Inference for Sub-survival Functions Under Order Restrictions

We consider the competing risks problem with two risks and when the data are grouped or discrete. We firstly obtain nonparametric maximum likelihood estimates of the sub-survival functions corresponding to the two risks under the restriction that they are uniformly ordered and then use them to derive the likelihood ratio statistic for testing the null hypothesis of equality of the two sub-survival functions against ordered alternatives. The asymptotic null distribution of the test statistic is seen to be of the chi-bar square (χ̄2) type. A simulation study has been performed to compare the power of the new test with an existing one. AMS 1980 Subject Classification: Primary: 62G10, 62G05; Secondary: 62E20, 62N06 Some key words and phrases: Isotonic regression, cause specific hazard rates, competing risks, two-sample problem. 1