When Reconstruction Is Not Enough: Doubly Robust Counterfactual and Interventional Mediation Analysis with Learned Multimodal Representations

Learned representations of high-dimensional multimodal health records are increasingly used to adjust for confounding, yet they are usually trained to reconstruct the data rather than preserve the information that causal identification requires.

高维多模态健康记录的学习表示正越来越多地被用于调整混杂因素，但它们通常是为了重构数据而训练的，而非为了保留因果识别所需的信息。

We study counterfactual outcomes under alternative treatments, including phenotype-specific effects and patient-level counterfactual risk profiles of the kind digital twins provide, and interventional direct and indirect effects under exposure-induced intermediate confounding.

我们研究了替代治疗下的反事实结果，包括表型特异性效应、数字孪生所提供的患者级反事实风险概况，以及暴露诱导的中介混杂下的干预性直接和间接效应。

We give conditions under which a representation preserves identification and show that interventional mediation is more demanding than counterfactual comparison.

我们给出了表示能够保持识别的条件，并证明了干预性中介分析比反事实比较要求更高。

We prove that no covariate-only training objective, whether reconstruction, contrastive, or physics-informed, can certify that a representation is sufficient, and that, in a linear structural model, a representation can lose arbitrarily little reconstruction accuracy yet induce arbitrarily large bias.

我们证明，没有任何仅基于协变量的训练目标（无论是重构、对比学习还是物理信息驱动）能够证明一个表示是充分的；并且在线性结构模型中，一个表示可能在几乎不损失重构精度的情况下，导致任意大的偏差。

We decompose the error of cross-fitted doubly robust estimators into a first-order representation bias, which neither double robustness nor cross-fitting removes, and a second-order remainder of nuisance-estimation errors, so coverage worsens as the sample size grows when the representation is insufficient.

我们将交叉拟合双重稳健估计量的误差分解为一阶表示偏差（双重稳健性或交叉拟合均无法消除）和二阶剩余的干扰估计误差，因此当表示不足时，随着样本量的增加，覆盖率会变差。

We propose a workflow combining modality-specific variational autoencoders trained outside the estimation sample, cross-fitted doubly robust estimators, locked phenotypes, select-then-confirm pathway analysis, portable representations, and diagnostics for representation insufficiency, exposure leakage, and sensitivity.

我们提出了一种工作流程，结合了在估计样本之外训练的模态特定变分自编码器、交叉拟合双重稳健估计量、锁定表型、选择后确认路径分析、可移植表示，以及针对表示不足、暴露泄露和敏感性的诊断方法。

In simulations, discarding a rare, moderately strong confounder gave indirect-effect intervals with 2% coverage at n = 3,000; reconstruction loss missed the problem, and a simple predictive diagnostic flagged it in every replicate.

在模拟中，丢弃一个罕见且中等强度的混杂因素导致在 n = 3,000 时，间接效应区间的覆盖率仅为 2%；重构损失未能发现该问题，而一个简单的预测性诊断在每次重复实验中都将其标记了出来。