Approximating the powers of order-restricted log rank tests at local alternatives

Under a proportional hazards model with continuous, right-censored data, tests of homogeneity with order-restricted alternatives are considered for survival curves. For such situations, analogues to the log rank test have been derived by applying order-restricted inference procedures to the score statistics. For local alternatives, approximations to the power functions of these tests are obtained by relating them to the likelihood ratio tests of homogeneity of normal means with order-restricted alternatives. The accuracies of the approximations are studied using Monte Carlo techniques for the simple order and the simple tree order restrictions.