Statistical Analysis For Two-Stage Adaptive Designs With Different Study Endpoints

In clinical research,adaptive trial design has attracted much attention in recent years due to its flexibility in modifying some aspects of an on-going trial.Without undermining the validity and integrity of the trial,modifications of a clinical trial based on accrued information are necessary to improve efficiency of drug development and achieve ethical gain.Examples of modifications include sample size re-calculation,change in inclusion/exclusion criteria,adjustment of study dose,early termination of the trial,and modification of statistical hypotheses.In some cases,the study endpoints in different stages of a clinical trial may be different due to long treatment duration or some other reasons.For example,a biomarker(or a surrogate endpoint) may be adopted at the first stage,and a survival endpoint is considered at the second stage when the treatment duration is too long.The change in study endpoint offers a challenge to combine data from both stages for a valid final analysis at the end of the trial.In this study,statistical methods utilizing data collected from both stages of a two-stage adaptive design are proposed for statistical analysis at the end of the trial, assuming that there is a well established relationship between the two different study endpoints.Three types of data from different study endpoints,i.e.,continuous data, event data,and survival data,are considered in this study.For each type of data, method is proposed for combining data of two different study endpoints.Especially, for continuous data,we assume a functional relationship between two study endpoints, by which the "predicted" values of the primary study endpoint are obtained from data collected at the first stage.Those "predicted" data as well as the observed data of the primary study endpoint at the second stage are utilized in the final analysis.For illustration,data of both stages from two normal populations are included to assess the population mean of the primary endpoint using the Graybill-Deal estimator,assuming that a linear relationship is established between the two study endpoints.For the event data,we assume occurrence of an event of interest is determined by an underlying lifetime distribution,by which the data observed from the two stages with different durations are included into the likelihood function.For the time-to-event data,the analysis is straightforward when the study endpoints are different in the sense of study duration. For the three types of data,tests for equality and equivalence between two treatments,test for superiority of the test treatment over the control treatment,and test for non-inferiority of the test treatment against the control are considered.Sample size calculations based on the proposed tests are addressed to achieve a pre-specific power. Sample size allocations at the two stages and between two treatments are also discussed.Simulations are conducted to investigate performance of the tests, including the typeâ… error rate and power.Superiority of inclusion of data from both stages is shown by theoretical and numerical results.