TMLE

Targeted maximum likelihood estimation (TMLE) is a general framework for estimating causal parameters in semi-parametric models. It blends data-adaptive machine learning with principled statistical inference to yield estimates that are consistent when either the outcome model or the treatment mechanism is correctly specified, and that are asymptotically efficient under regularity conditions. TMLE is widely used in epidemiology, biostatistics, and causal inference to estimate quantities such as average treatment effects, risk differences, and causal risks from observational data.

Conceptually, TMLE starts with an initial estimate of the outcome regression Q0(W) = E[Y|A,W] and, when needed, an estimate of the treatment mechanism g0(A|W) = P(A|W). It then constructs a clever covariate H(A,W) derived from g0 that targets the parameter of interest. A fluctuation (targeting) step updates Q0 to a targeted Q*(W) by fitting a submodel, typically logistic, with offset logit(Q0(W)) and covariate H, chosen to solve the estimating equation for the target parameter.

The final parameter estimate is obtained by plugging Q*(W) into the estimating equation for the causal parameter. Inference uses the efficient influence function to form standard errors and confidence intervals. TMLE can be combined with data-adaptive estimators (for Q and g) via the super learner, and cross-validated TMLE variants help mitigate overfitting. Under regularity, TMLE achieves semi-parametric efficiency and possesses double robustness.

Applications include estimating average treatment effects and other causal quantities from observational data with adjustment for covariates, and handling missingness or censoring. Limitations include the need for positivity, computational demands, and sensitivity to extreme weights or model misspecification of nuisance parameters; careful diagnostics and sensitivity analyses are recommended.