to zero throughout, which is perhaps expected given the statistical theory underpinning linear mixed models. Furthermore, when using REML (with or without a CI correction), there were generally no important differences in coverage performance between the stratified and random intercept models. Interestingly, the random intercept model (which assumes normality of the intercept) performed well even when the trial intercepts were drawn from a highly asymmetric beta distribution. Kahan and Morris[25](#sim7930-bib-0025){ref-type="ref"} also found that misspecifying the random intercept distribution of random effects models did not impact treatment effect results.

Secondly, the KR and Satterthwaite corrections generally performed similarly in terms of improving the coverage and were especially effective for scenarios involving at least 10 trials with a mix of small and large sample sizes, but also considerably increased mean run time in these instances (see Web Tables C.V to C.VII). The Satterthwaite correction always had a similar or quicker average run time than KR (sometimes by more than eight times). One could surmise from the similarity in coverage performance that the main impact of both corrections is in the use of a t‐distribution to derive CIs and that the KR adjusted variance of the summary estimate has relatively less impact.

Thirdly, when using ML estimation, the random intercept model always showed better or comparable coverage to the stratified intercept model (closer to 95%). This is likely due to the random intercept model having a reduced number of parameters, and thus improved ML estimation of the between‐trial variance. A similar finding was also recently shown by Jackson et al[26](#sim7930-bib-0026){ref-type="ref"} for one‐stage meta‐analysis models for a binary outcome. Nevertheless, even the random intercept model produced downwardly biased estimates of the between‐trial variance using ML and low coverage. Using REML is therefore important, to improve on this coverage. Indeed, coverage