Variability in individual causal effects, treatment effect heterogeneity (TEH), is important to the interpretation of clinical trial results, regardless of the marginal treatment effect. Unfortunately, it is usually ignored. In the setting of two-arm randomized studies with binary outcomes, there are estimators for bounds on the probability of control success and treatment failure for an individual, or the treatment risk. Here, those bounds were refined and the sampling properties were assessed using simulations of correlated multinomial data via the Dirichlet multinomial. Results indicated low bias and mean squared error. Moderate to high intraclass correlation (ICC) and large numbers of clusters allow narrower confidence interval widths for the treatment risk.