A one‐stage individual participant data (IPD) meta‐analysis synthesizes IPD from multiple studies using a general or generalized linear mixed model. This produces summary results (eg, about treatment effect) in a single step, whilst accounting for clustering of participants within studies (via a stratified study intercept, or random study intercepts) and between‐study heterogeneity (via random treatment effects). We use simulation to evaluate the performance of restricted maximum likelihood (REML) and maximum likelihood (ML) estimation of one‐stage IPD meta‐analysis models for synthesizing randomized trials with continuous or binary outcomes. Three key findings are identified. First, for ML or REML estimation of stratified intercept or random intercepts models, a t‐distribution based approach generally improves coverage of confidence intervals for the summary treatment effect, compared with a z‐based approach. Second, when using ML estimation of a one‐stage model with a stratified intercept, the treatment variable should be coded using “study‐specific centering” (ie, 1/0 minus the study‐specific proportion of participants in the treatment group), as this reduces the bias in the between‐study variance estimate (compared with 1/0 and other coding options). Third, REML estimation reduces downward bias in between‐study variance estimates compared with ML estimation, and does not depend on the treatment variable coding; for binary outcomes, this requires REML estimation of the pseudo‐likelihood, although this may not be stable in some situations (eg, when data are sparse). Two applied examples are used to illustrate the findings.

中文翻译：

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连续和二元结果的一阶段个体参与者数据元分析模型：治疗编码选项和估计方法的比较。

单阶段个体参与者数据 (IPD) 荟萃分析使用通用或广义线性混合模型从多项研究中综合 IPD。这在一个步骤中产生了总结结果（例如，关于治疗效果），同时考虑了研究中参与者的聚类（通过分层研究截距或随机研究截距）和研究之间的异质性（通过随机治疗效果）。我们使用模拟来评估单阶段 IPD 荟萃分析模型的受限最大似然 (REML) 和最大似然 (ML) 估计的性能，以综合具有连续或二元结果的随机试验。确定了三个主要发现。首先，对于分层截距或随机截距模型的 ML 或 REML 估计，与基于 az 的方法相比，基于分布的方法通常提高了汇总处理效果的置信区间的覆盖率。其次，当使用具有分层截距的单阶段模型的 ML 估计时，治疗变量应使用“研究特定中心化”（即 1/0 减去治疗组参与者的研究特定比例）进行编码，因为这减少了研究间方差估计的偏差（与 1/0 和其他编码选项相比）。第三，与 ML 估计相比，REML 估计减少了研究间方差估计的向下偏差，并且不依赖于处理变量编码；对于二元结果，这需要对伪似然进行 REML 估计，尽管这在某些情况下可能不稳定（例如，当数据稀疏时）。