Analysis of interval-censored failure time data with application to studies of HIV infection

In clinical trials and cohort studies the event of interest is often not observable, and is known only to have occurred between the visit when the event was first observed and the previous visit such data are called interval-censored. This thesis develops three pieces of research that build upon published methods for interval-censored data. Novel methods are developed which can be applied via self-written macros in the standard packages, with the aim of increasing the use of appropriate methods in applied medical research. The non-parametric maximum likelihood estimator 1,2 (NPMLE) is the most common statistical method for estimating of the survivor function for interval-censored data. However, the choice of method for obtaining confidence intervals for the survivor function is unclear. Three methods are assessed and compared using simulated data and data from the MRC Delta trial 3. Non- or semi-parametric methods that correctly account for interval-censoring are not readily available in statistical packages. Typically the event time is taken to be the right endpoint of the censoring interval and standard methods (e.g. Kaplan-Meier) for the analysis of right-censored failure time data are used, giving biased estimates of the survival curve. A simulation study compared simple imputation using the right endpoint and interval midpoint to the NPMLE and a proposed smoothed version of the NPMLE that extends the work of Pan and Chappell 4. These methods were also applied to data from the CHIPS study 5. Different approaches to the estimation of a binary covariate are compared: (i) a proportional hazards model 6, (ii) a piecewise exponential model 7, (iii) a simpler proportional hazards model based on imputed event times, and (iv) a proposed approximation to the piecewise exponential model that is a more rigorous alternative to simple imputation methods whilst simple to fit using standard software