The efficiency of a weighted log-rank test under a percent error misspecification model for the log hazard ratio

For comparison of two survival distributions, it is natural to use a weighted log-rank test with weight function given by the log hazard ratio function that is anticipated a priori. This paper investigates the efficiency of this test when the a priori estimate of the log hazard ratio is subject to a specified percentage error. The test is shown to be the maximin efficiency robust test over the class of alternatives in question and a simple expression for the maximin efficiency is established.