Data fusion is an important way to realize powerful and generalizable analyses across multiple sources. However, different capability of data collection across the sources has become a prominent issue in practice. This could result in the blockwise missingness (BM) of covariates troublesome for integration. Meanwhile, the high cost of obtaining gold-standard labels can cause the missingness of response on a large proportion of samples, known as the semi-supervised (SS) problem. In this paper, we consider a challenging scenario confronting both the BM and SS issues, and propose a novel Data-adaptive projecting Estimation approach for data FUsion in the SEmi-supervised setting (DEFUSE). Starting with a complete-data-only estimator, it involves two successive projection steps to reduce its variance without incurring bias. Compared to existing approaches, DEFUSE achieves a two-fold improvement. First, it leverages the BM labeled sample more efficiently through a novel data-adaptive projection approach robust to model misspecification on the missing covariates, leading to better variance reduction. Second, our method further incorporates the large unlabeled sample to enhance the estimation efficiency through imputation and projection. Compared to the previous SS setting with complete covariates, our work reveals a more essential role of the unlabeled sample in the BM setting. These advantages are justified in asymptotic and simulation studies. We also apply DEFUSE for the risk modeling and inference of heart diseases with the MIMIC-III electronic medical record (EMR) data.

翻译：数据融合是实现跨多源数据强大且可泛化分析的重要途径。然而，实践中不同数据源采集能力的差异已成为突出问题，这可能导致协变量的块缺失现象，为数据整合带来困难。同时，获取金标准标签的高成本可能导致大量样本的响应变量缺失，即半监督问题。本文针对同时存在块缺失与半监督问题的挑战性场景，提出了一种半监督环境下数据融合的自适应投影估计方法。该方法以完整数据估计量为起点，通过两个连续的投影步骤实现方差降低且不引入偏差。与现有方法相比，该方法具有双重优势：首先，通过一种对缺失协变量模型误设具有鲁棒性的自适应投影策略，更高效地利用了块缺失的标注样本，实现了更优的方差缩减；其次，通过插值与投影过程进一步融合大规模未标注样本以提升估计效率。相较于以往协变量完整的半监督研究，本文揭示了未标注样本在块缺失场景中更为本质的作用。理论渐近分析与仿真实验验证了上述优势。我们还将该方法应用于MIMIC-III电子病历数据的心脏疾病风险建模与推断研究。