Cox regression in a Markov renewal model : an application to the analysis of bone marrow transplant data

Abstract We discuss estimation and prediction in a Markov renewal model where intensities of the one-step transitions follow a Cox regression model with baseline hazards and covariates depending on the backward recurrence time. A modification of the Andersen and Gill results is given to extend the asymptotic properties of the partial likelihood estimates to this setting. We further consider prediction of the realization of the process in a single individual based on the follow-up information. Data of the International Bone Marrow Transplant Registry are used for illustration purposes.

[1]  P. Brémaud.  Point processes and queues, martingale dynamics , 1983 .

[2]  Alan F. Karr,et al.  Point Processes and Their Statistical Inference , 1991 .

[3]  J P Klein,et al.  Plotting summary predictions in multistate survival models: probabilities of relapse and death in remission for bone marrow transplantation patients. , 1993, Statistics in medicine.

[4]  Niels Keiding,et al.  Non- and semi-parametric estimation of transition probabilities from censored observation of a non-homogeneous Markov process , 1991 .

[5]  N. Keiding,et al.  Survival models and martingale dynamics: original text, discussion and reply , 1989 .

[6]  Eliane Gluckman,et al.  Risk factors for chronic graft-versus-host disease after HLA-identical sibling bone marrow transplantation. , 1990 .

[7]  Odd Aalen,et al.  Nonparametric Estimation of Partial Transition Probabilities in Multiple Decrement Models , 1978 .

[8]  J. Neyman,et al.  A simple stochastic model of recovery, relapse, death and loss of patients. , 1951, Human biology.

[9]  R S Weiner,et al.  Temporal relationships between the major complications of bone marrow transplantation for leukemia. , 1989, Bone marrow transplantation.

[10]  J. Jacod.  Multivariate point processes: predictable projection, Radon-Nikodym derivatives, representation of martingales , 1975 .

[11]  Joseph G. Voelkel,et al.  Nonparametric Inference for a Class of Semi-Markov Processes with Censored Observations , 1984 .

[12]  Richard D. Gill,et al.  Nonparametric estimation based on censored observations of a Markov renewal process , 1978 .

[13]  R. Hoffmann,et al.  Risk factors for acute graft‐versus‐host disease , 1987, British journal of haematology.

[14]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data , 1980 .

[15]  Robert Peter Gale,et al.  Methotrexate, cyclosporine, or both to prevent graft-versus-host disease after HLA-identical sibling bone marrow transplants for early leukemia? , 1993 .

[16]  Klaus J. Utikal,et al.  Inference for a Nonlinear Counting Process Regression Model , 1990 .

[17]  Elja Arjas,et al.  On predictive causality in longitudinal studies , 1993 .

[18]  P. Brémaud.  Point Processes and Queues , 1981 .

[19]  Niels Keiding,et al.  Statistical Models Based on Counting Processes , 1993 .

[20]  R. Gill,et al.  Cox's regression model for counting processes: a large sample study : (preprint) , 1982 .