Li, Z; Quartagno, M; Boerhinger, S; Van Geloven, N; (2021) Choosing and changing the analysis scale in non-inferiority trials with a binary outcome. Clinical Trials 10.1177/17407745211053790. (In press).

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Abstract

Background: The size of the margin strongly influences the required sample size in non-inferiority and equivalence trials. What is sometimes ignored however, is that for trials with binary outcomes the scale of the margin - absolute risk difference (ARD), risk ratio (RR) or odds ratio (OR)- has a large impact on power and thus on sample size requirement as well. When considering several scales at the design stage of the trial, these sample size consequences should be taken into account. Sometimes, changing the scale may be desirable at a later stage of the trial, e.g. when the event proportion in the control arm turns out different than expected. Also after completion of a trial a switch to another scale may be attractive, e.g. when using a regression model in a secondary analysis or when combining study results in a meta-analysis that requires unifying scales. The exact consequences of such switches are currently unknown. / Methods: This paper first outlines sample size consequences for different choices of analysis scale at the design stage of the study. We add a new result on sample size requirement comparing the ARD scale with the RR scale. Then we study two different approaches to changing the analysis scale after the trial has commenced: 1) mapping the original NI margin using the event proportion in the control arm that was anticipated at the design stage or 2) mapping the original NI margin using the observed event proportion in the control arm. We use simulations to illustrate consequences on type I and type II error. Methods are illustrated on the INES trial, a non-inferiority trial that compared single birth rates in subfertile couples after different fertility treatments. / Results: Our results demonstrate large differences in required sample size when choosing between ARD, RR and OR scales at the design stage of non-inferiority trials. In some cases the sample size requirement is twice as large on one scale compared to another. Changing the scale after commencing the trial using anticipated proportions mainly impacts type II error, whereas switching using observed proportions is not advised due to not maintaining type I error. Differences were more pronounced with larger margins. / Conclusions: Trialists should be aware that the analysis scale can have unexpectedly large impact on type I and type II error rates in non-inferiority trials.

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