Accuracy of predictive ability measures for survival models

One aspect of an analysis of survival data based on the proportional hazards model that has been receiving increasing attention is that of the predictive ability or explained variation of the model. A number of contending measures have been suggested, including one measure, R² (β), which has been proposed given its several desirable properties, including its capacity to accommodate time-dependent covariates, a major feature of the model and one that gives rise to great generality. A thorough study of the properties of available measures, including the aforementioned measure, has been carried out recently. In that work, the authors used bootstrap techniques, particularly complex in the setting of censored data, in order to obtain estimates of precision. The motivation of this work is to provide analytical expressions of precision, in particular confidence interval estimates for R² (β). We use Taylor series approximations with and without local linearizing transforms. We also consider a very simple expression based on the Fisher's transformation. This latter approach has two great advantages. It is very easy and quick to calculate, and secondly, it can be obtained for any of the methods given in the recent review. A large simulation study is carried out to investigate the properties of the different methods. Finally, three well-known datasets in breast cancer, lymphoma and lung cancer research are given as illustrations. Copyright © 2017 John Wiley & Sons, Ltd.