How Wrong Can Your Counterfactual Be? Quantifying Confounding Bias for Continuous Treatments without a Control Group

Prediction error is widely used to evaluate nuisance-function estimators in causal inference, but its relationship with the performance of the resulting causal estimator is not well understood. We studied this question in a partially linear model using Monte Carlo simulations, comparing ordinary least squares (OLS), generalized additive models (GAMs), XGBoost, and Double Machine Learning with XGBoost (DML-XGBoost) with independent and with clustered observations. We evaluated nuisance-function prediction error, bias, RMSE, and 95% confidence interval coverage, and derived the second-order remainder through which errors in the exposure and outcome nuisance functions jointly determine the bias of the residualized estimator. When all methods estimated the causal effect from the same training sample, DML-XGBoost had the lowest RMSE and the highest coverage among the non-oracle methods, although XGBoost fitted to the full training sample had lower out-of-sample prediction error for both nuisance functions. GAMs had the lowest prediction error of all methods but were biased, with coverage of 0.55 with independent observations. The remainder reproduced the average bias of OLS, GAMs, and DML-XGBoost, but only half to three-quarters of the bias of XGBoost, whose residuals were formed on the data used to fit it. A joint-error measure based on the absolute cross-product of the two nuisance errors was only weakly associated with causal bias. Prediction error is useful for assessing nuisance-function estimation, but it should not be treated as a direct measure of the quality of the resulting causal estimator.

Data-driven decision making frequently relies on predicting counterfactual outcomes. In practice, researchers commonly train counterfactual prediction models on a source dataset to inform decisions on a possibly separate target population. Conformal prediction has arisen as a popular method for producing assumption-lean prediction intervals for counterfactual outcomes that would arise under different treatment decisions in the target population of interest. However, existing methods require that every confounding factor of the treatment-outcome relationship used for training on the source data is additionally measured in the target population, risking miscoverage if important confounders are unmeasured in the target population. In this paper, we introduce a computationally efficient debiased machine learning framework that allows for valid prediction intervals when only a subset of confounders is measured in the target population, a common challenge referred to as runtime confounding. Grounded in semiparametric efficiency theory, we show the resulting prediction intervals achieve desired coverage rates with faster convergence compared to standard methods. Through numerous synthetic and semi-synthetic experiments, we demonstrate the utility of our proposed method.

Conformal counterfactual prediction constructs prediction sets with finite-sample coverage guarantees for counterfactual outcomes and individual treatment effects under the no-interference assumption. In this work, we relax this assumption by allowing each unit's potential outcomes to depend on other units' treatments and covariates. In this setting, propensity-score reweighting does not restore weighted exchangeability, and existing methods may fail to achieve valid coverage. To address this issue, we develop interference-adjusted weighted conformal prediction that accounts for interference by constructing an observable upper bound on the ideal and unobserved conformal $p$-value under the target intervention. The resulting prediction sets provide finite-sample marginal coverage guarantees for counterfactual outcomes and individual treatment effects in both transductive and inductive settings. We also derive a sharper construction when intervention-induced changes in nonconformity scores are bounded. Numerical experiments show that our methods preserve nominal coverage, whereas existing methods may not.