Quantifying inconsistency in one-stage individual participant data meta-analyses of treatment-covariate interactions: a simulation study

It is recommended that measures of between-study effect heterogeneity be reported when conducting individual-participant data meta-analyses (IPD-MA). Methods exist to quantify inconsistency between trials via I^2 (the percentage of variation in the treatment effect due to between-study heterogeneity) when conducting two-stage IPD-MA, and when conducting one-stage IPD-MA with approximately equal numbers of treatment and control group participants. We extend formulae to estimate I^2 when investigating treatment-covariate interactions with unequal numbers of participants across subgroups and/or continuous covariates. A simulation study was conducted to assess the agreement in values of I^2 between those derived from two-stage models using traditional methods and those derived from equivalent one-stage models. Fourteen scenarios differed by the magnitude of between-trial heterogeneity, the number of trials, and the average number of participants in each trial. Bias and precision of I^2 were similar between the one- and two-stage models. The mean difference in I^2 between equivalent models ranged between -1.0 and 0.0 percentage points across scenarios. However, disparities were larger in simulated datasets with smaller samples sizes with up to 19.4 percentage points difference between models. Thus, the estimates of I^2 derived from these extended methods can be interpreted similarly to those from existing formulae for two-stage models.