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Statistical analysis of right‐censored failure‐time data with partially specified hazard rates
Author(s) -
Qin Jing,
Sun Jianguo
Publication year - 1997
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315782
Subject(s) - nonparametric statistics , parametric statistics , hazard ratio , statistics , hazard , mathematics , failure rate , function (biology) , statistical hypothesis testing , econometrics , confidence interval , chemistry , organic chemistry , evolutionary biology , biology
This paper discusses the analysis of right‐censored failure‐time data in which the failure rate may have different forms in different time intervals. Such data occur naturally, for example, in demography studies and leukemia research, and a number of methods for the analysis have been proposed in the literature. However, most methods are purely parametric or nonparametric. Matthews and Farewell (1982), for example, discussed this problem and proposed a method for testing a constant failure rate against a failure rate involving a change point. To estimate an absolute limit on the attainable human life span, Zelterman (1992) discussed a hazard function that has different parametric forms over different time intervals. We consider a different situation in which the hazard function may follow a parametric form before a change point and is completely unknown after the change point. To test the existence of the change point, a modified maximal‐censored‐likelihood‐ratio test is proposed and its asymptotic properties are studied. A bootstrap method is described for finding critical values of the proposed test. Simulation results indicate that the test performs well.