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Biostatistics Advance Access published online on March 23, 2007
Biostatistics, doi:10.1093/biostatistics/kxm006
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© The Author 2007. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

On the potential for illogic with logically defined outcomes

Xianbin Li*, Brian Caffo and Daniel Scharfstein

Department of Biostatistics, Johns Hopkins University, Baltimore, MD 21205, USA xli{at}jhsph.edu

* To whom correspondence should be addressed.

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. In this note, we consider 2 binary original outcomes, which are missing completely at random. For estimating the prevalence of a logically defined "or" outcome, we discuss the properties of 4 estimators: the complete-case estimator, the available-case estimator, the maximum likelihood estimator (MLE), and a moment-based estimator. With the exception of the available-case case estimator, all the estimators are consistent. The MLE exhibits superior performance and should be generally adopted.

Keywords: Available-case estimator; Complete-case estimator; Hypertension; Maximum likelihood estimator; Missing data; Moment-based estimator

Received November 5, 2006; revised January 12, 2007; accepted for publication February 7, 2007.


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