The current research focuses on the analysis of discrete-time data arising from periodic follow-up using discrete-time hazard models (analogs to the Cox proportional hazards model) when the model is misspecified. We begin by providing scientific examples that motivate the present research and provide some background and notation that lays the foundation for the remainder of the dissertation. We then describe methods for analyzing grouped proportional hazards data, and present simulation results to convey their relative performances.
Focusing on discrete hazard models for analyzing grouped survival data, we then explore the impact of model misspecification, namely a time-varying treatment effect, on the maximum likelihood (ML) estimator of commonly used discrete-time models in the two-sample setting (e.g., clinical trials). We show that the ML estimator is consistent to a quantity that depends on the censoring pattern of the observations and the maximum follow-up time of the study. We propose a censoring-robust estimator that removes the influence of censoring by re-weighing observations based on the inverse of the Kaplan-Meier estimator of the censoring times for each group and derive its asymptotic distribution. Simulation is used to compare the two estimators in different scenarios and the proposed estimator is applied to data from clinical trial in HIV/AIDS.
Next, we describe how robust inference can be extended to the observational study setting where multiple (possibly continuous) covariates are involved. In this setting, we rely on survival trees to identify group-specific censoring to aid in the estimation of the censoring distribution.
Finally, we explore the use of the censoring-robust estimator in an interim testing context that is typical of late stage clinical trials. To that end, we derive the joint asymptotic distribution of the censoring-robust estimator calculated over time. We note that the estimating equation of the censoring-robust estimator lacks an independent increments structure, rendering standard group sequential methods inapplicable. We then propose a strategy for designing and evaluating group sequential trials based on the censoring-robust estimator using existing pilot data.
|Advisor:||Gillen, Daniel L.|
|Commitee:||Johnson, Wesley O., Stern, Hal S.|
|School:||University of California, Irvine|
|Department:||Statistics - Ph.D.|
|School Location:||United States -- California|
|Source:||DAI-B 73/01, Dissertation Abstracts International|
|Keywords:||Clinical trials, Discrete hazards, Discrete time, Group sequence, Interim testing, Model misspecification, Robust inference, Survival analysis|
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