A modified log rank test for highly stratified data

Clinical trials often employ a stratified randomization so that treatment arms are balanced within prognostic factors. In these circumstances the use of the ordinary log rank test for comparing treatment groups with respect to survival is invalid. The stratified log rank test, although valid, loses efficiency as the number of strata increases. This paper proposes a modified log rank test that is fully efficient when there is no strata effect and is more efficient than the stratified log rank test when the number of strata is large. Furthermore, the test has been designed so as to remain valid when the censoring pattern depends on the treatment group as it would in a historically controlled study.