Conformal Prediction for Causal Effects of Continuous Treatments

Uncertainty quantification of causal effects is crucial for safety-critical applications such as personalized medicine. A powerful approach for this is conformal prediction, which has several practical benefits due to model-agnostic finite-sample guarantees. Yet, existing methods for conformal prediction of causal effects are limited to binary/discrete treatments and make highly restrictive assumptions such as known propensity scores. In this work, we provide a novel conformal prediction method for potential outcomes of continuous treatments. We account for the additional uncertainty introduced through propensity estimation so that our conformal prediction intervals are valid even if the propensity score is unknown. Our contributions are three-fold: (1) We derive finite-sample prediction intervals for potential outcomes of continuous treatments. (2) We provide an algorithm for calculating the derived intervals. (3) We demonstrate the effectiveness of the conformal prediction intervals in experiments on synthetic and real-world datasets. To the best of our knowledge, we are the first to propose conformal prediction for continuous treatments when the propensity score is unknown and must be estimated from data.

💡 Research Summary

This paper tackles the problem of quantifying uncertainty for causal effects when the treatment variable is continuous—a setting that is common in safety‑critical domains such as personalized medicine, where clinicians need not only point estimates of outcomes (e.g., tumor size after a given chemotherapy dose) but also reliable intervals that reflect the range of possible responses. The authors adopt conformal prediction (CP), a distribution‑free, model‑agnostic framework that offers finite‑sample coverage guarantees, and extend it to the causal inference context with continuous treatments.

Two fundamental challenges are identified. First, intervening on the treatment changes the propensity score (the conditional probability of receiving a particular dose given covariates), which in turn shifts the joint distribution of covariates and treatment. This distribution shift breaks the exchangeability assumption that underlies standard CP, so naïve application would lead to invalid coverage. Second, in observational data the propensity score is rarely known and must be estimated, introducing additional uncertainty that cannot be handled by a simple plug‑in approach.

To address these issues, the authors introduce a “tilting function” f that mathematically characterizes the shift from the observational propensity π(a|x) to the interventional propensity \tildeπ(a|x):
\tildeπ(a|x) = f(a,x) · E_P