Estimating Treatment Effect Heterogeneity for Binary Outcomes via Dirichlet Multinomial Constraints

Abstract

In a randomized two-group parallel trial the mean causal effect is typically estimated as the difference in means or proportions for patients receiving, say, either treatment (T) or control (C). Treatment effect heterogeneity (TEH), or unit-treatment interaction, the variability of the causal effect (defined in terms of potential outcomes) across individuals, is often ignored. Since only one of the outcomes, either Y(T) or Y(C), is observed for each unit in such studies, the TEH is not directly estimable. For convenience, it is often assumed to be minimal or zero. We are particularly interested in the 'treatment risk' for binary outcomes, that is, the proportion of individuals who would succeed on C but fail on T. Previous work has shown that the treatment risk can be bounded (Albert, Gadbury and Mascha, 2005), and that the confidence interval width around it can be narrowed using clustered or correlated data (Mascha and Albert, 2006). Without further parameter constraints, treatment risk is unidentifiable. We show, however, that the treatment risk can be directly estimated when the four underlying population counts comprising the joint distribution of the potential outcomes, Y(T) and Y(C), follow constraints consistent with the Dirichlet multinomial. We propose a test of zero treatment risk and show it to have good size and power. Methods are applied to both a randomized as well as a non-randomized study. Implications for medical decision-making at the policy and individual levels are discussed.

Mediation analysis via potential outcomes models

“…A Bayesian approach might alternatively be considered for this problem. In the context of clustered data, bounding or estimation of a correlation between potential outcomes is possible [32,35]. These sort of methods can perhaps be incorporated into the causal model approach to assessing mediation in the presence of an interaction.…”

Assessing Treatment Effect Heterogeneity in Clinical Trials with Blocked Binary Outcomes

“…Research by Mascha (2005) has examined the effects of key conditions (in particular, the marginal success probabilities, the within-block correlations, and the number of blocks) on the widths of the bounds for p 2 . He has also explored (in work yet to be published) possible improvements on the bounds and confidence interval estimates, and has further showed that p 2 (alternatively, the correlation between the two potential outcomes) can be estimated under certain model assumptions.…”