Causal isotonic regression

TL;DR

This paper introduces a nonparametric, tuning-parameter-free estimator for causal dose-response curves that are monotone, with theoretical guarantees and practical applications in biomedical research.

Contribution

It generalizes classical isotonic regression to causal inference, providing a robust, invariant, and theoretically sound estimator for monotone causal dose-response relationships.

Findings

Estimator is tuning-parameter-free and invariant to transformations.

Theoretical properties include irregular limit distribution.

Numerical studies demonstrate effective performance.

Abstract

In observational studies, potential confounders may distort the causal relationship between an exposure and an outcome. However, under some conditions, a causal dose-response curve can be recovered using the G-computation formula. Most classical methods for estimating such curves when the exposure is continuous rely on restrictive parametric assumptions, which carry significant risk of model misspecification. Nonparametric estimation in this context is challenging because in a nonparametric model these curves cannot be estimated at regular rates. Many available nonparametric estimators are sensitive to the selection of certain tuning parameters, and performing valid inference with such estimators can be difficult. In this work, we propose a nonparametric estimator of a causal dose-response curve known to be monotone. We show that our proposed estimation procedure generalizes the classical least-squares isotonic regression estimator of a monotone regression function. Specifically, it does not involve tuning parameters, and is invariant to strictly monotone transformations of the exposure variable. We describe theoretical properties of our proposed estimator, including its irregular limit distribution and the potential for doubly-robust inference. Furthermore, we illustrate its performance via numerical studies, and use it to assess the relationship between BMI and immune response in HIV vaccine trials.