Choosing and changing the analysis scale in non-inferiority trials with a binary outcome

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 - risk difference, risk ratio or odds ratio - also has a large impact on power and thus on sample size requirement. When considering several scales at the design stage of a trial, these sample size consequences should be taken into account. Sometimes, changing the scale may be needed at a later stage of a trial, for example, when the event proportion in the control arm turns out different from expected. Also after completion of a trial, a switch to another scale is sometimes made, for example, 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 and results: This article first outlines sample size consequences for different choices of analysis scale at the design stage of a trial. We add a new result on sample size requirement comparing the risk difference scale with the risk ratio scale. Then, we study two different approaches to changing the analysis scale after the trial has commenced: (1) mapping the original non-inferiority margin using the event proportion in the control arm that was anticipated at the design stage or (2) mapping the original non-inferiority margin using the observed event proportion in the control arm. We use simulations to illustrate consequences on type I and type II error rates. Methods are illustrated on the INES trial, a non-inferiority trial that compared single birth rates in subfertile couples after different fertility treatments. Our results demonstrate large differences in required sample size when choosing between risk difference, risk ratio and odds ratio scales at the design stage of non-inferiority trials. In some cases, the sample size requirement is twice as large on one scale compared with another. Changing the scale after commencing the trial using anticipated proportions mainly impacts type II error rate, whereas switching using observed proportions is not advised due to not maintaining type I error rate. Differences were more pronounced with larger margins.

Conclusions: Trialists should be aware that the analysis scale can have large impact on type I and type II error rates in non-inferiority trials.

Keywords: Non-inferiority trial; non-inferiority margin; odds ratio; risk difference; risk ratio; sample size calculation.

Figure 1.

Comparison of sample size when considering different analysis scales at the design stage of the study assuming the boundary proportions for the success rate in treatment group is the same for each scale.

Figure 2.

Comparisons of power and type I error rate. (a) comparison of power when mapping using the observed control proportion; (b) comparison of power when mapping using the anticipated control proportion; (c) comparison of type I error rate when mapping using the observed control proportion; (d) comparison of type I error rate when mapping using the anticipated control proportion.