On model specification and selection of the Cox proportional hazards model

Prognosis plays a pivotal role in patient management and trial design. A useful prognostic model should correctly identify important risk factors and estimate their effects. In this article, we discuss several challenges in selecting prognostic factors and estimating their effects using the Cox proportional hazards model. Although a flexible semiparametric form, the Cox's model is not entirely exempt from model misspecification. To minimize possible misspecification, instead of imposing traditional linear assumption, flexible modeling techniques have been proposed to accommodate the nonlinear effect. We first review several existing nonparametric estimation and selection procedures and then present a numerical study to compare the performance between parametric and nonparametric procedures. We demonstrate the impact of model misspecification on variable selection and model prediction using a simulation study and an example from a phase III trial in prostate cancer.