Proportional hazards analysis for survival data and some alternative approaches

Clinical trials designed to compare treatments often employ a Cox Proportional Hazards (PH) model for the analysis of survival data. Typically, a treatment group indicator is used as an explanatory variable in the model (possibly with other variables which affect survival prognosis) and the hazard ratio between treatment groups is calculated and reported, together with an estimated confidence interval. This is often accompanied by a test of the hypothesis 'no treatment effect' using the log-rank test, together with plots of the estimated survival functions for each group.Several authors have noted that this style of analysis may not be appropriate in all cases where it is used. In particular, the hazard ratio may provide an over-simplified summary of the treatment effect where the assumption of proportional hazards does not hold, while the log-rank test is known to be less powerful in cases where the estimated survival functions cross.After a general introduction to survival data, the Cox model, and other techniques commonly used in survival analysis, this report examines criticisms of the indiscriminate use of the Cox model hazard ratio and log-rank test, and some alternative approaches proposed by Royston & Parmar. In particular, their 'joint' and 'combined' tests for treatment effect are examined. Aalen's linear regression model is introduced as an alternative model for survival data which does not require the PH assumption, and its interpretation is discussed. Illustrative examples are given, using data collected for a randomized trial to compare different treatment regimes for advanced ovarian cancer.