A partially grouped logrank test

We propose a modified version of the standard logrank test for survival data in which the first contribution to the statistic is based on grouping of data before a pre-selected grouping time. The grouping is accomplished by artificially constructing the first table based on the product limit estimates of the proportions surviving at the grouping time. Remaining contributions to the statistic are identical to that of the standard logrank statistic. The approach has the advantage of being uninfluenced by non-proportional hazards differences prior to the grouping time while being almost as efficient as the usual logrank test for proportional-hazards alternatives. The statistic is particularly useful for interim monitoring in situations where early difference between treatments are unimportant and/or lagged treatment effects are anticipated. We report simulation studies to verify and investigate the test's properties.