The Study Of Key Issues In Group Sequential Design For Clinical Trials

During the process of the trial, the group sequential design allows to evaluate theefficacy and safety of the drug based on the accumulated data. The trial could stop earlierfor efficacy/futility as long as it provides the enough evidence. Compared with thetraditional designs in clinical trials, the group sequential design is more flexible. Theinterim analysis in group sequential design makes it possible to decrease the sample size,shorten the trial time and save the trial costs. It also satisfies the ethical consideration more.Furthermore, from the administrative viewpoint, the interim analysis enables clinicalinvestigators and CRAs to know the problems about the trial as soon as possible. Accordingly, the quality of the trial will be improved. Now, the group sequential designhas been applied in overseas clinical trials. But the application of group sequential designin clinical trials is just at the beginning stage in China. Therefore, it is necessary for thebiostatisticians in China to solve the key problems in the application of group sequentialdesign in local trials and promote their applications. The key issues of the application ofgroup sequential design in actual clinical trials includes the determination of the numberand timing of interim analyses, the control of overall type I error rate due to the multipletests and the sample size estimation, etc. Especially, the sample size estimation of survivaltrials is more complicated because of the ambiguous parametric distribution of survivaldata, the different way to analyze drop-out data, the effect of censored data and accruedinformation and so forth. On the other hand, in the group sequential designs, α spendingfunction is the most widely used method in actual clinical trials. It employs the type I errorrate spent during the trial to calculate the stopping boundaries and nominal significancelevels. The overall type I error rate is well controlled. However, the stiff functional form inthe α spending function makes it difficult to understand and communicate by theclinical investigators when choosing the optimal interim monitoring plan. The conditionalpower is considered as a better communicative tool for clinical investigators. But thefamily-wise type I error rate cannot be well controlled in the stochastic curtailmentappraoch based on conditional power. Therefore, this study was conduncted based on thetwo issues we have metioned above. The main works are as following.I．A simulation-based method to calculate the sample size of group sequentialtrials for time-to-event data.Considering the different characteristics of survival data and the flexibility ofsimulation-based method, the Monte Carlo simulation-based approach is suggested tocalculate the sample size of survival group sequential trial and the SAS macro%n_gssurwas developed accordingly. Compared with the other methods, the proposed method iseasier to implement in an actual clinical trial. It not only employs the simplest exponentialdistribution. The Weibull distribution, which is more suitable to describe the time-to-event data, was also considered. Due to the pecularity of drop-out cases in survival trials, theprobability of the discontinuation is directly incorporated into the process of sample sizeestimation, which leads to a more accurate estimate. Because it is difficult for clinicalinvestigators to predict the accrual information, such as accrual time, accrual rate andaccrual distribution. It is assumed that the subject should enter the cohort as long as theformer one completes the trial, which simplifies the simulative trial process and the formof interim data. The assumption makes the simulation-based sample size estimationmethod more practical in the actual clinical trial. Furthermore, the conservative samplesize estimate does not affect the actual clinical trial much because of the interim analysis.The simulation-based approach mingles the process of sample size estimation and thechoice of the optimal interim monitoring plan. It not only estimates the sample size andthe total number of preplanned events, but calculates and compares the expected numberof the events, the stage-wise empirical power and the cumulative empirical power in orderto choose the optimal interim monitoring plan. However, the proposed method is only forthe double-arm group sequential trial, which considers the early stopping for efficacy, butfutility.If the survival data is from the Weibull distribution, the magnitude of shapeparameter γ also directly affects the sample size. Considering that the shape parametr γ,the median survival time of the treatment groupM TRT, the median survival time of thecontrol groupM CTLand the hazard ratio satisfy HR=(M TRT/M)γCTL, a simulation studywas conducted to explore the impact of the shape parameter on the sample size in twoscenarios:(A)M TRTandM CTLare fixed;(B)M CTLand HR are fixed. The resultsshow that the sample size is more sensitive to the change of the hazared ratio due to theshape parameter than the change ofM TRT. But the number of the preplanned events andthe expected number of the events only depend on the hazard ratio. A formula to estimatethe shape parameter of the Weibull distribution was proposed based on the simulationresults. Moreover, more than10simulations for the different random seeds were suggested in order to get the robust estimate of the sample size.II．A new α spending function based on conditional powerConsidering the characteristics of conditional power and α spending functionapproach, a new α spending function based on conditional power, which is called CPfunction, was constructed by borrowing the conditional power into the α spendingfunction approach. It keeps the advantages of α spending function and conditionalpower and overcomes their shortcomings. The CP function is given the explanation of theconditional power and becomes a better communicative tool for clinical investigators. Theoverall type I error rate is also well controlled. However, the CP function can be onlyemployed to reject, not to accept the null hypothesis in the interim analysis.Because of the inclusion of the CP critical value for efficacyρ0, the CP function notonly has the meaning of conditional power, but enhances the flexibility of the functionalform. By adjustingρ0, it could approximately simulate the classical Pocock function,O’Brien-Fleming function and the quardratic spending function. Even a much betterfunctional form may be found on the stage-wise power and sample size. According to thesimulation results, it is not suggestedρ0>0.6in the two-stage design and the values ofρ0at the two interim time points be also larger than0.6in the three-stage design becauseit will make the CP function too conservative. Furthermore, when employing thestochastic curtailment method based on conditional power to accept the null hypothesis inthe interim evaluation, the CP critical value for futilityρ1is proposed in [0.5,0.7) when1/3<tk≤1/2and the interim evaluaton for futility is not suggested when t k≤1/3.The major achievements of this paper are concluded as follows. Firstly, an easy andpractical Monte Carlo simulation-based method is proposed to calculate the sample size ofdouble-arm survival trials under the exponential and Weibull distribution. Secondly, theeffect of the shape parameter on the sample size is discussed by employing simulationstudies when the Weibull distribution is considered. Especially, a formula to estimate theshape parameter is given for the actual clinical trial. Finally, a new α spending function, called CP function, is constructed. And the choice ofρ0is discussed for the CP functionby employing Monte Carlo simulations.This study targets the group sequential design and takes the actual clinical trials intoaccount. It focuses on the simulation-based method to calculate the sample size of survivalgroup sequential trial and a new α spending function based on conditional power inorder to work out the main problems of the application of group sequential and promote itsapplication in the clinical trials in China. Moreover, the generalization of the proposedmethods in the adaptive design needs further discussion and development.