| Randomized clinical trials with binary outcomes typically focus on the mean treatment effect for patients on treatment (T) and control (C), and in doing so ignore the possibility of unit-treatment interaction, or individual treatment effect heterogeneity (TEH). We assume an individual falls into one of four categories based on his/her potential outcomes: failure on T and C, success on T and C, or success on one or the other. We want to learn about the four underlying probabilities corresponding to membership in these categories. Our problem is that in a parallel group study only half the potential outcomes are observed for each individual. We use a potential outcome framework to make inference about the amount of TEH that is likely to exist in a randomized or non-randomized study.; We focus on bounds for the probability of latently doing worse on a new T than on C, which we call pi01, and which may be understood as the treatment risk. We evaluate properties of existing bound estimators on pi01 which make use of the marginal success probabilities and clustering. Data are simulated from the Dirichlet multinomial (DMN), and estimator properties are assessed under varying degrees of underlying intraclass correlation (ICC) and TEH. Confidence intervals (CI) and coverage properties for lower and upper bound estimators of the heterogeneity parameters of interest are assessed.; Bounds on pi01 are shown to depend heavily on the marginal success probabilities. Bound estimators are shown to have low bias and mean squared error which increases with the ICC. Joint confidence intervals of the lower and upper bounds allow inference on the plausible underlying values of pi01, with widths narrowing with increasing cluster size and ICC.; We also show that assuming the DMN model for the underlying potential outcomes, the heterogeneity parameters of interest can be estimated. Under fewer assumptions, we are able to test the independence of the potential outcomes using a novel declustering technique. We analyze two datasets, a randomized trial and an observational study, to demonstrate the applicability of these methods and how they can be interpreted and utilized. |
