Three Routes to One Answer: Reconciling AIPW, TMLE, and Double Machine Learning for Applied Researchers

Abstract

Augmented inverse probability weighting (AIPW), targeted maximum likelihood estimation (TMLE), and double/debiased machine learning (DML) are three asymptotically equivalent routes to the same efficient influence function for the average treatment effect. We contribute a worked, shared-nuisance reconciliation on real data: what a practitioner must hold fixed for the routes and their software to agree, and when they do not. Using open data on smoking cessation and weight change (n = 1566), one Super Learner library, and folds matched within schemes, we build all three by hand, in full-sample, cross-fit, and double-cross-fit variants. A semi-synthetic benchmark with known sample-average effects on a fixed design grades interval coverage. The six doubly robust estimates span 3.32--3.39 kg over repeated splits. Single runs of our code and the tmle, AIPW, DoubleML, and tmle3 packages span 3.32--3.49 kg, compatible with fitting-scheme differences and single-split noise. Over 20 seeds, the three implementations sharing our library agree within 0.01 kg in median, although one is a TMLE. Agreement can fail: with in-sample nuisance fits on a binary mortality outcome, and under poor overlap in a job-training example. We recommend diagnosing overlap before choosing an estimator, and provide a reporting checklist and software code.

arXiv comment64 pages, 10 figures, 12 tables. Tutorial. v2: revised throughout; updates the double cross-fitting implementation and its results, the software-reconciliation account and the RHC repetition finding. Code at https://github.com/ehsanx/dml-alternatives, R package at https://github.com/ehsanx/dr3