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Publication Detail
Augmenting the logrank test in the design of clinical trials in which non-proportional hazards of the treatment effect may be anticipated
  • Publication Type:
    Journal article
  • Authors:
    Royston P, Parmar MKB
  • Publication date:
  • Journal:
    BMC Medical Research Methodology
  • Volume:
  • Issue:
  • Status:
  • Print ISSN:
  • Language:
  • Keywords:
    Time-to-event data, Randomized controlled trials, Hazard ratio, Restricted mean survival time, Non-proportional hazards, Logrank test, Permutation test, Design, Simulation, Flexible parametric model
  • Notes:
    © 2016 Royston and Parmar. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
© 2016 Royston and Parmar. Background: Most randomized controlled trials with a time-to-event outcome are designed assuming proportional hazards (PH) of the treatment effect. The sample size calculation is based on a logrank test. However, non-proportional hazards are increasingly common. At analysis, the estimated hazards ratio with a confidence interval is usually presented. The estimate is often obtained from a Cox PH model with treatment as a covariate. If non-proportional hazards are present, the logrank and equivalent Cox tests may lose power. To safeguard power, we previously suggested a 'joint test' combining the Cox test with a test of non-proportional hazards. Unfortunately, a larger sample size is needed to preserve power under PH. Here, we describe a novel test that unites the Cox test with a permutation test based on restricted mean survival time. Methods: We propose a combined hypothesis test based on a permutation test of the difference in restricted mean survival time across time. The test involves the minimum of the Cox and permutation test P-values. We approximate its null distribution and correct it for correlation between the two P-values. Using extensive simulations, we assess the type 1 error and power of the combined test under several scenarios and compare with other tests. We investigate powering a trial using the combined test. Results: The type 1 error of the combined test is close to nominal. Power under proportional hazards is slightly lower than for the Cox test. Enhanced power is available when the treatment difference shows an 'early effect', an initial separation of survival curves which diminishes over time. The power is reduced under a 'late effect', when little or no difference in survival curves is seen for an initial period and then a late separation occurs. We propose a method of powering a trial using the combined test. The 'insurance premium' offered by the combined test to safeguard power under non-PH represents about a single-digit percentage increase in sample size. Conclusions: The combined test increases trial power under an early treatment effect and protects power under other scenarios. Use of restricted mean survival time facilitates testing and displaying a generalized treatment effect.
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