Graphical displays for clarifying how allocation ratio affects total sample size for the two sample logrank test

For time-to-event data, the power of the two sample logrank test for the comparison of two treatment groups can be greatly influenced by the ratio of the number of patients in each of the treatment groups. Despite the possible loss of power, unequal allocations may be of interest due to a need to collect more data on one of the groups or to considerations related to the acceptability of the treatments to patients. Investigators pursuing such designs may be interested in the cost of the unbalanced design relative to a balanced design with respect to the total number of patients required for the study. We present graphical displays to illustrate the sample size adjustment factor, or ratio of the sample size required by an unequal allocation compared to the sample size required by a balanced allocation, for various survival rates, treatment hazards ratios, and sample size allocation ratios. These graphical displays conveniently summarize information in the literature and provide a useful tool for planning sample sizes for the two sample logrank test.