Parametric Cause-Specific Hazard Modeling with Nonproportional Covariate Effects: A Case Study Using Liver Transplant Data

摘要

We wanted to determine if parametric cause-specific hazard modeling, including log-linear generalizations of underlying parameters to incorporate covariate effects, would provide accurate representations, particularly with nonproportional hazards. Nonparametric cumulative hazard estimates were used for visual display. In the case study, the hazard rate of death-with-a-functioning-graft-due-to-infection following orthotopic liver transplantation (OLT) was modeled (N = 877, 82 such deaths). The three-parameter Makeham-Gompertz hazard, decreasing exponentially from time zero towards an asymptotic lower bound, and a more flexible, four-parameter mixture of generalized gamma functions (MGGF), increasing from time 0 towards a maximum value, then decreasing over time towards an asymptotic lower bound, were fitted. Both underlying hazards provided close fits, with a more accurate fit of MGGF during the first few months post-OLT. Parametric modeling of the important prognosticator donor agea??s (a?￥ 60 vs. < 60yr) disappearing effect over time was achieved using two additional parameters in each case; a similar result was obtained using Coxa??s model and a covariate by quadratic function of time interaction effect; however, Cox model fitted hazard ratios were overly inflated towards the end of the range of observed death times. In conclusion, the main lesson learned was the practicality in using a complete parametric modeling approach to better explain nonproportionality.