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Bayesian modeling of the accuracy of diagnostic tests

Bayesian modeling of the accuracy of diagnostic tests. Adam Branscum - Dept. of Statistics, U.C. Davis Wes Johnson - Dept. of Statistics, U.C. Davis Ian Gardner - Dept. of Medicine and Epidemiology, U.C. Davis.

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Bayesian modeling of the accuracy of diagnostic tests

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  1. Bayesian modeling of the accuracy of diagnostic tests Adam Branscum - Dept. of Statistics, U.C. Davis Wes Johnson - Dept. of Statistics, U.C. Davis Ian Gardner - Dept. of Medicine and Epidemiology, U.C. Davis EPIDEMIOLOGY UC Davis

  2. Background • Problem: Estimate the sensitivity, Se, and specificity, Sp, of a single diagnostic test. • Solution 1: Apply the test to n randomly sampled animals from a herd with prevalence • The number of T+ animals assuming binomial sampling is T+| ,Se,Sp ~ Bin[n, Se + (1- )(1-Sp)]

  3. Background • Hence T+ / n estimates Se + (1- )(1-Sp) • Cannot estimate Se and Sp without other information or assumptions.

  4. Background • Solution 2: Given a second test and a distinct second population, apply both tests to randomly sampled animals from the two populations. Then all 6 parameters are estimable (Hui and Walter, 1980).

  5. Background • KEY ASSUMPTION: Conditional Independence – test outcomes for a given animal are independent, conditional on disease status. • Valid, for instance, if the 2 tests measure different biological processes. • What if the two tests are conditionally dependent?

  6. A Bayesian Solution • This adds 2 correlation parameters to the model: • But not all 8 parameters are estimable from the data. • Inclusion of prior information saves the day.

  7. A Bayesian Solution • Prior Information: Usually one test will be well known as will the two prevalences (Dendukuri and Joseph 2001; Georgiadis et al.,2003). • Easy to extend this idea to the 3-test, 2-population setting. - Yields more precise parameter estimates as compared to the 2-tests, 2-population setting.

  8. Example: Estimate Se and Sp of an ELISA for Toxoplasmosis • A new test, ELISA, is considered to replace a standard test MAT=microscopic agglutination test. ELISA and MAT are conditionally dependent. • Third independent test (Mouse Bioassay) is available with Sp of essentially 1 and moderate Se. • Data: Random samples of pigs from 2 populations and each pig was tested with all 3 tests.

  9. Toxoplasmosis Data

  10. 3-tests, 2-population • Assume 2 response vectors are multinomial • Informative priors for Se and Sp of both the MAT and Mouse bioassay and for the 2 prevalences. • Fit model in WinBUGS (code on our webpage) - Multinomial likelihood: y ~ dmulti(.,.) - Beta Priors: Se ~ dbeta(.,.)

  11. Posterior Medians for the Se and Sp of the ELISA

  12. 95% Probability Intervals for the Se and Sp of the ELISA

  13. Conclusions • With informative prior information, estimation of the accuracies of dependent tests is possible. • Models are easily fitted in WinBUGS.

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