Non-parametric Sequential and Adaptive Designs for Survival Trials

Abstract

This thesis deals with fixed samples size, sequential and adaptive survival trials and consists of two major parts. In the first part fixed sample size, sequential and adaptive testing methods are derived that utilize data from a survival as well as a categorical surrogate endpoint in a fully non-parametric way without the need to assume any type of proportional hazards. In the second part extensions to quality-adjusted survival endpoints are discussed. In existing adaptive methods for confirmatory survival trials with flexible adaptation rules strict type-I-error control is only ensured if the interim decisions are based solely on the primary endpoint. In trials with long-term follow-up it is often desirable to base interim decisions also on correlated short-term endpoints, such as a surrogate marker. Surrogate information available at the interim analysis may be used to predict future event times. If interim decisions, such as selection of a subgroup or changes to the recruitment process, depend on this information, control of the type-I-error is no longer formally guaranteed for methods assuming an independent increments structure. In this thesis the weighted Kaplan-Meier estimator, a modification of the classical Kaplan-Meier estimator incorporating discrete surrogate information, is used to construct a non-parametric test statistic for the comparison of survival distributions, a generalization of the average hazard ratio. It is shown in this thesis how this test statistic can be used in fixed design, group-sequential and adaptive trials, such that the type-I-error is controlled. Asymptotic normality of the multivariate average hazard ratio is first verified in the fixed sample size context and then applied to noninferiority testing in a three-arm trial with non-proportional hazards survival data. In the next step the independent increments property is shown to hold asymptotically for the weighted Kaplan-Meier estimator. Consequently, for all test statistics based on it. Standard methods for the calculation of group-sequential rejection boundaries are applicable. For adaptive designs the weighted Kaplan-Meier estimator is modified to support stage-wise left-truncated and right-censored data to ensure independence of the stage-wise test statistics, even when interim decisions are based on surrogate information. Standard combination test methodology can then be used to ensure strict type-I-error control. Quality-adjusted survival is an integrated measure of quality-of-life data, which has gained interest in recent years. In this thesis a novel non-parametric two-sample test for quality-adjusted survival distributions is developed, that allows adjustment for covariate-dependent censoring, whereby the censoring is assumed to follow a proportional hazards model. It is shown how this result can be used to design adaptive trials with a quality-adjusted survival endpoint.