Properties Of Bound Estimators On Treatment Effect Heterogeneity For Binary Outcomes

Abstract

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.

Estimating Treatment Effect Heterogeneity for Binary Outcomes via Dirichlet Multinomial Constraints

“…This method can be shown to assume a zero correlation among the potential outcomes, an assumption that we are in fact trying to test by our methods! It has been shown that higher number of clusters and increasing intraclass correlation reduce confidence interval width for existing bounds on treatment risk (Mascha and Albert, 2006). Similar properties were observed for the estimation of treatment risk here, although only variations on the ICC are reported.…”

“…As we have shown, and as shown by Mascha and Albert (2006) in their work assessing properties of the AGM bounds, clustering helps to tighten the confidence intervals on bounds and on estimates for the treatment risk and potential outcome correlation. We therefore created the same 40 post-hoc clusters as did AGM using quantiles of the logit score of each individual from a model predicting their observed success on either treatment or control from baseline factors (not including treatment).…”

“…Thus the AGM confidence intervals account for uncertainty on two levels: the nonidentifiability of the parameters of interest in the population and the sampling error. Mascha and Albert (2006) further show that confidence interval widths based on the AGM bounds are generally rather wide, unless at least one of the marginal probabilities is close to 0 or 1 or the intraclass correlation is very high. Estimation of the treatment risk and other TEH parameters may therefore be preferred over bounds.…”

“…We now proceed to set up a data model and distributional constraints which will permit us to estimate q po and p 01 . Albert et al (2005) and in more detail, Mascha and Albert (2006), showed that clustered data can help narrow the bounds on p 01 , the treatment risk. Mascha and Albert (2006) found that a higher number of clusters and higher intraclass correlation (or ICC) reduce the width of confidence intervals around modified AGM bounds for the treatment risk.…”

“…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.…”