Empirical power comparison of statistical tests in contemporary phase III randomized controlled trials with time-to-event outcomes in oncology

Abstract

Background: More than 95% of recent cancer randomized controlled trials used the log-rank test to detect a treatment difference making it the predominant tool for comparing two survival functions. As with other tests, the log-rank test has both advantages and disadvantages. One advantage is that it offers the highest power against proportional hazards differences, which may be a major reason why alternative methods have rarely been employed in practice. The performance of statistical tests has traditionally been investigated both theoretically and numerically for several patterns of difference between two survival functions. However, to the best of our knowledge, there has been no attempt to compare the performance of various statistical tests using empirical data from past oncology randomized controlled trials. So, it is unknown whether the log-rank test offers a meaningful power advantage over alternative testing methods in contemporary cancer randomized controlled trials. Focusing on recently reported phase III cancer randomized controlled trials, we assessed whether the log-rank test gave meaningfully greater power when compared with five alternative testing methods: generalized Wilcoxon, test based on maximum of test statistics from multiple weighted log-rank tests, difference in t-year event rate, and difference in restricted mean survival time with fixed and adaptive $\tau$.

Methods: Using manuscripts from cancer randomized controlled trials recently published in high-tier clinical journals, we reconstructed patient-level data for overall survival (69 trials) and progression-free survival (54 trials). For each trial endpoint, we estimated the empirical power of each test. Empirical power was measured as the proportion of trials for which a test would have identified a significant result (p value < .05).

Results: For overall survival, t-year event rate offered the lowest (30.4%) empirical power and restricted mean survival time with fixed $\tau$ offered the highest (43.5%). The empirical power of the other types of tests was almost identical (36.2%-37.7%). For progression-free survival, the tests we investigated offered numerically equivalent empirical power (55.6%-61.1%). No single test consistently outperformed any other test.

Conclusion: The empirical power assessment with the past cancer randomized controlled trials provided new insights on the performance of statistical tests. Although the log-rank test has been used in almost all trials, our study suggests that the log-rank test is not the only option from an empirical power perspective. Near universal use of the log-rank test is not supported by a meaningful difference in empirical power. Clinical trial investigators could consider alternative methods, beyond the log-rank test, for their primary analysis when designing a cancer randomized controlled trial. Factors other than power (e.g. interpretability of the estimated treatment effect) should garner greater consideration when selecting statistical tests for cancer randomized controlled trials.

Keywords: Hazard ratio; log-rank test; restricted mean survival time; survival data analysis; weighted log-rank test.