Clustered data, which arise when observations are nested within groups, are incredibly common in clinical, education, and social science research. Traditionally, a linear mixed model, which includes random effects to account for within-group correlation, would be used to model the observed data and make new predictions on unseen data. Some work has been done to extend the mixed model approach beyond linear regression into more complex and non-parametric models, such as decision trees and random forests. However, existing methods are limited to using the global fixed effects for prediction on data from out-of-sample groups, effectively assuming that all clusters share a common outcome model. We propose a lightweight sum-of-trees model in which we learn a decision tree for each sample group. We combine the predictions from these trees using weights so that out-of-sample group predictions are more closely aligned with the most similar groups in the training data. This strategy also allows for inference on the similarity across groups in the outcome prediction model, as the unique tree structures and variable importances for each group can be directly compared. We show our model outperforms traditional decision trees and random forests in a variety of simulation settings. Finally, we showcase our method on real-world data from the sarcoma cohort of The Cancer Genome Atlas, where patient samples are grouped by sarcoma subtype.

翻译：聚类数据，即观测值嵌套于组内的数据，在临床、教育和社会科学研究中极为常见。传统上，线性混合模型通过引入随机效应来捕捉组内相关性，被用于建模观测数据并对未见数据做出新预测。已有研究将混合模型方法从线性回归扩展到更复杂的非参数模型，如决策树和随机森林。然而，现有方法在预测样本外组群数据时仅限于使用全局固定效应，这实质上假设所有聚类共享相同的结果模型。我们提出一种轻量级树和模型，为每个样本组学习一个决策树。通过加权方式整合这些树的预测结果，使得样本外组群的预测更贴近训练数据中最相似的组群。该策略还可用于推断结果预测模型中组间相似性，因为可直接比较各组的独特树结构和变量重要性。我们通过多种模拟场景证明，该模型性能优于传统决策树和随机森林。最后，我们在癌症基因组图谱肉瘤队列的真实数据中展示了该方法的应用，其中患者样本按肉瘤亚型分组。