Sample size requirements for comparing time-to-failure among k treatment groups

Clinical trials are commonly undertaken to compare three or more treatment groups. In this paper sample size requirements are provided for the k group comparative clinical trial in which time-to-failure is the measure of treatment efficacy. Time-to-failure is assumed to have an exponential distribution and so these results generalize those of George and Desu. When the alternative hypothesis specifies only the magnitude of the largest difference among the treatment groups, a particularly simple expression is obtained. It is shown that heuristic use of sample size formulae or tables for comparing two treatment groups is not adequate for obtaining sufficient power and properly accounting for the multiple comparisons possible with k greater than or equal to 3 treatment groups.