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.

References

Gruber, Susan, and Mark J. van der Laan. 2009. “Targeted Maximum Likelihood Estimation: A Gentle Introduction.” 252. Division of Biostatistics Working Paper Series: U.C. Berkeley.