Bayesian modeling of the accuracy of diagnostic tests

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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
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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 Binn, Se (1- )(1-Sp)

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Background

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

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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).

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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?

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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.

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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.

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Example Estimate Se and Sp of an ELISA for
Toxoplasmosis

• A new test, ELISA, is considered to replace a
  standard test MATmicroscopic 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.

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Toxoplasmosis Data

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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(.,.)

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Posterior Medians for the Se and Sp of the ELISA
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95 Probability Intervals for the Se and Sp of
the ELISA
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Conclusions

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

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