Pulling back the curtain: the road from statistical estimand to machine-learning based estimator for epidemiologists (no wizard required)

TL;DR

This paper provides epidemiologists with an accessible guide to deriving machine-learning-based causal estimators using influence functions, emphasizing their robustness and practical implementation in epidemiological research.

Contribution

It introduces a clear, algebra-based explanation of deriving estimators via influence functions and demonstrates their ability to incorporate machine learning with rate double robustness.

Findings

Estimator derivation using influence functions explained

Demonstration of rate double robustness property

Guidance on integrating machine learning into causal inference

Abstract

Epidemiologists increasingly use causal inference methods that rely on machine learning, as these approaches can relax unnecessary model specification assumptions. While deriving and studying asymptotic properties of such estimators is a task usually associated with statisticians, it is useful for epidemiologists to understand the steps involved, as epidemiologists are often at the forefront of defining important new research questions and translating them into new parameters to be estimated. In this paper, our goal was to provide a relatively accessible guide through the process of (i) deriving an estimator based on the so-called efficient influence function (which we define and explain), and (ii) showing such an estimator's ability to validly incorporate machine learning, by demonstrating the so-called rate double robustness property. The derivations in this paper rely mainly on algebra and some foundational results from statistical inference, which are explained.