UC Irvine

Analysis of time-to-event data using Cox's proportional hazards model is ubiquitous in scientific research. Most commonly, a sample is taken from the population of interest and covariate information is collected on everyone. If the event of interest is rare and it is difficult or not feasible to collect full covariate information for all study participants, the nested case-control design reduces costs with minimal impact on inferential precision. However, no work has been done to investigate the performance of the nested case-control design under model mis-specification. In this dissertation we show that under model mis-specification the quantity being estimated under the nested case-control design will depend not only on the censoring distribution, but also on the number of controls sampled at each event time. This is true in the case of a binary covariate when the proportional hazards assumption is not satisfied, and in the case of a continuous covariate where the functional form is mis-specified. We propose several estimators that allow us to recover the statistic that would have been computed under the full cohort data as well as a censoring-robust estimator. We also investigate the performance of time-dependent receiver operating characteristic curves under the full cohort and nested case-control sampling scenarios. We show that if the risk score model is mis-specified, estimates of the area under the curve will also depend on the censoring distribution and we propose the use of censoring-robust risk scores that allow us to recover censoring-independent area under