Data integration has become increasingly common in aligning multiple heterogeneous datasets. With high-dimensional outcomes, data integration methods aim to extract low-dimensional embeddings of observations to remove unwanted variations, such as batch effects and unmeasured covariates, inherent in data collected from different sources. However, multiple hypothesis testing after data integration can be substantially biased due to the data-dependent integration processes. To address this challenge, we introduce a robust post-integrated inference (PII) method that adjusts for latent heterogeneity using negative control outcomes. By leveraging causal interpretations, we derive nonparametric identification conditions that form the basis of our PII approach. Our assumption-lean semiparametric inference method extends robustness and generality to projected direct effect estimands that account for mediators, confounders, and moderators. These estimands remain statistically meaningful under model misspecifications and with error-prone embeddings. We provide deterministic quantifications of the bias of target estimands induced by estimated embeddings and finite-sample linear expansions of the estimators with uniform concentration bounds on the residuals for all outcomes. The proposed doubly robust estimators are consistent and efficient under minimal assumptions, facilitating data-adaptive estimation with machine learning algorithms. Using random forests, we evaluate empirical statistical errors in simulations and analyze single-cell CRISPR perturbed datasets with potential unmeasured confounders.

翻译：数据整合在协调多个异构数据集方面已变得日益普遍。针对高维结果变量，数据整合方法旨在提取观测的低维嵌入表示，以消除来自不同来源数据中固有的非期望变异，例如批次效应和未测量的协变量。然而，数据整合后的多重假设检验可能因数据依赖的整合过程而产生显著偏差。为应对这一挑战，我们提出了一种稳健的后整合推断方法，该方法利用负控制结果对潜在异质性进行校正。通过借助因果解释，我们推导了非参数识别条件，这些条件构成了我们后整合推断方法的基础。我们提出的假设松弛半参数推断方法将稳健性和普适性扩展到考虑中介变量、混杂变量和调节变量的投影直接效应估计量。即使在模型设定错误和嵌入表示存在误差的情况下，这些估计量仍保持统计学意义。我们针对由估计嵌入引起的目标估计量偏差提供了确定性量化，并给出了估计量的有限样本线性展开式，同时对所有结果变量的残差给出了均匀浓度界。所提出的双重稳健估计量在最小假设条件下具有一致性和有效性，便于利用机器学习算法进行数据自适应估计。通过使用随机森林，我们在模拟中评估了经验统计误差，并分析了存在潜在未测量混杂变量的单细胞CRISPR扰动数据集。