Marginal Methods for Multivariate Time to Event Data

Abstract

This thesis considers a variety of statistical issues related to the design and analysis of clinical trials involving multiple lifetime events. The use of composite endpoints, multivariate survival methods with dependent censoring, and recurrent events with dependent termination are considered. Much of this work is based on problems arising in oncology research.

Composite endpoints are routinely adopted in multi-centre randomized trials designed to evaluate the effect of experimental interventions in cardiovascular disease, diabetes, and cancer. Despite their widespread use, relatively little attention has been paid to the statistical properties of estimators of treatment effect based on composite endpoints. In Chapter 2 we consider this issue in the context of multivariate models for time to event data in which copula functions link marginal distributions with a proportional hazards structure. We then examine the asymptotic and empirical properties of the estimator of treatment effect arising from a Cox regression model for the time to the first event. We point out that even when the treatment effect is the same for the component events, the limiting value of the estimator based on the composite endpoint is usually inconsistent for this common value. The limiting value is determined by the degree of association between the events, the stochastic ordering of events, and the censoring distribution. Within the framework adopted, marginal methods for the analysis of multivariate failure time data yield consistent estimators of treatment effect and are therefore preferred. We illustrate the methods by application to a recent asthma study.

While there is considerable potential for more powerful tests of treatment effect when marginal methods are used, it is possible that problems related to dependent censoring can arise. This happens when the occurrence of one type of event increases the risk of withdrawal from a study and hence alters the probability of observing events of other types. The purpose of Chapter 3 is to formulate a model which reflects this type of mechanism, to evaluate the effect on the asymptotic and finite sample properties of marginal estimates, and to examine the performance of estimators obtained using flexible inverse probability weighted marginal estimating equations. Data from a motivating study are used for illustration.

Clinical trials are often designed to assess the effect of therapeutic interventions on occurrence of recurrent events in the presence of a dependent terminal event such as death. Statistical methods based on multistate analysis have considerable appeal in this setting since they can incorporate changes in risk with each event occurrence, a dependence between the recurrent event and the terminal event and event-dependent censoring. To date, however, there has been limited methodology for the design of trials involving recurrent and terminal events, and we addresses this in Chapter 4. Based on the asymptotic distribution of regression coefficients from a multiplicative intensity Markov regression model, we derive sample size formulae to address power requirements for both the recurrent and terminal event processes. Superiority and non-inferiority trial designs are dealt with. Simulation studies confirm that the designs satisfy the nominal power requirements in both settings, and an application to a trial evaluating the effect of a bisphosphonate on skeletal complications is given for illustration.