eltmle: Ensemble learning targeted maximum likelihood estimation

Modern Epidemiology has been able to identify significant limitations of classic epidemiological methods, like outcome regression analysis, when estimating causal quantities such as the average treatment effect (ATE) for observational data. For example, using classical regression models to estimate the ATE requires assuming the effect measure is constant across levels of confounders included in the model, i.e. that there is no effect modification. Other methods do not require this assumption, including g-methods (e.g. the g- formula) and targeted maximum likelihood estimation (TMLE). Many estimators of the ATE but not all rely on parametric modeling assumptions. Therefore, the correct model specification is crucial to obtain unbiased estimates of the true ATE. TMLE is a semiparametric, efficient substitution estimator allowing for data-adaptive estimation while obtaining valid statistical inference based on the targeted minimum loss-based estimation. Being doubly robust, TMLE allows inclusion of machine learning algorithms to minimise the risk of model misspecification, a problem that persists for competing estimators. Evidence shows that TMLE typically provides the least unbiased estimates of the ATE compared with other double robust estimators. eltmle is a Stata program implementing the targeted maximum likelihood estimation for the ATE for a binary outcome and binary treatment. eltmle includes the use of a super-learner called from the Super Learner R-package v.2.0-21 (Polley E., et al. 2011). The Super-Learner uses V-fold cross-validation (10-fold by default) to assess the performance of prediction regarding the potential outcomes and the propensity score as weighted averages of a set of machine learning algorithms. We used the default Super Learner algorithms implemented in the base installation of the tmle-R package v.1.2.0- 5 (Susan G. and Van der Laan M., 2017), which included the following: i) stepwise selection, ii) generalized linear modelling (GLM), iii) a GLM variant that includes second order polynomials and two-by-two interactions of the main terms included in the model. Additionally, eltmle users will have the option to include Bayes Generalized Linear Models and Generalised Additive Models as additional Super-Learner algorithms. Future implementations will offer more advanced machine learning algorithms.