EVALUATION OF LONG-TERM SURVIVAL - USE OF DIAGNOSTICS AND ROBUST ESTIMATORS WITH COXS PROPORTIONAL HAZARDS MODEL

We consider methodological problems in evaluating long-term survival i n clinical trials. In particular we examine the use of several methods that extend the basic Cox regression analysis. In the presence of a l ong term observation, the proportional hazard (PH) assumption may easi ly be violated and a few long term survivors may have a large effect o n parameter estimates. We consider both model selection and robust est imation in a data set of 474 ovarian cancer patients enrolled in a cli nical trial and followed for between 7 and 12 years after randomizatio n, Two diagnostic plots for assessing goodness-of-fit are introduced. One shows the variation in time of parameter estimates and is an alter native to PH checking based on time-dependent covariates. The other ta kes advantage of the martingale residual process in time to represent the lack of fit with a metric of the type 'observed minus expected' nu mber of events. Robust estimation is carried out by maximizing a weigh ted partial likelihood which downweights the contribution to estimatio n of influential observations. This type of complementary analysis of long-term results of clinical studies is useful in assessing the sound ness of the conclusions on treatment effect, In the example analysed h ere, the difference in survival between treatments was mostly confined to those individuals who survived at least two years beyond randomiza tion.