Rank tests of maximal power against Lehmann-type alternatives

The comparison, is considered of two groups of independent observations on the times of death of experimental subjects; some of the observations may be right-censored. It is assumed that censoring is applied randomly in a similar manner to all subjects. The null hypothesis is that the ratio of the death rates in the two groups is unity at all times; the Lehmann-type alternative hypothesis is that this ratio is constant but has some particular value other than unity. The rank invariant test procedures of maximal power against such alternatives are constructed, and from them the locally most powerful rank invariant test procedure is generated. In the absence of tied ranks, this is the same as the log rank test (Peto & Peto, 1972).