Towards efficient and interpretable assumption-lean generalized linear modeling of continuous exposure effects.

Abstract

Advances in causal inference have largely ignored continuous exposures, apart from model-based approaches, which face criticism due to potential model misspecification. Model-free approaches based on modified treatment policies, such as uniformly shifting each subject's observed exposure, have emerged as promising alternatives. However, because such interventions are impractical, it is necessary to evaluate a range of possible shifts to generate actionable insights. To address this, we introduce models that parameterize the effects of shift interventions across varying magnitudes, coupled with assumption-lean estimation strategies. To ensure validity and interpretability under model misspecification, we tailor these to minimize (squared) bias in estimating the effects of realistic shifts. We employ debiased machine learning procedures for this but observe them to exhibit erratic behavior under certain data-generating mechanisms, prompting two key innovations. First, we propose a broadly applicable debiasing procedure that yields estimators with significantly improved finite-sample properties and is of independent methodological interest. Second, we develop debiased machine learning estimators for estimands with a more favorable efficiency bound, but more nuanced interpretation when models are misspecified. Unlike existing projection estimators, our methods avoid inverse exposure density weighting and do not demand tailored shift interventions to address positivity violations. Extensive simulations and a re-analysis of the Bangladesh Wash Benefits study demonstrate the effectiveness, stability, and utility of our approach. This work advances assumption-lean methods that balance validity, interpretability, and efficiency.