title: A two-stage Bayesian method for estimating accuracy and disease prevalence for two dependent dichotomous screening tests when the status of individuals who are negative on both tests is unverified.
abstract: BACKGROUND
  Estimating the disease prevalence and test accuracy (sensitivity and specificity) for two dependent screening tests when the status of individuals who are negative on both tests is unverified represents a considerable challenge, as the disease rates for individuals negative on both tests are not identifiable without additional assumptions.
  
  
  METHODS
  This article presents a unified framework for handling this non-identifiability problem using two-step hierarchical informative prior on the sensitivities by two-stage Bayesian modeling with the characterized by joint testing strategies based on the inherent attribute of screening/diagnostic tests. We assign a diffuse and less risky two-step hierarchical informative uniform prior to the sensitivities while assigning a uniform (0,1) prior distribution to the specificities and prevalence. Strategies for model evaluation, general global evaluations, and individual cell checking are presented. Simulations are conducted under various scenarios to evaluate the performance of the proposed method. Applications to real data are also presented to illustrate the potential impact and benefit of the proposed method.
  
  
  RESULTS
  Our results indicate that when the priors of sensitivities are assigned as appropriate two-step hierarchical informative priors, or even in the absence of the priors for the specificities and prevalence, the parameters involved in this study can still be estimated well. The advantages and limitations of this method in solving such problems are discussed and compared with other two-stage methods.
  
  
  CONCLUSIONS
  We developed a two-stage Bayesian method for two dependent dichotomous screening tests with unverified individuals who are negative on both tests, and addressed the ad hoc model evaluation and checking procedures. The method can be understood easily and used conveniently by non-statisticians.
authors.forename: Jin
authors.initials: J
authors.lastname: Liu
authors.affiliation: Department of Epidemiology and Biostatistics, School of Public Health, Nanjing Medical University, Nanjing, Jiangsu, PR China. dr.chenfeng@163.com.
authors.forename: Feng
authors.initials: F
authors.lastname: Chen
authors.forename: Hao
authors.initials: H
authors.lastname: Yu
authors.forename: Ping
authors.initials: P
authors.lastname: Zeng
authors.forename: Liya
authors.initials: L
authors.lastname: Liu
mesh_terms: D000328:Adult; D001499:Bayes Theorem; D015179:Colorectal Neoplasms / Q000175:diagnosis / Q000453:epidemiology*; D003198:Computer Simulation; D005260:Female; D006801:Humans; D008297:Male; D008403:Mass Screening / Q000379:methods / Q000706:statistics & numerical data*; D008875:Middle Aged; D015233:Models, Statistical; D009780:Occult Blood; D015995:Prevalence; D012680:Sensitivity and Specificity