The prevalence of a disease in a population is defined as the proportion of people
who are infected. Selection bias in disease prevalence estimates occurs if non-participation
in testing is correlated with disease status. Missing data are commonly encountered
in most medical research. Unfortunately, they are often neglected or not
properly handled during analytic procedures, and this may substantially bias the results
of the study, reduce the study power, and lead to invalid conclusions. The goal
of this study is to illustrate how to estimate prevalence in the presence of missing data.
We consider a case where the variable of interest (response variable) is binary and
some of the observations are missing and assume that all the covariates are fully observed.
In most cases, the statistic of interest, when faced with binary data is the prevalence.
We develop a two stage approach to improve the prevalence estimates; in
the first stage, we use the logistic regression model to predict the missing binary observations
and then in the second stage we recalculate the prevalence using the observed
data and the imputed missing data. Such a model would be of great interest in
research studies involving HIV/AIDS in which people usually refuse to donate blood
for testing yet they are willing to provide other covariates. The prevalence estimation
method is illustrated using simulated data and applied to HIV/AIDS data from the
Kenya AIDS Indicator Survey, 2007.