Network meta-analysis combines aggregate data (AgD) from multiple randomised controlled trials, assuming that any effect modifiers are balanced across populations. Individual patient data (IPD) meta-regression is the ``gold standard'' method to relax this assumption, however IPD are frequently only available in a subset of studies. Multilevel network meta-regression (ML-NMR) extends IPD meta-regression to incorporate AgD studies whilst avoiding aggregation bias, but currently requires the aggregate-level likelihood to have a known closed form. Notably, this prevents application to time-to-event outcomes. We extend ML-NMR to individual-level likelihoods of any form, by integrating the individual-level likelihood function over the AgD covariate distributions to obtain the respective marginal likelihood contributions. We illustrate with two examples of time-to-event outcomes, showing the performance of ML-NMR in a simulated comparison with little loss of precision from a full IPD analysis, and demonstrating flexible modelling of baseline hazards using cubic M-splines with synthetic data on newly diagnosed multiple myeloma. ML-NMR is a general method for synthesising individual and aggregate level data in networks of all sizes. Extension to general likelihoods, including for survival outcomes, greatly increases the applicability of the method. R and Stan code is provided, and the methods are implemented in the multinma R package.

翻译：网络Meta分析综合来自多个随机对照试验的汇总数据（AgD），假设任何效应修饰因子在各人群间保持平衡。个体患者数据（IPD）Meta回归是放宽这一假设的“金标准”方法，但IPD通常仅在一部分研究中可用。多层次网络Meta回归（ML-NMR）扩展了IPD Meta回归，在纳入AgD研究的同时避免了聚合偏倚，但当前要求汇总层面的似然函数具有已知的闭合形式。这尤其限制了其在时间-事件结局中的应用。通过将个体水平的似然函数对AgD协变量分布进行积分以获得相应的边际似然贡献，我们将ML-NMR扩展至任意形式的个体水平似然函数。我们以两个时间-事件结局的示例说明：在模拟比较中展示ML-NMR的性能（与完整IPD分析相比仅产生微小精度损失），并利用新诊断多发性骨髓瘤的合成数据，通过三次M样条对基线风险函数进行灵活建模。ML-NMR是一种适用于各种规模网络中综合个体与汇总数据的通用方法。将其扩展至一般似然函数（包括生存结局）可显著增强该方法的应用性。本文提供了R和Stan代码，该方法已在multinma R包中实现。