  We offer a non-parametric plug-in estimator for an important measure of
treatment effect variability and provide minimum conditions under which the
estimator is asymptotically efficient. The stratum specific treatment effect
function or so-called blip function, is the average treatment effect for a
randomly drawn stratum of confounders. The mean of the blip function is the
average treatment effect (ATE), whereas the variance of the blip function
(VTE), the main subject of this paper, measures overall clinical effect
heterogeneity, perhaps providing a strong impetus to refine treatment based on
the confounders. VTE is also an important measure for assessing reliability of
the treatment for an individual. The CV-TMLE provides simultaneous plug-in
estimates and inference for both ATE and VTE, guaranteeing asymptotic
efficiency under one less condition than for TMLE. This condition is difficult
to guarantee a priori, particularly when using highly adaptive machine learning
that we need to employ in order to eliminate bias. Even in defiance of this
condition, CV-TMLE sampling distributions maintain normality, not guaranteed
for TMLE, and have a lower mean squared error than their TMLE counterparts. In
addition to verifying the theoretical properties of TMLE and CV-TMLE through
simulations, we point out some of the challenges in estimating VTE, which lacks
double robustness and might be unavoidably biased if the true VTE is small and
sample size insufficient. We will provide an application of the estimator on a
data set for treatment of acute trauma patients.
