A log rank test for clustered data with informative within-cluster group size

The log rank test is a popular nonparametric test for comparing survival distributions among groups. When data are organized in clusters of potentially correlated observations, adjustments can be made to account for within-cluster dependencies among observations, eg, tests derived from frailty models. Tests for clustered data can be further biased when the number of observations within each cluster and the distribution of groups within cluster are correlated with survival times, phenomena known as informative cluster size and informative within-cluster group size. In this manuscript, we develop a log rank test for clustered data that adjusts for the potentially biasing effect of informative cluster size and within-cluster group size. We provide the results of a simulation study demonstrating that our proposed test remains unbiased under cluster-based informativeness, while other candidate tests not accounting for the clustering structure do not properly maintain size. Furthermore, our test exhibits power advantages under scenarios in which traditional tests are appropriate. We demonstrate an application of our test by comparing time to functional progression between groups defined initial functional status in a spinal cord injury data set.