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.

翻译：在进行个体参与者数据荟萃分析（IPD-MA）时，建议报告研究间效应异质性的度量指标。现有方法可通过I^2（治疗效应中由研究间异质性导致的变异百分比）来量化试验间的不一致性，这适用于两阶段IPD-MA，以及治疗组与对照组参与者数量大致相等的单阶段IPD-MA。我们扩展了公式以估计I^2，用于研究治疗-协变量交互作用时各亚组参与者数量不相等和/或连续协变量的情况。通过一项模拟研究，评估了使用传统方法从两阶段模型推导的I^2值与从等效单阶段模型推导的I^2值之间的一致性。十四个模拟场景在试验间异质性程度、试验数量和每个试验的平均参与者数量方面有所不同。单阶段与两阶段模型的I^2估计偏倚和精度相似。在等效模型之间，I^2的平均差异在各场景中介于-1.0至0.0个百分点之间。然而，在样本量较小的模拟数据集中，差异更大，模型间差异最高可达19.4个百分点。因此，通过这些扩展方法估计的I^2值可以类似于现有两阶段模型公式的结果进行解释。