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Abstract:
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Studies for assessing the effect of a treatment on multivariate outcome variables present technical challenges because the dependence structure of the joint outcomes cannot be ignored. From this perspective, useful insights can be achieved using the class of regression graphs for modeling sequences of non-independent regressions. An appealing aspect is the definition of the treatment effect on joint sets of outcomes rather than on single ones. We introduce a set of "new outcomes" of interest defined as function of subsets of outcomes, and novel treatment effect estimators for these new targets. This approach is particularly interesting in case of discrete variables where, given a multi-way contingency table representation, the cells of the table are used to identify these "new outcomes". Using the log-mean linear parameterization of Lupparelli and Roverato (2015) for discrete regression graphs, we derive a set of estimators for a novel class of relative risks for multiple outcomes. These quantities will allow us to easily disentangle the treatment effect on the "new outcomes" in two components: the effect on marginal outcomes and the effect on their dependence structure.
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