Hetoregenous literally means differentiated by nature or content, and thus, when we speak of the treatment effects of
heterogeneous treatments, we recognize that each experimental group might respond differently to an intervention. Depending
on the adopted design, there might be cases where certain groups are assigned to some treatments in an disproportionate
manner, making heterogeneous effects difficult to estimate precisely. The extreme case is individual-treatment effects, which
attempt to establish the causal effects of each experimental arm individually; these, however, are essentially impossible to
assess without making a number of powerful assumptions.
Consistently, we were unable to reject the null hypothesis in the majority of cases (25 out of 27 opportunities), suggesting
that, whatever heterogeneity there might be in the treatment effects, this pattern did not vary much between samples. Based
on a fine-grained analysis of 27 pairs of survey experiments conducted in representative and nonrepresentative samples, and
different methods for assessing patterns of effect heterogeneity within each study, we have shown that effect heterogeneity
is generally restricted, and thus conclude that treatment effect homogeneity is the best explanation of concordance of
condition between samples.
If we compare the cost-effectiveness of increasing the binary outcome between different-cost treatment arms (see previous
discussions of this design here and here), then nulls are for a proportionally larger impact for the higher-cost arms; in
this case, a power increase with larger numbers of observations is likely as well; a power gain from larger numbers of
observations is likely as well. Thus, where expected effects of a treatment on the binary outcome are small, treatment
effects on outcome SDs will be also small, and an optimal design would be closer to 50% treatment/50% control.
A key new feature in the proposed $R$-learner is to enforce different regularization terms on HTEs and confounding functions,
such that possible smoothness or sparsity in confounding functions may be exploited to improve the HTE estimates.