The Comparison Of Sample Sizes And Research Of Analysis Methods In Enrichment Designs For High Placebo Effect

Objective:In recent years,high placebo effect has become one of the most important reasons that lead to plenty of failures in clinical trials.In addition to psychiatric diseases,this problem has also been seen in clinical trials for other diseases,such as pain disorders and functional bowel disorders.Sponsors proposed to use Placebo lead-in phase,Sequential Placebo Comparison Design,Two-way Enriched Deign and Sequential Enriched Design to solve the problem of high placebo effect.To analyze the results of these designs,people also proposed several statistical methods according to different types of outcome variables.This article aims to compare the sample sizes of these designs and comprehensively evaluate these analysis methods for reaching power and controlling type I error.Methods:Firstly,the article compared power calculated or the sample sizes required in Sequential Placebo Comparison Design,Two-way Enriched Deign and Sequential Enriched Design under different parameter setting conditions.To analyze continuous outcome variable,the method of two-stage weighted effects was utilized to calculate power and parameter settings were divided into three scenarios.To analyze binary outcome variable,the method of Score Test was used to estimate sample size and both scenarios of equal effects and unequal effects between two stages were considered here.Secondly,the article compared the difference of various analysis methods which were applied to these designs for their abilities in reaching power and controlling type I error.Methods like Seemingly Unrelated Regression,Least Square and Mixed Models for Repeated Measure were utilized to analyze continuous outcome variable.At the same time,methods like z test and score test were used to analyze binary outcome variable.Finally,the research chose a practical example to guide other researchers for applying this type of design.Results:First of all,the article compared the sample size required in these enrichment designs.For continuous outcome variable,if the effect sizes were preset to be equal between stage I and stage II in scenario one,the power of SPCD would be considerately less than TED and SED after fixing sample size previously.The powers of SPCD（61.47%）,TED（72.87%）and SED（77.10%）were maximized when（b,w）=（0.65,0.54）,（0.50,0.45）and（0.35,0.54）,respectively.For binary outcome variable,if the effect sizes of two stages were pre-fixed to be unequal,when r₂ or r₃<1,the sample sizes required in all three designs were large.However,the value descended dramatically with the increasing of r₂ and r₃,followed by a steady state（r₂,r₃>2）.The relation of sample sizes among these three designs was SED>TED>SPCD.If the effect sizes of two stages were pre-fixed to be equal,the sample sizes of both SPCD and TED ascended at first and then dropped with the raising of b.Secondly,the research compared the power and type I error of several analysis methods.For continuous outcome variable,under different parameter setting conditions,the powers of LS and SUR were nearly same,which were slightly lower than MMRM.When the actual effects in stage I and stage II were preset to be relatively large（0.3SD₁,0.5SD₁）,the powers of all three methods raised firstly and then dropped with the ascending of missing rate.However,when the parameter was set previously to be small（0.1SD₁）,inverse could be seen about the relationship between missing rate and power.For binary outcome variable,when the differences of effect between two groups in two stages were set to be equal,the powers of two methods were nearly similar.When the effect size of stage II was prefixed to be larger than stage I,score test could reach higher power.Conclusions:If the effect sizes in both stages could be estimated accurately,we could acquire the optimal b and w through mathematic calculation,which,nevertheless,was not realistic in actual work.According to the results of research,the values of b for SPCD,TED and SED were recommended to be 2/3,1/2 and 1/3.When analyzing continuous outcome variable,MMRM was more advantageous than LS and SUR.When analyzing binary outcome variable,slight difference could be seen between two methods and score test showed more obvious benefits.SPCD is recommended when non-threatening and high placebo-effect diseases were considered in a trial;SED is preferred if it is unethical that patients take placebo for long period;TED is superior while the study aims to find out the subgroup,from the whole population,where either placebo group or treatment group can response to new drugs highly.