Which interactions matter in economic evaluations? A systematic review and simulation study

The interaction:effect ratio differs from the “interaction ratio” used by McAlister et al. [10]. McAlister’s interaction ratio is simply the relative effect (e.g. odds ratio) of A vs. not-A for patients also receiving B, divided by the relative effect of A vs. not-A for patients not receiving B (interaction ratio = (odds_ab/odds_b) ÷ (odds_a/odds₀)) and therefore equals the interaction on a logarithmic scale (interaction on log-scale = exp[(ln[odds_ab] − ln[odds_b]) − (ln[odds_a] − ln[odds₀])]). Unlike our interaction:effect ratio, McAlister’s interaction ratio is appropriate only for data interpreted on a multiplicative scale and does not distinguish between qualitative and non-qualitative interactions. At least one previous paper has used the interaction divided by simple effect to describe the ranges of interaction magnitude in which different analytical approaches performed best [3]. However, this study did not include any adjustment for mixed interactions, did not link the ranges of ratio values with different types of interaction and did not propose this ratio as a method for describing interactions in general.

One study meeting inclusion criteria was terminated early due to poor recruitment but was published as a monograph without analysis of economic results; this is considered in the review alongside protocols.

Since four of these studies were larger than 2 × 2 or reported results by subgroup, this gave 24 interactions for each of three outcomes (cost, QALYs and NMB): 72 interactions in total.

Three of these studies were included in the review as the authors described them as factorial [38‐40]. In one study [40], general practitioners randomised to one of the three active treatment groups received a training session not given to the control group. Conversely, two trials gave patients in the control group an additional intervention not given to the other three groups. A fourth trial, in which the second factor compared physiotherapy against reinforcement of the advice given as part of factor 1 (a whiplash book or usual advice), was excluded from the review as the authors did not describe it as factorial [41]. A further study that was included in the review allowed information sharing between practitioners within the ab group that was not possible within the groups receiving < 2 interventions [19].