Regression Models and the Analysis of Censored Survival Data

A problem which frequently arises in the analysis of censored survival data in medical statistics is that of obtaining treatment comparisons while adjusting for and evaluating the effects of many uncontrolled independent variables. Recent interest in this area has centred around the use of non-linear regression models which assume that independent variables affect the hazard function in a multiplicative way. A non-parametric and several parametric models of this type have been proposed in the literature. These models, with extensions which stratify according to the independent variables to incorporate situations where the proportional hazards assumption is violated, are discussed and associated methods of inference presented Results, in the single independent variable case, concerning the efficiency of inferences based on the non-parametric model when the true model for survival time is of the exponential parametric form are extended to incorporate the within strata models and the case of two independent variables. The effect of censoring on these efficiency results is assessed using computer simulation. The important question of assessing goodness of fit to the data is considered and finally an example with data arising from a clinical trial is used to illustrate the techniques discussed in the study.