# Principal stratification analysis using principal scores

arXiv: https://arxiv.org/abs/1602.01196 · HTML: https://mlsanity.com/paper/1602.01196/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Feb 2016.

## Built on by (most cited first, 6 of 6)

- [Multi-Source Causal Inference Using Control Variates](https://mlsanity.com/paper/2103.16689/) (2021)
- [Policy Learning with Asymmetric Counterfactual Utilities](https://mlsanity.com/paper/2206.10479/) (2022)
- [Variance reduction combining pre-experiment and in-experiment data](https://mlsanity.com/paper/2410.09027/) (2024)
- [Inverting estimating equations for causal inference on quantiles](https://mlsanity.com/paper/2401.00987/) (2024)
- [What Does a Skill Actually Do? Estimands and Evaluation Validity for Tool and Skill Use in LLM Agents: A Critical Review](https://mlsanity.com/paper/2609.33153/) (2026)
- [Assessing Surrogate Heterogeneity in Real World Data Using Meta-Learners](https://mlsanity.com/paper/2504.15386/) (2025)

## Abstract (arXiv)

Practitioners are interested in not only the average causal effect of the treatment on the outcome but also the underlying causal mechanism in the presence of an intermediate variable between the treatment and outcome. However, in many cases we cannot randomize the intermediate variable, resulting in sample selection problems even in randomized experiments. Therefore, we view randomized experiments with intermediate variables as semi-observational studies. In parallel with the analysis of observational studies, we provide a theoretical foundation for conducting objective causal inference with an intermediate variable under the principal stratification framework, with principal strata defined as the joint potential values of the intermediate variable. Our strategy constructs weighted samples based on principal scores, defined as the conditional probabilities of the latent principal strata given covariates, without access to any outcome data. This principal stratification analysis yields robust causal inference without relying on any model assumptions on the outcome distributions. We also propose approaches to conducting sensitivity analysis for violations of the ignorability and monotonicity assumptions, the very crucial but untestable identification assumptions in our theory. When the assumptions required by the classical instrumental variable analysis cannot be justified by background knowledge or cannot be made because of scientific questions of interest, our strategy serves as a useful alternative tool to deal with intermediate variables. We illustrate our methodologies by using two real data examples, and find scientifically meaningful conclusions.