Asymptotically Efficient Rank Invariant Test Procedures

Asymptotically efficient rank invariant test procedures for detecting differences between two groups of independent observations are derived. These are generalized to test between two groups of independent censored observations, to test between many groups of observations, and to test between groups after allowance for the effects of .concomitant variables.

One of these test procedures—the logrank—is particularly appropriate for comparing life tables, and can therefore be used in the analysis of clinical trials, industrial life-testing experiments and laboratory studies of animal carcinogenesis. It has greater local power than any other rank-invariant test procedure for detecting Lehmann-type differences between groups of independent observations subject to some right-censoring. The logrank test, although a rank test, can be presented in a format which exhibits the physical significance as well as the statistical significance of any important differences between groups of events.