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An approach to trial design and analysis in the era of non-proportional hazards of the treatment effect

Royston, P; Parmar, MKB; (2014) An approach to trial design and analysis in the era of non-proportional hazards of the treatment effect. Trials , 15 (1) 10.1186/1745-6215-15-314. Green open access

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Abstract

Background: Most randomized controlled trials with a time-to-event outcome are designed and analysed under the proportional hazards assumption, with a target hazard ratio for the treatment effect in mind. However, the hazards may be non-proportional. We address how to design a trial under such conditions, and how to analyse the results. Methods: We propose to extend the usual approach, a logrank test, to also include the Grambsch-Therneau test of proportional hazards. We test the resulting composite null hypothesis using a joint test for the hazard ratio and for time-dependent behaviour of the hazard ratio. We compute the power and sample size for the logrank test under proportional hazards, and from that we compute the power of the joint test. For the estimation of relevant quantities from the trial data, various models could be used; we advocate adopting a pre-specified flexible parametric survival model that supports time-dependent behaviour of the hazard ratio. Results: We present the mathematics for calculating the power and sample size for the joint test. We illustrate the methodology in real data from two randomized trials, one in ovarian cancer and the other in treating cellulitis. We show selected estimates and their uncertainty derived from the advocated flexible parametric model. We demonstrate in a small simulation study that when a treatment effect either increases or decreases over time, the joint test can outperform the logrank test in the presence of both patterns of non-proportional hazards. Conclusions: Those designing and analysing trials in the era of non-proportional hazards need to acknowledge that a more complex type of treatment effect is becoming more common. Our method for the design of the trial retains the tools familiar in the standard methodology based on the logrank test, and extends it to incorporate a joint test of the null hypothesis with power against non-proportional hazards. For the analysis of trial data, we propose the use of a pre-specified flexible parametric model that can represent a time-dependent hazard ratio if one is present.

Type: Article
Title: An approach to trial design and analysis in the era of non-proportional hazards of the treatment effect
Open access status: An open access version is available from UCL Discovery
DOI: 10.1186/1745-6215-15-314
Publisher version: http://dx.doi.org/10.1186/1745-6215-15-314
Language: English
Additional information: © 2014 Royston and Parmar; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. 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.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Population Health Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Population Health Sciences > Inst of Clinical Trials and Methodology
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Population Health Sciences > Inst of Clinical Trials and Methodology > MRC Clinical Trials Unit at UCL
URI: https://discovery.ucl.ac.uk/id/eprint/1443522
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