Additive hazards Markov regression models illustrated with bone marrow transplant data
1 Centocor, Inc., 200 Great Valley Parkway, Mailstop C-4-1, Malvern, Pennsylvania 19355, U.S.A yshu{at}cntus.jnj.com, 2 Division of Biostatistics, Medical College of Wisconsin, Milwaukee, Wisconsin 53226, U.S.A. klein{at}mcw.edu
When there are covariate effects to be considered, multi-state survival analysis is dominated either by parametric Markov regression models or by semiparametric Markov regression models using Cox's (1972) proportional hazards models for transition intensities between the states. The purpose of this research work is to study alternatives to Cox's model in a general finite-state Markov process setting. We shall look at two alternative models, Aalen's (1989) nonparametric additive hazards model and Lin & Ying's (1994) semiparametric additive hazards model. The former allows the effects of covariates to vary freely over time, while the latter assumes that the regression coefficients are constant over time. With the basic tools of the product integral and the functional delta-method, we present an estimator of the transition probability matrix and develop the large-sample theory for the estimator under each of these two models. Data on 1459 HLA identical sibling transplants for acute leukaemia from the International Bone Marrow Transplant Registry serve as illustration.
Key Words: Additive hazards; Additive risk; Bone marrow transplant; Markov regression model; Multi-state model; Multi-state survival analysis; Product integral
Received January 2003. Revised October 2004.