Properties of the Hui and Walter and Related Methods for Estimating Prevalence Rates and Error Rates of Diagnostic Testi
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PROPERTIES OF THE HUI AND WALTER AND RELATED METHODS FOR ESTIMATING PREVALENCE RATES AND ERROR RATES OF DIAGNOSTIC TESTING PROCEDURES MICHAEL D. SINCLAIR, PHD Senior Statistician, Mathematica Policy Research, Princeton, New Jersey
JOSEPHL. GASTWIRTH, PHD Visiting Scientist, Division of Cancer Epidemiology and Genetics, National Cancer Institute, and Professor of Economics and Statistics. The George Washington University Department of Statistics, Washington, District of Columbia
When a confirmatory test is completely accurate or has known low error rates, the sensitivity and the specificity of a screening test can be estimated. When the error rates for the confirmatory test are unknown, Hui and Walter ( 2 ) presented a method for estimating the sensitivity and specificity of both the screening and the confirmatory tests using the tests on two populations with diferent prevalence rates of the infection. The method requires that the tests have equal error rates in the two populations, When this requirement is not met, we show that the estimated prevalence rates are robust when the difference in the prevalence rates of the two subpopulations is large. An alternative design, requiring only one population, but other assumptions, is also described. Key Words: Diagnostic tests; Classification errors; Sensitivity; Specificity; Evaluation
design
INTRODUCTION
has the same error rates. Goldberg (3) noted that obtaining two subpopulations satisfying A RECENT PAPER BY Hui and Xiao ( l ) this criteria may be difficult. For example, discusses the evaluation of diagnostic tests Gastwirth (4)cited data showing that the acwhen a gold standard Or perfect confimato9’ curacy of the early ELISA screening test for test is not available. Hui and Walter (2) de- the HIV virus differed in men and veloped a method to estimate the error rates paper explores the bias in the Hui in a diagnostic test when it and a second test and Walter (2) method when the assumption are to groups Of This of equal classification errors in the two subprocedure requires two subpopulations with populations is violated. First, we will review different prevalence rates in which each test the Hui Walter ( 2 ) method and discuss its properties when the assumption of equal classification errors is violated. Second, we Reprint address: Dr. Michael D. Sinclair, Mathematica present an alternative design using only one Policy Research, 600 Alexander Park, P.O. Box 2393, population. Finally, we di!Xuss a ~ u ~ e r i c a l Princeton, NJ 08543-2393. study which examines the sensitivity of the 605
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Michael D. Sinclair and Joseph L. Gastwirth
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estimated accuracy rates to violations in the assumptions required for both methods.
error rates, the probabilities, Pglj,are as in (1).
Study Designs for Estimating the Accuracy of Screening Tests We will assume that two tests with dichotomous responses are applied to a sample of ng
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