| For ethical, practical and statistical considerations, group sequential tests have been widely used to control the type I error rate at a pre-specified level in comparative clinical trials. Due to the optional sampling effect of the stopping time, conventional estimates will exaggerate the treatment difference. In this thesis, we consider the bias estimation and reduction for group sequentially monitored clinical trials.;First, an analytical expression of the bias of the maximum likelihood estimate for a Brownian motion drift is derived. We examine the bias for various group sequential boundaries and interim analysis patterns. A bias adjusted estimator is considered and its properties are studied. It is shown that this bias adjusted estimate not only reduces the bias substantially, but also keeps the variance smaller than or in the same magnitude as that of the maximum likelihood estimate for small or moderate treatment effects.;Second, we consider a group sequentially monitored survival trial. A method of estimating the bias for the Cox proportional hazards model is given. A bias adjusted estimator is studied.;In a group sequentially monitored clinical trial of comparing two failure time distributions, we also wish to test whether the proportional hazards assumption holds sequentially in addition to monitoring the major endpoints. A formal sequential test is needed since simply repeated implementation of the tests for the fixed sample size will inflate the type I error again. In this thesis, the asymptotic joint distribution of the sequentially computed test statistics based on the test by Lin (1991) is derived. A consistent estimate of the covariance matrix is given. Implementation of the test based on the alpha spending function approach by Lan & DeMets (1983) is discussed.;Finally, we illustrate the bias adjusted estimate and the model checking method using two real clinical trials. |
