Keywords: AFT violation, Conditional hazard estimation, PH violation, Nonparametric inference
In many clinical applications of survival analysis with covariates, the commonly used semiparametric models, e.g., proportional hazards (PH), proportional odds (PO), accelerated failure time (AFT) etc. may turn out to be stringent and unrealistic, particularly when there is scientific background to believe that survival curves under different covariate combinations will cross during the study period. This talk presents a relatively new class of nonparametric regression models for the conditional hazard function. The new methodology has three key features: (i) the smooth estimator of the conditional hazard rate is shown to be a unique solution of a strictly convex optimization problem for a wide range of applications; making it computationally attractive, (ii) the model is shown to encompass a proportional hazards structure, and (iii) large sample properties including consistency and convergence rates are established under a set of mild regularity conditions. Empirical results based on several simulated data scenarios indicate that the proposed model has reasonably robust performance compared to other semiparametric models particularly when such semiparametric modeling assumptions are violated. Real case studies are also illustrated using data from several well-known clinical trails.