# Treatment response as a latent variable

arXiv: https://arxiv.org/abs/2502.08776 · HTML: https://mlsanity.com/paper/2502.08776/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 56 references that are in the map.
- First posted on arXiv 12 Feb 2025.

## Builds on (most cited first, 16 of 16)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Estimating the Effects of Continuous-valued Interventions using Generative Adversarial Networks](https://mlsanity.com/paper/2002.12326/) (2020)
- [Generalization Bounds and Representation Learning for Estimation of Potential Outcomes and Causal Effects](https://mlsanity.com/paper/2001.07426/) (2020)
- [Bayesian regression tree models for causal inference: regularization, confounding, and heterogeneous effects](https://mlsanity.com/paper/1706.09523/) (2017)
- [Optimal Transport for Treatment Effect Estimation](https://mlsanity.com/paper/2310.18286/) (2023)
- [AdaPT: An interactive procedure for multiple testing with side information](https://mlsanity.com/paper/1609.06035/) (2016)
- [Multiple testing with the structure adaptive Benjamini-Hochberg algorithm](https://mlsanity.com/paper/1606.07926/) (2016)
- [Multiply robust estimation of causal effects under principal ignorability](https://mlsanity.com/paper/2012.01615/) (2020)
- [False discovery rate smoothing](https://mlsanity.com/paper/1411.6144/) (2014)
- [NeuralFDR: Learning Discovery Thresholds from Hypothesis Features](https://mlsanity.com/paper/1711.01312/) (2017)
- [False discovery rate regression: an application to neural synchrony detection in primary visual cortex](https://mlsanity.com/paper/1307.3495/) (2013)
- [Black Box FDR](https://mlsanity.com/paper/1806.03143/) (2018)
- [Principal Stratification with Continuous Post-Treatment Variables: Nonparametric Identification and Semiparametric Estimation](https://mlsanity.com/paper/2309.12425/) (2023)
- [Identification of Causal Effects Within Principal Strata Using Auxiliary Variables](https://mlsanity.com/paper/2008.02703/) (2020)
- [Interactive identification of individuals with positive treatment effect while controlling false discoveries](https://mlsanity.com/paper/2102.10778/) (2021)

## Built on by (most cited first, 1 of 1)

- [Empirically Calibrated Conditional Independence Tests](https://mlsanity.com/paper/2602.21036/) (2026)

## Abstract (arXiv)

Scientists often need to analyze the samples in a study that responded to treatment in order to refine their hypotheses and find potential causal drivers of response. Natural variation in outcomes makes teasing apart responders from non-responders a statistical inference problem. To handle latent responses, we introduce the causal two-groups (C2G) model, a causal extension of the classical two-groups model. The C2G model posits that treated samples may or may not experience an effect, according to some prior probability. We propose two empirical Bayes procedures for the causal two-groups model, one under semi-parametric conditions and another under fully nonparametric conditions. The semi-parametric model assumes additive treatment effects and is identifiable from observed data. The nonparametric model is unidentifiable, but we show it can still be used to test for response in each treated sample. We show empirically and theoretically that both methods for selecting responders control the false discovery rate at the target level with near-optimal power. We also propose two novel estimands of interest and provide a strategy for deriving estimand intervals in the unidentifiable nonparametric model. On a cancer immunotherapy dataset, the nonparametric C2G model recovers clinically-validated predictive biomarkers of both positive and negative outcomes. Code is available at https://github.com/tansey-lab/causal2groups.