Application of a hazard-based visual predictive check to evaluate parametric hazard models

Parametric models used in time to event analyses are evaluated typically by survival-based visual predictive checks (VPC). Kaplan-Meier survival curves for the observed data are compared with those estimated using model-simulated data. Because the derivative of the log of the survival curve is related to the hazard--the typical quantity modeled in parametric analysis--isolation, interpretation and correction of deficiencies in the hazard model determined by inspection of survival-based VPC's is indirect and thus more difficult. The purpose of this study is to assess the performance of nonparametric hazard estimators of hazard functions to evaluate their viability as VPC diagnostics. Histogram-based and kernel-smoothing estimators were evaluated in terms of bias of estimating the hazard for Weibull and bathtub-shape hazard scenarios. After the evaluation of bias, these nonparametric estimators were assessed as a method for VPC evaluation of the hazard model. The results showed that nonparametric hazard estimators performed reasonably at the sample sizes studied with greater bias near the boundaries (time equal to 0 and last observation) as expected. Flexible bandwidth and boundary correction methods reduced these biases. All the nonparametric estimators indicated a misfit of the Weibull model when the true hazard was a bathtub shape. Overall, hazard-based VPC plots enabled more direct interpretation of the VPC results compared to survival-based VPC plots.