Likelihood based inference for cause specific hazard rates under order restrictions
We consider the competing risks model with grouped data or with discrete failure times where a unit is exposed to several risks, but its eventual failure is due to exactly one of the causes. We assume a discrete-time framework and allow for independent random censoring on the right. We obtain maximum likelihood estimates (MLEs) of the cause specific hazard rates under the various alternatives. The restricted maximum likelihood estimators of the cause specific hazard rates under \(H_1\) can be computed by finding the isotonic regression of the usual estimates across risks. This will be discussed in Section 2. In Section 3 we derive a likelihood ratio test for testing \(H_0\) versus \(H_1 - H_0\) and obtain the asymptotic null distribution of the test statistic. This asymptotic test is distribution-free and its null distribution is found to be of the chi-bar squared type. Finally, in the last section, the procedures are illustrated with the help of a data set involving survival rates for mice exposed to radiation.
restricted maximum likelihood estimators
scientific article; zbMATH DE number 797147