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The Smooth Away From Expected (SAFE) non-inferiority frontier: theory and implementation with an application to the D3 trial

Quartagno, Matteo; Chan, Man; Turkova, Anna; Ford, Deborah; White, Ian R; (2023) The Smooth Away From Expected (SAFE) non-inferiority frontier: theory and implementation with an application to the D3 trial. Trials , 24 (1) , Article 556. 10.1186/s13063-023-07586-5. Green open access

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Abstract

Background In a non-inferiority trial, the choice of margin depends on the expected control event risk. If the true risk differs from expected, power and interpretability of results can be affected. A non-inferiority frontier pre-specifies an appropriate non-inferiority margin for each value of control event risk. D3 is a non-inferiority trial comparing two treatment regimens in children living with HIV, designed assuming a control event risk of 12%, a non-inferiority margin of 10%, 80% power and a significance level (α) of 0.025. We consider approaches to choosing and implementing a frontier for this already funded trial, where changing the sample size substantially would be difficult. Methods In D3, we fix the non-inferiority margin at 10%, 8% and 5% for control event risks of ≥9%, 5% and 1%, respectively. We propose four frontiers which fit these fixed points, including a Smooth Away From Expected (SAFE) frontier. Analysis approaches considered are as follows: using the pre-specified significance level (α=0.025); always using a reduced significance level (to achieve α≤0.025 across control event risks); reducing significance levels only when the control event risk differs significantly from expected (control event risk <9%); and using a likelihood ratio test. We compare power and type 1 error for SAFE with other frontiers. Results Changing the significance level only when the control event risk is <9% achieves approximately nominal (<3%) type I error rate and maintains reasonable power for control event risks between 1 and 15%. The likelihood ratio test method performs similarly, but the results are more complex to present. Other analysis methods lead to either inflated type 1 error or badly reduced power. The SAFE frontier gives more interpretable results with low control event risks than other frontiers (i.e. it uses more reasonable non-inferiority margins). Other frontiers do not achieve power close (i.e. within 1%) to SAFE across the range of likely control event risks while controlling type I error. Conclusions The SAFE non-inferiority frontier will be used in D3, and the non-inferiority margin and significance level will be modified if the control event risk is lower than expected. This ensures results will remain interpretable if design assumptions are incorrect, while achieving similar power. A similar approach could be considered for other non-inferiority trials where the control event risk is uncertain.

Type: Article
Title: The Smooth Away From Expected (SAFE) non-inferiority frontier: theory and implementation with an application to the D3 trial
Open access status: An open access version is available from UCL Discovery
DOI: 10.1186/s13063-023-07586-5
Publisher version: https://doi.org/10.1186/s13063-023-07586-5
Language: English
Additional information: Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. 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 in a credit line to the data.
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 > 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/10175930
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