Point estimation in adaptive confirmatory clinical trials with time-to-event data and treatment or subgroup selection

Adaptive designs are increasingly adopted to make the process of drug development more efficient. In particular, seamless phase II/III clinical trials allow interim adaptations such as early stopping for futility or selection of the most promising treatment. Furthermore, targeted therapy trials include an interim analysis to select a subgroup with the largest observed treatment effect. However, despite their efficiency, data dependent adaptations lead to multiplicity and selection issues. This is because data are used for both treatment or subgroup selection as well as for the confirmatory analysis of treatment efficacy. Specifically, selection rules applied at the interim stage lead to overoptimistic and thus biased effect estimates. In this thesis, we investigate the bias that arises due to selection and develop unbiased estimators that correct for treatment or subgroup selection in two-stage confirmatory clinical trials with time-to-event data. When analysis is based on time-to-event data, censoring at the interim analysis violates the assumption of independence between stage 1 and stage 2 data, which is a crucial assumption of existing methods for normally distributed data. The independent increments structure of stagewise log-rank test statistics has been beneficial for hypothesis testing in this setting, where group sequential methods have been utilised based on the log-rank test statistic for time-to-event data. We therefore incorporate the independent increments structure to derive unbiased estimators based on asymptotic normality of the log-rank test statistic. Additionally, when considering treatment selection, we address the issue of correlation between stage 1 estimates due to the common control arm for time-to-event outcomes. We give the joint distribution of stagewise log hazard ratios and using the technique of Rao-Blackwellisation, we derive asymptotically uniformly minimum variance unbiased estimators conditional on selection rules for time-to-event outcomes. We examine the bias and mean squared error of conventional estimates and compare these, by simulation, to our unbiased and efficient estimators, which correct for treatment or subgroup selection and correlation due to both censoring and the common control arm. We show that, due to the asymptotic normality assumptions, our estimators are appropriate for large samples and small to moderate effect sizes