title: Estimation of infection prevalence and sensitivity in a stratified two-stage sampling design employing highly specific diagnostic tests when there is no gold standard.
abstract: In this work, we describe a two-stage sampling design to estimate the infection prevalence in a population. In the first stage, an imperfect diagnostic test was performed on a random sample of the population. In the second stage, a different imperfect test was performed in a stratified random sample of the first sample. To estimate infection prevalence, we assumed conditional independence between the diagnostic tests and develop method of moments estimators based on expectations of the proportions of people with positive and negative results on both tests that are functions of the tests' sensitivity, specificity, and the infection prevalence. A closed-form solution of the estimating equations was obtained assuming a specificity of 100% for both tests. We applied our method to estimate the infection prevalence of visceral leishmaniasis according to two quantitative polymerase chain reaction tests performed on blood samples taken from 4756 patients in northern Ethiopia. The sensitivities of the tests were also estimated, as well as the standard errors of all estimates, using a parametric bootstrap. We also examined the impact of departures from our assumptions of 100% specificity and conditional independence on the estimated prevalence.
authors.affiliation: The Kuvin Center for the Study of Infectious & Tropical Diseases, Department of Microbiology and Molecular Genetics, Institute for Medical Research Israel-Canada, Faculty of Medicine, The Hebrew University of Jerusalem, Jerusalem, 91120, Israel.|The Biostatistics Unit, The Gertner Institute for Epidemiology and Health Policy Research, Sheba Medical Center, Tel Hashomer, Ramat Gan, 52621, Israel.
authors.forename: Ezer
authors.initials: E
authors.lastname: Miller
authors.affiliation: The Biostatistics Unit, The Gertner Institute for Epidemiology and Health Policy Research, Sheba Medical Center, Tel Hashomer, Ramat Gan, 52621, Israel.
authors.forename: Amit
authors.initials: A
authors.lastname: Huppert
authors.affiliation: The Biostatistics Unit, The Gertner Institute for Epidemiology and Health Policy Research, Sheba Medical Center, Tel Hashomer, Ramat Gan, 52621, Israel.
authors.forename: Ilya
authors.initials: I
authors.lastname: Novikov
authors.affiliation: The Kuvin Center for the Study of Infectious & Tropical Diseases, Department of Microbiology and Molecular Genetics, Institute for Medical Research Israel-Canada, Faculty of Medicine, The Hebrew University of Jerusalem, Jerusalem, 91120, Israel.
authors.forename: Alon
authors.initials: A
authors.lastname: Warburg
authors.affiliation: Department of Microbiology, Immunology & Parasitology, Faculty of Medicine, Addis Ababa University, PO Box 28017, Code 1000, Addis Ababa, Ethiopia.
authors.forename: Asrat
authors.initials: A
authors.lastname: Hailu
authors.affiliation: The Kuvin Center for the Study of Infectious & Tropical Diseases, Department of Microbiology and Molecular Genetics, Institute for Medical Research Israel-Canada, Faculty of Medicine, The Hebrew University of Jerusalem, Jerusalem, 91120, Israel.
authors.forename: Ibrahim
authors.initials: I
authors.lastname: Abbasi
authors.affiliation: The Biostatistics Unit, The Gertner Institute for Epidemiology and Health Policy Research, Sheba Medical Center, Tel Hashomer, Ramat Gan, 52621, Israel.
authors.forename: Laurence S
authors.identifier: http://orcid.org/0000-0002-6767-7900
authors.initials: LS
authors.lastname: Freedman
mesh_terms: D015982:Bias; D015331:Cohort Studies; D003141:Communicable Diseases / Q000175:diagnosis* / Q000453:epidemiology*; D003955:Diagnostic Tests, Routine; D004812:Epidemiologic Methods; D005002:Ethiopia / Q000453:epidemiology; D006801:Humans; D007898:Leishmaniasis, Visceral / Q000097:blood / Q000175:diagnosis / Q000453:epidemiology; D015233:Models, Statistical; D016133:Polymerase Chain Reaction; D015995:Prevalence; D011336:Probability; D018401:Sample Size; D012680:Sensitivity and Specificity
keywords: double sampling; prevalence estimation; quantitative PCR; sensitivity; specificity; two-stage design