Binary outcomes defined by logical (Boolean) "and" or "or" operations on original continuous and discrete outcomes arise commonly in medical diagnoses and epidemiological research. In this manuscript,we consider applying the “or” operator to two continuous variables above a threshold and a binary variable, a setting that occurs frequently in the modeling of hypertension. Rather than modeling the resulting composite outcome defined by the logical operator, we present a method that models the original outcomes thus utilizing all information in the data, yet continues to yield conclusions on the composite scale. A stratified propensity score adjustment is proposed to account for confounding variables. A Mantel-Haenszel style combination of strata-specific odds ratios is proposed to evaluate a risk factor. The benefits of the proposed approach include easy handling of missing data and the ability to estimate the correlations between the original outcomes. We emphasize that the model retains the ability to evaluate odds ratios on the simpler and more easily interpreted composite scale. The approach is evaluated by Monte Carlo simulations. An example of the analysis of the impact of sleep disordered breathing on a standard composite hypertension measure, based on blood pressure measurements and medication usage,is included.


Statistical Models