Power and sample-size analysis for the Royston–Parmar combined test in clinical trials with a time-to-event outcome
Patrick Royston
MRC Clinical Trials Unit
University College London
London, UK
[email protected]
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Abstract. Randomized controlled trials with a time-to-event outcome are usually designed
and analyzed assuming proportional hazards (PH) of the treatment effect. The
sample-size calculation is based on a log-rank test or the nearly identical Cox
test, henceforth called the Cox/log-rank test. Nonproportional hazards (non-PH)
has become more common in trials and is recognized as a potential threat to
interpreting the trial treatment effect and the power of the log-rank
test—hence to the success of the trial. To address the issue, in 2016,
Royston and Parmar (BMC Medical Research Methodology 16: 16) proposed a
"combined test" of the global null hypothesis of identical survival curves in
each trial arm. The Cox/logrank test is combined with a new test derived from
the maximal standardized difference in restricted mean survival time (RMST)
between the trial arms. The test statistic is based on evaluations of the
between-arm difference in RMST over several preselected time points. The
combined test involves the minimum p-value across the Cox/log-rank and
RMST-based tests, appropriately standardized to have the correct distribution
under the global null hypothesis. In this article, I introduce a new command,
power_ct, that uses simulation to implement power and sample-size
calculations for the combined test. power_ct supports designs with PH or
non-PH of the treatment effect. I provide examples in which the power of the
combined test is compared with that of the Cox/log-rank test under PH and
non-PH scenarios. I conclude by offering guidance for sample-size calculations
in time-to-event trials to allow for possible non-PH.
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Patrick Royston
View all articles with these keywords:
power_ct, randomized controlled trial, time-to-event outcome, restricted mean survival time, log-rank test, Cox test, combined test, treatment effect, hypothesis testing, flexible parametric model
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