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个数据源的强大且可泛化分析的重要途径。然而，实践中不同数据源在数据收集能力上的差异已成为一个突出问题。这可能导致协变量的块状缺失，为数据整合带来困难。同时，获取金标准标签的高昂成本可能导致大量样本的响应变量缺失，即半监督问题。本文考虑同时面临块缺失与半监督问题的挑战性场景，提出了一种新颖的半监督设置下数据融合的自适应投影估计方法。该方法从一个仅基于完整数据的估计量出发，通过两个连续的投影步骤来降低其方差而不引入偏差。与现有方法相比，DEFUSE 实现了双重改进。首先，它通过一种对缺失协变量模型设定错误具有鲁棒性的新型自适应投影方法，更高效地利用了块缺失的标记样本，从而实现了更好的方差缩减。其次，我们的方法进一步结合了大量未标记样本，通过插值与投影来提升估计效率。与先前协变量完整的半监督设置相比，我们的工作揭示了未标记样本在块缺失设置中更为本质的作用。这些优势在渐近理论和仿真研究中得到了验证。我们还应用 DEFUSE 方法，基于 MIMIC-III 电子病历数据对心脏疾病进行了风险建模与推断。