Abstract

Mixed effects (ME) models inform a vast array of problems in the physical and social sciences, and are pervasive in meta-analysis. We consider ME models where the random effects component is linear. We then develop an efficient approach for a broad problem class that allows nonlinear measurements, priors, and constraints, and finds robust estimates in all of these cases using trimming in the associated marginal likelihood. The software accompanying this article is disseminated as an open-source Python package called LimeTr. LimeTr is able to recover results more accurately in the presence of outliers compared to available packages for both standard longitudinal analysis and meta-analysis, and is also more computationally efficient than competing robust alternatives. Supplementary materials that reproduce the simulations, as well as run LimeTr and third party code are available online. We also present analyses of global health data, where we use advanced functionality of LimeTr, including constraints to impose monotonicity and concavity for dose–response relationships. Nonlinear observation models allow new analyses in place of classic approximations, such as log-linear models. Robust extensions in all analyses ensure that spurious data points do not drive our understanding of either mean relationships or between-study heterogeneity.

摘要

混合效应 (ME) 模型反映了物理和社会科学中的大量问题，并且在荟萃分析中无处不在。我们考虑随机效应分量是线性的 ME 模型。然后，我们为广泛的问题类别开发了一种有效的方法，该方法允许非线性测量、先验和约束，并在所有这些情况下使用相关边际似然的修剪找到稳健的估计。本文随附的软件以名为 LimeTr 的开源 Python 包的形式传播。与用于标准纵向分析和元分析的可用软件包相比，LimeTr 能够在存在异常值的情况下更准确地恢复结果，并且与竞争的强大替代方案相比，计算效率也更高。再现模拟的补充材料，以及运行 LimeTr 和第三方代码可在线获得。我们还提供了对全球健康数据的分析，其中我们使用了 LimeTr 的高级功能，包括对剂量-反应关系施加单调性和凹度的约束。非线性观测模型允许使用新的分析来代替经典的近似值，例如对数线性模型。所有分析中的稳健扩展确保虚假数据点不会推动我们对平均关系或研究间异质性的理解。