Targeted Maximum Likelihood Estimation (Epidemiology)

Double robustness means the estimator is consistent (converges to the true causal effect) if at least one of two nuisance models is correctly specified: the outcome regression or the propensity score. If both are right, TMLE is also asymptotically efficient, attaining the smallest possible variance in the semiparametric model. This is a substantial safeguard over single-model approaches like plain g-computation (which needs the outcome model right) or plain IPTW (which needs the propensity model right). With super learner estimating both, the practical hope is that flexible learning makes at least one — usually both — adequately correct.

Both AIPW and TMLE are doubly-robust estimators that combine an outcome model and a propensity model, and both can use machine learning with cross-fitting. The key difference is that TMLE is a substitution (plug-in) estimator: it updates the outcome model with a targeting step and then plugs predictions in, so the estimate always respects the parameter's natural bounds. AIPW is an estimating-equation estimator that adds an augmentation term and can occasionally produce out-of-range values under sparse data or extreme weights. In practice TMLE tends to be more stable when propensities are extreme, while AIPW is conceptually simpler; both target the same efficiency bound.

TMLE's robustness and efficiency arguments rely on estimating the nuisance functions well, but the true functional forms are unknown. A super learner is a cross-validated ensemble that combines many candidate algorithms and weights them by out-of-sample performance, so it adapts to whatever structure the data hold without the analyst guessing. Using it for both the outcome and propensity models maximizes the chance that each is approximately correct, which is precisely what TMLE needs. A single misspecified parametric model would undercut the whole rationale, so the super learner is considered an integral part of the method rather than an optional add-on.