×

Estimation of parameters in a general hazard regression change-point model. (English) Zbl 1462.62668

Summary: Covariates or explanatory variables play a very important role in medical studies. For instance, there have been quite a many discussions in the literature on the impact of French American British (FAB) sub types on the prognosis of acute myelocytic leukemia (AML) patients post bone marrow transplant. To study such phenomena, in this paper, we propose a general hazard regression change-point model, wherein the impact of covariate on the life time starts only after an unknown point of time, referred to as a change-point. The model has a baseline hazard function \(h(x,\theta)\) which is an arbitrary function, however, it depends on an unknown parameter \(\theta\), called the model parameter. To account for the impact of covariate, we take a particular link function with the unknown regression parameter. Maximum likelihood estimators (MLEs) of the model parameter, regression parameter, and the change-point, under right censoring, are obtained by using a stepwise maximization procedure. The proposed estimation method is illustrated for two specific models and simulation study is carried out to evaluate the performance of the estimators. The proposed model (3.7) is applied to bone marrow transplant data for AML patients and the model gives a very good fit to the data. The analysis indicates that the risk of death or relapse for the patients with FAB sub type of M4 and M5, is higher than that of other types beyond 31 days of transplantation, which in a sense supports an earlier remark regarding this by J. P. Klein and M. L. Moeschberger [Survival analysis. Techniques for censored and truncated data. 2nd ed. New York, NY: Springer (2003; Zbl 1011.62106)]. Further, preference to change-point model and change-point being 31 days are statistically validated using the likelihood ratio tests (LRTs).

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62J02 General nonlinear regression
62N01 Censored data models

Citations:

Zbl 1011.62106
PDFBibTeX XMLCite
Full Text: Link