Utility of Generalized Hazards Model Incorporating Cubic B-spline Function into the Baseline Hazard Function

Abstract

A generalized hazards model incorporating a cubic B-spline function into the baseline hazard function (GHMBS) was proposed as a model for estimating covariate effects in survival data analysis. The GHMBS integrated the three types of hazard models: the proportional hazards model (PHM), accelerated failure time model (AFTM), and accelerated hazards model (AHM), which enabled the likelihood principle for estimation and hypothesis testing to be applied irrespective of submodels (i.e., PHM, AFTM, and AHM). A procedure for adaptively choosing suitable knots from a set of candidate knots was proposed in order to actualize an appropriate baseline hazard function in GHMBS. The characteristic of the proposal was evaluated with bias and mean squared error of the estimation of covariate effects through a Monte-Carlo simulation experiment. A method for identifying a submodel appropriate for the data to be analyzed was also proposed based on GHMBS. The performance of the proposed model selection method was evaluated with the probability of selecting the true model through a Monte-Carlo simulation experiment based on PHM and AFTM. As a result, the proposed method achieved fairly high probabilities of identifying the true model. An application of the proposed method to actual data in a clinical trial provided a reasonable conclusion.