Sample Size Requirements for the Log-Rank and Gehan–Wilcoxon Tests Under Censoring: A Simulation Study

Sammanfattning

Survival analysis is widely used to compare time-to-event outcomes, but the perfor- mance of commonly used tests can be compromised in small samples and under censoring. This thesis investigates the sample size requirements for the log-rank test and Gehan’s test to achieve control of the Type I error rate and adequate power under varying censor- ing structures. A Monte Carlo simulation study was conducted in which survival data were generated from exponential and Weibull distributions under different censoring proportions and patterns. Test performance was evaluated using empirical Type I error rates and statisti- cal power, and minimum sample size thresholds were found. The results show that required sample sizes are primarily driven by the hazard ratio and the number of observed events, with censoring proportion having a substantial impact. In contrast, censoring pattern and survival distribution have limited influence in this set-up. Gehan’s test shows more stable Type I error behavior, while the log-rank test generally achieves slightly higher power. For moderate group differences, about 200 observations per group are sufficient, whereas 50 to 100 are adequate for larger effects. Overall, ensuring enough observed events is more important than the choice of test when proportional hazards hold.