LIKELIHOOD-BASED INFERENCE FOR CAUSE-SPECIFIC HAZARD RATES UNDER ORDER RESTRICTIONS

We consider the competing risks model with grouped data or with discre te Failure times where a unit is exposed to several risks, but its eve ntual failure is due to exactly one of the causes. Nonparametric maxim um likelihood estimates of the cause specific hazard rates are obtaine d under the restriction that these risks are uniformly ordered. We all ow for random censoring. Unlike most papers on this topic, no assumpti on is made about the independence of the various risks, although we do assume that the censoring mechanism is acting independently of the li fe distribution. We derive the likelihood ratio statistic for testing the null hypothesis of equality of cause specific hazard rates against ordered alternatives. The asymptotic null distribution of the test st atistic is seen to be of the chi-bar squared (($) over bar chi(2)) typ e. The procedures developed here are illustrated with the help of an e xample involving survival rates for mice exposed to radiation. (C) 199 4 Academic Press, Inc.