Analysis of Survival Data under the Proportional Hazards Model

Summary Methodology is reviewed for the statistical analysis of censored survival data which arise from a model in which the factors under investigation act multiplicatively on the hazard function of an underlying nonparametric survival distribution. This flexible approach provides computationally feasible solutions to the following problems: (i) one-sample problem (relative death rate); (ii) multi-sample problem; (iii) regression with continuous covariates; (iv) regression in matched-pair designs; (v) evaluation of changes in treatment or prognostic status (time dependent covariates). For the multi-sample problem with stratification, numerical results are presented contrasting maximum likelihood with simple chi-square analyses. While several of the methods described have been used on an ad hoc basis for many years, study of their common theoretical underpinnings has commenced only recently. This paper reviews a general methodology for the statistical analysis of survival or response time data such as accrue from the long-term follow-up of patients with chronic disease. The theoretical basis for this methodology is the assumption that prognostic or treatment factors under investigation have multiplicative effects on the hazard (instantaneous death rate) function of an underlying survival distribution. No particular parametric form is