                                          Doubling τ ^2^ to 15.6

\*Each scenario was repeated under the following data generating mechanisms: (1) random treatment effect with a normally distributed intercept, (2) random treatment effect with a 220\*beta(15, 3) distribution for the intercept (except scenarios C1 and C2), and (3) common treatment effect with a normally distributed intercept (except scenarios D1 and D2).

Abbreviations: K = number of trials, n ~i~ = number of participants in trial i, θ = summary treatment effect, τ ^2^ = between trial variation in summary treatment effect, β = mean response in control group, τ ~β~ ^2^ = between trial variation in mean response in control group, σ ^2^ = residual variance, U (a, b) = uniform distribution over the interval (a, b).

We varied the number of trials (scenarios A1 and A2), so that K = 5, 10, and 20 were considered, which cover the typical sizes of IPD meta‐analyses in our experience. We also considered trials with differing sample sizes within an IPD, so that n ~i~ (number of participants within trial i) was drawn from a uniform distribution, n ~i~ ∼U(a, b). Fixing a = 30, b = 1000 (scenario B1) allowed for mixed sample sizes, and having 5 trials with a = 30, b = 100 and 5 with a = 900, b = 1000 within an IPD (scenario B2) tested the effect of a mix of small and large sample sizes only. Lastly, fixing a = 30, b = 100 tested the effect of having only small trials (scenario B3).

We also tested the combined effect of varying the number of trials and number of participants per trial simultaneously (scenarios B1‐A1, B1‐A2, B2‐A1, B2‐A2), and we tested the effects of adjusting the magnitude of the intercept or treatment effect heterogeneity (scenarios C1, C2, D1, D2).

Scenarios 15 to 38 replicate the first 14 scenarios where possible, for modifications to the base case data generating mechanism. First, to test the robustness of the normality of the intercept assumption in the random intercept model, 