Logrank-type tests with presmoothing.

The logrank test is the most popular choice for testing the equality of two survival distributions with time-to-event data. It is based on the comparison of the Nelson-Aalen estimates of the corresponding cumulative hazard functions. The improvements of the logrank test in the literature have been accomplished using weighted logrank tests, with the weight chosen appropriately to maximize power. Notwithstanding, power also depends on the efficiency of the estimation of the cumulative hazard function. The presmoothed estimator has been shown to be more efficient than the Nelson-Aalen estimator under some general assumptions. We introduce a new logrank-type test that, instead of the Nelson-Aalen estimator, is based on its presmoothed counterpart. An extensive simulation study has been conducted to compare the performance of this new test with the classical one. This study shows that the new test has the proper size under the null hypothesis, while improving the power over a wide range of alternatives. The new test is illustrated with several real data examples.