Comparative Study of Burr-XII Nested Hazard Models: Simulation under Mixed Directional Effects and AML Data Analysis

Abstract

Choosing an appropriate hazard-based regression model is critical in survival analysis. The proportional hazards (PH), accelerated failure time (AFT), and accelerated hazard (AH) models make distinct assumptions about covariate effects, yet real data often violate these assumptions. The general hazard (GH) model nests all three frameworks, allowing both time-scale and hazard-scale effects within a single structure. This paper presents a comparative study of the four nested models (PH, AFT, AH, GH) using the three-parameter Burr XII baseline hazard. Extensive simulations under ten scenarios, including both positive and negative covariate effects, evaluate maximum likelihood estimators via bias, standard errors, mean squared error, coverage probability, and information criteria. Sample sizes of 1000 and 5000 with 20% and 40% censoring are considered. A dedicated simulation examines the recovery of increasing, decreasing, and unimodal hazard shapes. Results show that the GH model consistently recovers the true data-generating structure and all three hazard patterns. The GH model yields the lowest information criterion values among its submodels, supporting its utility as a data-driven model selection tool. Practical relevance is illustrated using real survival data from 801 acute myeloid leukemia (AML) patients who received allogeneic stem cell transplantation. This comparative framework offers applied researchers a systematic, evidence‑based approach to select the most appropriate hazard structure for right-skewed, heavily censored survival data.