Causal isotonic regression

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 by 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. Non‐parametric estimation in this context is challenging because in a non‐parametric model these curves cannot be estimated at regular rates. Many available non‐parametric estimators are sensitive to the selection of certain tuning parameters, and performing valid inference with such estimators can be difficult. We propose a non‐parametric 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 body mass index and immune response in human immunodeficiency virus vaccine trials.