Estimation of the distribution of time to first event in a composite endpoint from interval censored observations with incomplete non-fatal event status

In many clinical trials individuals are intermittently assessed for the occurrence of a disease-related non-fatal event and death. Estimation of the distribution of non-fatal event-free survival time, that is, the time to the first occurrence of the non-fatal event or death, is the primary focus of the data analysis, leading to tests of equality of the estimated distribution functions for independent groups of observations. A complication in the usual estimation procedures is that the intermittent assessment of individuals results in two types of incomplete data. First, the occurrence times of observed non-fatal events are not known exactly, or are interval-censored. Second, when non-fatal events have not occurred prior to the last study assessment, the non-fatal event status for an individual is unknown from the last assessment time until the end of follow-up for death. In this thesis, two different methods are proposed and developed to simultaneously address both forms of incompleteness. The first is in the framework of Markov illness-death models to obtain nonparametric maximum likelihood estimators of the model parameters. The second method involves a multiple imputation procedure to account for incomplete non-fatal event status. The performance of the proposed methods are examined under a range of assumptions that include differing proportions of observations known to have an event in the complete data, varying quantities of incomplete data and varying levels of association between non-fatal and fatal events. These methods are applied to simulated data sets that would be typical of long term clinical trials with multiple endpoints. Performance of the methods using estimated mean biases, estimated standard errors, and coverage of estimated nominal 95% confidence intervals. The proposed methods are also applied the data from a recently reported cardiovascular clinical trial (Schwartz et al., 2001). In this illustration, estimation results for the proposed methods are compared against several methods where both forms of incompleteness are not formally accounted for in the analysis. The impact of the different estimation methods on the statistical significance of tests of equality of the estimated treatment group distribution functions is also documented.