Chapter 23 Targeted minimum loss estimation
Targeted minumum loss estimation (or maximum likelihood estimation) is a semi-parametric method for obtaining a causal effect. It uses a superlearner (or stacked generalizations, or weighted ensemblings) to choose between different machine learning algorithms using cross-validation. In particular, its basic method estimates both the outcome regression and the propensity score.
23.1 Adjustment
Having obtained the nuisance models, we then estimate the regression of \(Y\) on \[ h(X, A) = \frac{A}{\widehat{P}(A=1)} \left(\frac{A}{\widehat{g}(X,1)} - \frac{1-A}{\widehat{g}(X,0)}\right), \] where \(\widehat{g}(X, \cdot)\) is the estimate of the propensity score. This is known as the clever covariate in the TMLE literature.
See Gruber and Laan (2009) for more details.