Effect of unequal censoring on the size and power of the logrank and Wilcoxon types of tests for survival data

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Abstract
This paper examines the effect of random unequal censoring on the size and power of two‐sample logrank and Wilcoxon types of tests for comparing two survival distributions by simulation with small samples from censored exponential distributions. We compared equal‐sized samples of n = 8, 16, and 32 with 1000 (size) and 500 (power) simulation trials for 16 combinations of the censoring proportions of 0, 20, 40, and 60 per cent in each of the two samples. For n = 8, the asymptotic normality (AN), Peto‐Peto, and the two Wilcoxon‐type tests performed at nominal 5 per cent size expectations, but the Mantel test exceeded the 5 per cent size acceptance region in 6 of 16 censoring combinations. For n = 16 and 32, all tests showed proper size, with the Peto‐Peto test being most conservative in the presence of unequal censoring. We compared powers of all tests for exponential hazard ratios of 1·4 and 2·0. The Mantel test showed 90 to 95 per cent power efficiency relative to the parametric AN test. Both Wilcoxon tests performed identically and had the lowest relative power of all tests examined but appeared most robust to the differential censoring patterns studied. A modified version of the Peto‐Peto test showed power comparable to the Mantel test.