Testing equality of survival functions based on both paired and unpaired censored data

We introduce two test procedures for comparing two survival distributions o n the basis of randomly right-censored data consisting of both paired and u npaired observations. Our procedures are based on generalizations of a pool ed rank test statistic previously proposed for uncensored data. One general ization adapts the Prentice Wilcoxon score, while the other adapts the Akri tas score. The use of these particular scoring systems in pooled rank tests with randomly right-censored paired data has been advocated Ly several res earchers. Our test procedures utilize the permutation distributions of the test statistics based on a novel manner of permuting the scores. Permutatio n versions of tests for right-censored paired data and for two independent right-censored samples that use the proposed scoring systems are obtained a s special cases of our test procedures. Simulation results show that our te st procedures have high power for detecting scale and location shifts in ex ponential and log-logistic distributions for the survival times. We also de monstrate the advantages of our test procedures in terms of utilizing rando mly occurring unpaired observations that are discarded in test procedures f or paired data. The tests are applied to skin graft data previously reporte d elsewhere.