An omnibus test for several hazard alternatives in prevention randomized controlled clinical trials

The logrank test is optimal for testing the equality of survival distributions against a proportional hazards alternative. Under a late effects alternative, it is no longer appropriate, and one may turn to Fleming-Harrington's class of weighted logrank tests instead. In some settings, such as in preventive clinical trials where the statistical analysis has to be designed before the trial begins, it can be difficult to choose a priori between the logrank and Fleming-Harrington tests. A solution to this issue is provided. A decision rule is constructed for the problem of testing the equality of two survival distributions when the expected alternative may be one of the proportional hazards and late effects. A formula for computing the necessary sample size is obtained for this decision rule. A comprehensive simulation study is conducted to assess finite sample properties of the proposed test statistic. The proposed test improves both the logrank test and Fleming-Harrington's test for late effects. Finally, the methodology is illustrated on a data set in the field of prevention of Alzheimer's disease.