Logically defined outcomes are commonly used in medical diagnoses and epidemiological research. When missing values in the original outcomes exist, the method of handling the missingness can have unintended consequences, even if the original outcomes are missing completely at random. Complicating the issue is that the default behavior of standard statistical packages yields different results. In this paper, we consider two binary original outcomes, which are missing completely at random. For estimating the prevalence of a logically defined "or" outcome, we discuss the properties of four estimators: complete case estimator, all-available case estimator, maximum likelihood estimator (MLE), and moment-based estimator. With the exception of the all-available case estimator, the estimators are consistent. A simulation study is conducted to evaluate the finite sample performance of the four estimators and an analysis of hypertension data from the Sleep Heart Health Study is presented.



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