionary. 我花了20元买这本词典。 6. 表示所属关系或用途,意为“为、适于……的”。如: It’s time for school. 到上学的时间了。 Here is a letter for you. 这儿有你的一封信。 7. 表示“支持、赞成”。如: Are you for this plan or against it? 你是支持还是反对这个计划? 8. 用于一些固定搭配中。如: Who are you waiting for? 你在等谁? For example, Mr Green is a kind teacher. 比如,格林先生是一位心地善良的老师。尽管for 的用法较多，但记住常用的几个就可以了。 to的用法: 一：表示相对，针对 be strange (common, new, familiar, peculiar) to This injection will make you immune to infection. 二：表示对比，比较 1：以-ior结尾的形容词，后接介词to表示比较，如：superior ,inferior,prior,senior,junior 2: 一些本身就含有比较或比拟意思的形容词，如equal，similar，equivalent，analogous A is similar to B in many ways.

单片机C延时时间怎样计算

C程序中可使用不同类型的变量来进行延时设计。经实验测试，使用unsigned char类型具有比unsigned int更优化的代码，在使用时应该使用unsigned char作为延时变量。以某晶振为12MHz的单片机为例，晶振为12M H z即一个机器周期为1u s。一. 500ms延时子程序程序: void delay500ms(void) { unsigned char i,j,k; for(i=15;i>0;i--) for(j=202;j>0;j--) for(k=81;k>0;k--); } 计算分析: 程序共有三层循环一层循环n:R5*2 = 81*2 = 162us DJNZ 2us 二层循环m:R6*(n+3) = 202*165 = 33330us DJNZ 2us + R5赋值 1us = 3us 三层循环: R7*(m+3) = 15*33333 = 499995us DJNZ 2us + R6赋值 1us = 3us

循环外: 5us 子程序调用 2us + 子程序返回2us + R7赋值 1us = 5us 延时总时间 = 三层循环 + 循环外 = 499995+5 = 500000us =500ms 计算公式:延时时间=[(2*R5+3)*R6+3]*R7+5 二. 200ms延时子程序程序: void delay200ms(void) { unsigned char i,j,k; for(i=5;i>0;i--) for(j=132;j>0;j--) for(k=150;k>0;k--); } 三. 10ms延时子程序程序: void delay10ms(void) { unsigned char i,j,k; for(i=5;i>0;i--) for(j=4;j>0;j--) for(k=248;k>0;k--);

中职生网络安全教育教案

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for和to区别

1.表示各种“目的”，用for （1）What do you study English for 你为什么要学英语？（2）went to france for holiday. 她到法国度假去了。（3）These books are written for pupils. 这些书是为学生些的。（4）hope for the best, prepare for the worst. 作最好的打算，作最坏的准备。 2．“对于”用for （1）She has a liking for painting. 她爱好绘画。（2）She had a natural gift for teaching. 她对教学有天赋/ 3．表示“赞成、同情”，用for （1）Are you for the idea or against it 你是支持还是反对这个想法？（2）He expresses sympathy for the common people.. 他表现了对普通老百姓的同情。（3）I felt deeply sorry for my friend who was very ill. 4. 表示“因为，由于”（常有较活译法），用for （1）Thank you for coming. 谢谢你来。

（2）France is famous for its wines. 法国因酒而出名。 5．当事人对某事的主观看法，“对于（某人），对…来说”，（多和形容词连用），用介词to，不用for. （1）He said that money was not important to him. 他说钱对他并不重要。（2）To her it was rather unusual. 对她来说这是相当不寻常的。（3）They are cruel to animals. 他们对动物很残忍。 6．和fit, good, bad, useful, suitable 等形容词连用，表示“适宜，适合”，用for。（1）Some training will make them fit for the job. 经过一段训练，他们会胜任这项工作的。（2）Exercises are good for health. 锻炼有益于健康。（3）Smoking and drinking are bad for health. 抽烟喝酒对健康有害。（4）You are not suited for the kind of work you are doing. 7. 表示不定式逻辑上的主语，可以用在主语、表语、状语、定语中。（1）It would be best for you to write to him. （2） The simple thing is for him to resign at once.

51单片机延时时间计算和延时程序设计

一、关于单片机周期的几个概念 ●时钟周期时钟周期也称为振荡周期，定义为时钟脉冲的倒数（可以这样来理解，时钟周期就是单片机外接晶振的倒数，例如12MHz的晶振，它的时间周期就是1/12 us），是计算机中最基本的、最小的时间单位。在一个时钟周期内，CPU仅完成一个最基本的动作。 ●机器周期完成一个基本操作所需要的时间称为机器周期。以51为例,晶振12M，时钟周期(晶振周期)就是(1/12)μs，一个机器周期包执行一条指令所需要的时间，一般由若干个机器周期组成。指令不同，所需的机器周期也不同。对于一些简单的的单字节指令，在取指令周期中，指令取出到指令寄存器后，立即译码执行，不再需要其它的机器周期。对于一些比较复杂的指令，例如转移指令、乘法指令，则需要两个或者两个以上的机器周期。 1.指令含义 DJNZ：减1条件转移指令这是一组把减1与条件转移两种功能结合在一起的指令，共2条。 DJNZ Rn，rel ；Rn←（Rn）-1 ；若（Rn）=0，则PC←（PC）+2 ；顺序执行；若（Rn）≠0，则PC←（PC）+2+rel，转移到rel所在位置DJNZ direct，rel ；direct←（direct）-1 ；若（direct）= 0，则PC←（PC）+3；顺序执行；若（direct）≠0，则PC←（PC）+3+rel，转移到rel 所在位置 2.DJNZ Rn,rel指令详解例：

MOV R7，#5 DEL:DJNZ R7,DEL; rel在本例中指标号DEL 1.单层循环由上例可知，当Rn赋值为几，循环就执行几次，上例执行5次，因此本例执行的机器周期个数=1（MOV R7，#5）+2（DJNZ R7,DEL）×5=11，以12MHz的晶振为例，执行时间（延时时间）=机器周期个数×1μs=11μs，当设定立即数为0时，循环程序最多执行256次，即延时时间最多256μs。 2.双层循环 1）格式： DELL:MOV R7，#bb DELL1:MOV R6，#aa DELL2:DJNZ R6,DELL2; rel在本句中指标号DELL2 DJNZ R7,DELL1; rel在本句中指标号DELL1 注意：循环的格式，写错很容易变成死循环，格式中的Rn和标号可随意指定。 2）执行过程

双宾语 to for的用法

1.两者都可以引出间接宾语，但要根据不同的动词分别选用介词to 或for：(1) 在give, pass, hand, lend, send, tell, bring, show, pay, read, return, write, offer, teach, throw 等之后接介词to。如：请把那本字典递给我。正：Please hand me that dictionary. 正：Please hand that dictionary to me. 她去年教我们的音乐。正：She taught us music last year. 正：She taught music to us last year. (2) 在buy, make, get, order, cook, sing, fetch, play, find, paint, choose,prepare, spare 等之后用介词for 。如：他为我们唱了首英语歌。正：He sang us an English song. 正：He sang an English song for us. 请帮我把钥匙找到。正：Please find me the keys. 正：Please find the keys for me. 能耽搁你几分钟吗(即你能为我抽出几分钟吗)? 正：Can you spare me a few minutes? 正：Can you spare a few minutes for me? 注：有的动词由于搭配和含义的不同，用介词to 或for 都是可能的。如：do sb a favour＝do a favour for sb 帮某人的忙 do sb harm＝do harm to sb 对某人有害

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双宾语tofor的用法

1. 两者都可以引出间接宾语，但要根据不同的动词分别选用介词to 或for： (1) 在give, pass, hand, lend, send, tell, bring, show, pay, read, return, write, offer, teach, throw 等之后接介词to。如：请把那本字典递给我。正：Please hand me that dictionary. 正：Please hand that dictionary to me. 她去年教我们的音乐。正：She taught us music last year. 正：She taught music to us last year. (2) 在buy, make, get, order, cook, sing, fetch, play, find, paint, choose,prepare, spare 等之后用介词for 。如：他为我们唱了首英语歌。正：He sang us an English song. 正：He sang an English song for us. 请帮我把钥匙找到。正：Please find me the keys. 正：Please find the keys for me. 能耽搁你几分钟吗(即你能为我抽出几分钟吗)? 正：Can you spare me a few minutes? 正：Can you spare a few minutes for me? 注：有的动词由于搭配和含义的不同，用介词to 或for 都是可能的。如： do sb a favou r do a favour for sb 帮某人的忙 do sb harnn= do harm to sb 对某人有害

浅析中职学校的网络安全

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对中职学校计算机网络的破坏，会对教学进度和学校正常办公造成不可估计的影响。网络安全技术是提高校园网络安全的关键，对于网络攻击事件的预防、抵御以及应对来说至关重要，只有在计算机网络搭建过程中，充分考虑网络的安全防护，才能保证学校计算机的网络安全，才能保障学校教学工作的顺利开展。所以针对中职学校计算机网络安全进行研究，才能进一步提升校园网络的工作效率和性能。 2中职学校网络安全的潜在威胁 2.1网络非法入侵非法入侵或非授权访问是中职学校计算机网络较为常见的安全问题，IP地址被盗用、非法口令入侵等情况不时出现。1P地址被盗用主要是恶意攻击者使用编程的方式来绕过计算机网络中的IPMAC地址，实现动态IP地址的修改，或使用MS-DOS命令来执行查询未使用的IP地址资源，从而达到静态的方式来修改IP地址，最终非法占有学校计算机局域网络中的IP地址资源，而进行其他的非法行为。此外，一些非法用户通过各种手段获取学校网络的口令与密码，访问学校的内部网络后窃取内部各种教学资源和课件，这对于中职教学资源的数据安全、版权保护来说造成很大危害，更有甚者，通过非法口令入侵去改变乃至破坏学校网络，会对学校教学活动的正常开展造成严重影响。 2.2网络病毒与木马种植

to和for的用法有什么不同(一)

to和for的用法有什么不同（一）一、引出间接宾语时的区别两者都可以引出间接宾语，但要根据不同的动词分别选用介词to 或for，具体应注意以下三种情况： 1. 在give, pass, hand, lend, send, tell, bring, show, pay, read, return, write, offer, teach, throw 等之后接介词to。如：请把那本字典递给我。正：Please hand me that dictionary. 正：Please hand that dictionary to me. 她去年教我们的音乐。正：She taught us music last year. 正：She taught music to us last year. 2. 在buy, make, get, order, cook, sing, fetch, play, find, paint, choose, prepare, spare 等之后用介词for 。如：他为我们唱了首英语歌。正：He sang us an English song. 正：He sang an English song for us. 请帮我把钥匙找到。正：Please find me the keys. 正：Please find the keys for me. 能耽搁你几分钟吗(即你能为我抽出几分钟吗)? 正：Can you spare me a few minutes?

正：Can you spare a few minutes for me? 3. 有的动词由于用法和含义不同，用介词to 或for 都是可能的。如： do sb a favor＝do a favor for sb 帮某人的忙 do sb harm＝do harm to sb 对某人有害在有的情况下，可能既不用for 也不用to，而用其他的介词。如： play sb a trick＝play a trick on sb 作弄某人请比较： play sb some folk songs＝play some folk songs for sb 给某人演奏民歌有时同一个动词，由于用法不同，所搭配的介词也可能不同，如leave sbsth 这一结构，若表示一般意义的为某人留下某物，则用介词for 引出间接宾语，即说leave sth for sb；若表示某人死后遗留下某物，则用介词to 引出间接宾语，即说leave sth to sb。如： Would you like to leave him a message? / Would you like to leave a message for him? 你要不要给他留个话？ Her father left her a large fortune. / Her father left a large fortune to her. 她父亲死后给她留下了一大笔财产。二、表示目标或方向的区别两者均可表示目标、目的地、方向等，此时也要根据不同动词分别对待。如： 1. 在come, go, walk, move, fly, ride, drive, march, return 等动词之后通常用介词to 表示目标或目的地。如： He has gone to Shanghai. 他到上海去了。 They walked to a river. 他们走到一条河边。

延时计算

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结实了一位社会青年,该青年常以向家长,向老师通报他上网吧为由,向该中学生勒索香烟,钱等.后来有一次发展到在路上争吵,该生被社会青年动手毒打,幸好被“110”巡警发现,在家长的强烈要求下,开始了立案侦查.有少数学生被欺负,一直不敢告诉老师和家长,而是请社会青年来“摆平” ,终于酿成了流氓斗殴, 给学校,家庭带来了很大的负面影响。（二）采取的应对措施: 第一, 要学法,守法,懂法,用法。第二,要有及时报告的意识.特别是个子矮小,体力单薄的学生遇欺时,要及时报告家长,老师,请求其出面解决。第三,要有机警的报警意识,即遇危急时临危不惧,寻找脱身之遇,求助于警方帮助. 第四,要谨慎交友。紧急情况下的逃生策略—— 1976 年 7 月 28 日凌晨 3 时 49 分 56 秒,唐山市发生 7.8 级强烈地震,有 24.24 万人死亡,重伤 16 万,轻伤 36 万. 2004 年2 月 15 日中午 11 时 20 分,吉林省吉林市中百商厦发生特大火灾,造成 54 人死亡,70 人受伤. 2005 年 6 月 10 日 12 时 20 分,广东省汕头市潮南区峡山街道华南宾馆发生火灾,至 15 时 30 分大火被扑灭,造成 31 人死亡,23 人轻伤,3 人重伤. 2005 年 6 月 10 日下午,黑龙江省牡丹江地区宁安市沙兰镇遭受百年不遇的山洪和泥石流灾害,沙兰镇小学被冲,死亡人数 109 人,其中学生 105 人. 一条条触目惊心的报道,有多少人无故的丧命于这些自然的或人为的

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I will study for our country. 3.of表示所属关系意思是：---的 a map of the world a friend of mine

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6.几个大功率用电器不要同时使用，避免造成电源线超负荷使用。 7.电熨斗、电炉等电热器具不要直接放在木质物体上或靠近易燃物品，一些没有自动控制的电热器具使用后要随手关电源，以防引起火灾。 8.家用电器的金属外壳必须接地，绝不允许将三脚插头改为两脚插头插入两孔插座中使用。 9.开关、插座和用电器损坏或外壳破坏时，应及时维修或更换，没有修好的不能使用，在维修家用电器时，必须先切断电源。 10.发现用电器冒烟或闻到异味时，一定要先切断电源，再进行检查。 11.在雷雨天最好不要使用电器，而且要拔掉各种电源插座。 12.不要用湿手触摸开关、插座和用电器;擦拭灯头、开关、电器时，要断开电源后进行;更换灯泡要站在绝缘物体上。【小提示】千万不要用湿布擦拭正在使用的家用电器哟! 13.家用电热设备、暖气设备一定要远离煤气罐、煤气管道，发现煤气漏气时千万不要闭合电源、打手机，要先开窗通风，并及时请专业人员修理。