%0 Journal Article
%T Estimating Prevalence Using an Imperfect Test
%A Peter J. Diggle
%J Epidemiology Research International
%D 2011
%I Hindawi Publishing Corporation
%R 10.1155/2011/608719
%X The standard estimate of prevalence is the proportion of positive results obtained from the application of a diagnostic test to a random sample of individuals drawn from the population of interest. When the diagnostic test is imperfect, this estimate is biased. We give simple formulae, previously described by Greenland (1996) for correcting the bias and for calculating confidence intervals for the prevalence when the sensitivity and specificity of the test are known. We suggest a Bayesian method for constructing credible intervals for the prevalence when sensitivity and specificity are unknown. We provide R code to implement the method. 1. Introduction The prevalence, , of a disease is the proportion of subjects in the population of interest who have the disease in question [1, page 46]. A standard way to estimate prevalence is to apply a diagnostic test to a random sample of individuals and use the estimator where is the number of individuals who test positive. The sensitivity, , of a diagnostic test for presence/absence of a disease is the probability that the test will give a positive result, conditional on the subject being tested having the disease, whilst the specificity, , is the probability that the test will give a negative result, conditional on the subject not having the disease. An imperfect test is one for which at least one of and is less than one. An imperfect test may give either or both of a false positive or a false negative result, with respective probabilities and . A similar issue arises in individual diagnostic testing. In that context, prevalence is assumed to be known and the objective is to make a diagnosis for each subject tested. Important quantities are then the positive and negative predictive values, defined as the conditional probabilities that a subject does or does not have the disease in question, given that they show a positive or negative test result, respectively. Even when both and are close to one, the positive and negative predictive values of a diagnostic test depend critically on the true prevalence of the disease in the population being tested. In particular, for a rare disease, the positive predictive value can be much smaller than either or . 2. Estimation of Prevalence Suppose that an imperfect test is applied to a random sample of subjects, of whom give a positive result. The standard estimator given by (1) is now biased for . Let denote the expectation of . Then, the relationship between and is linear, and given by [2]. Under the reasonable assumption that , that is, that the test is superior to the toss
%U http://www.hindawi.com/journals/eri/2011/608719/