# Assumption-Lean Post-Integrated Inference with Surrogate Control Outcomes

arXiv: https://arxiv.org/abs/2410.04996 · HTML: https://mlsanity.com/paper/2410.04996/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 67 references that are in the map.
- First posted on arXiv 7 Oct 2024.

## Builds on (most cited first, 22 of 22)

- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [Consistency of random forests](https://mlsanity.com/paper/1405.2881/) (2014)
- [A confounding bridge approach for double negative control inference on causal effects](https://mlsanity.com/paper/1808.04945/) (2018)
- [Identifying effects of multiple treatments in the presence of unmeasured confounding](https://mlsanity.com/paper/2011.04504/) (2020)
- [Data Integration in Causal Inference](https://mlsanity.com/paper/2110.01106/) (2021)
- [Bagging in overparameterized learning: Risk characterization and risk monotonization](https://mlsanity.com/paper/2210.11445/) (2022)
- [Assumption-lean inference for generalised linear model parameters](https://mlsanity.com/paper/2006.08402/) (2020)
- [Structured Latent Factor Analysis for Large-scale Data: Identifiability, Estimability, and Their Implications](https://mlsanity.com/paper/1712.08966/) (2017)
- [Confounder Adjustment in Multiple Hypothesis Testing](https://mlsanity.com/paper/1508.04178/) (2015)
- [Is your data alignable? Principled and interpretable alignability testing and integration of single-cell data](https://mlsanity.com/paper/2308.01839/) (2023)
- [Extrapolated cross-validation for randomized ensembles](https://mlsanity.com/paper/2302.13511/) (2023)
- [Causal Inference with High-dimensional Discrete Covariates](https://mlsanity.com/paper/2405.00118/) (2024)
- [The Promises of Parallel Outcomes](https://mlsanity.com/paper/2012.05849/) (2020)
- [Inference in High-dimensional Multivariate Response Regression with Hidden Variables](https://mlsanity.com/paper/2201.08003/) (2022)
- [Simultaneous inference for generalized linear models with unmeasured confounders](https://mlsanity.com/paper/2309.07261/) (2023)
- [Assumption Lean Regression](https://mlsanity.com/paper/1806.09014/) (2018)
- [Doubly Robust Inference when Combining Probability and Non-probability Samples with High-dimensional Data](https://mlsanity.com/paper/1903.05212/) (2019)
- [The Frisch--Waugh--Lovell Theorem for Standard Errors](https://mlsanity.com/paper/2009.06621/) (2020)
- [Augmented Doubly Robust Post-Imputation Inference for Proteomic Data](https://mlsanity.com/paper/2403.15802/) (2024)
- [Substitute adjustment via recovery of latent variables](https://mlsanity.com/paper/2403.00202/) (2024)
- [Causal Inference for Genomic Data with Multiple Heterogeneous Outcomes](https://mlsanity.com/paper/2404.09119/) (2024)

## Abstract (arXiv)

Data integration methods aim to extract low-dimensional embeddings from high-dimensional outcomes to remove unwanted variations, such as batch effects and unmeasured covariates, across heterogeneous datasets. However, multiple hypothesis testing after integration can be biased due to data-dependent processes. We introduce a robust post-integrated inference method that accounts for latent heterogeneity by utilizing control outcomes. Leveraging causal interpretations, we derive nonparametric identifiability of the direct effects using negative control outcomes. By utilizing surrogate control outcomes as an extension of negative control outcomes, we develop semiparametric inference on projected direct effect estimands, accounting for hidden mediators, confounders, and moderators. These estimands remain statistically meaningful under model misspecifications and with error-prone embeddings. We provide bias quantifications and finite-sample linear expansions with uniform concentration bounds. The proposed doubly robust estimators are consistent and efficient under minimal assumptions and potential misspecification, facilitating data-adaptive estimation with machine learning algorithms. Our proposal is evaluated using random forests through simulations and analysis of single-cell CRISPR perturbed datasets, which may contain potential unmeasured confounders.