Prognostic Factors and Predictions of Survival Data Using Cox PH Models and Random Survival Forest Approaches

Abstract

Survival outcome has been one of major endpoints for clinical trials; it gives information on the probability of time-to-event of interest. Recently, there has been increasing demands for survival analysis tools, especially for high dimensional survival data. Most of the classical statistical approaches including nonparametric, semi-parametric and complete parametric models, have limitations. Typical nonparametric approaches, such as the logrank (or Cox-Mantel) test, do not have stringent models assumptions, but can only deal with a limited number of categorical predictors. Typical semi-parametric approaches, such as Cox proportional hazard (PH) model, have stringent model assumptions, such as linearity, interactions and proportionality; and they can only deal a limited number of predictors. Complete parametric models, such as accelerated failure time models, are similar to semi-parametric models except that they make further assumptions about the baseline hazard function. In this paper, non-parametric random survival forest approaches were introduced with many advantages over typical nonparametric, semi-parametric or parametric approaches. They have very no model assumptions and can deal with many more predictors than typical survival models. Two Cox PH models were evaluated and the model performances were compared with the random survival forest models based on a simulation study. Additionally, the random survival forest approaches were further studied based on a real world case study, which included more predictors then a typical Cox PH model can handle.