Targeted minimum loss based estimation of a causal effect on an outcome with known conditional bounds

This paper presents a targeted minimum loss based estimator (TMLE) that incorporates known conditional bounds on a continuous outcome. Subject matter knowledge regarding the bounds of a continuous outcome within strata defined by a subset of covariates, X, translates into statistical knowledge that constrains the model space of the true joint distribution of the data. In settings where there is low Fisher Information in the data for estimating the desired parameter, as is common when X is high dimensional relative to sample size, incorporating this domain knowledge can improve the fit of the targeted outcome regression, thereby improving bias and variance of the parameter estimate. We show that TMLE, a substitution estimator defined as a mapping from a density to a (possibly d-dimensional) real number, readily incorporates this global knowledge, resulting in improved finite sample performance.