### Abstract

Most neuropsychologists are aware that, given the specificity and sensitivity of a test and an estimate of the base rate of a disorder, Bayes' theorem can be used to provide a post-test probability for the presence of the disorder given a positive test result (and a post-test probability for the absence of a disorder given a negative result). However, in the standard application of Bayes' theorem the three quantities (sensitivity, specificity, and the base rate) are all treated as fixed, known quantities. This is very unrealistic as there may be considerable uncertainty over these quantities and therefore even greater uncertainty over the post-test probability. Methods of obtaining interval estimates on the specificity and sensitivity of a test are set out. In addition, drawing and extending upon work by Mossman and Berger (2001), a Monte Carlo method is used to obtain interval estimates for post-test probabilities. All the methods have been implemented in a computer program, which is described and made available (www.abdn.ac.uk/similar to psy086/dept/BayesPTP.htm). When objective data on the base rate are lacking (or have limited relevance to the case at hand) the program elicits opinion for the pre-test probability.

Original language | English |
---|---|

Pages (from-to) | 624-644 |

Number of pages | 21 |

Journal | Clinical Neuropsychologist |

Volume | 23 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2009 |

### Keywords

- post-test probabilities
- Bayesian methods
- diagnostic testing
- interval estimates
- quantitative methods
- test score
- distributions
- confidence
- limits

### Cite this

*Clinical Neuropsychologist*,

*23*(4), 624-644. https://doi.org/10.1080/13854040802524229

**Bayes' theorem and diagnostic tests in neuropsychology : interval estimates for post-test probabilities.** / Crawford, John R.; Garthwaite, Paul H.; Betkowska, Karolina.

Research output: Contribution to journal › Article

*Clinical Neuropsychologist*, vol. 23, no. 4, pp. 624-644. https://doi.org/10.1080/13854040802524229

}

TY - JOUR

T1 - Bayes' theorem and diagnostic tests in neuropsychology

T2 - interval estimates for post-test probabilities

AU - Crawford, John R.

AU - Garthwaite, Paul H.

AU - Betkowska, Karolina

PY - 2009

Y1 - 2009

N2 - Most neuropsychologists are aware that, given the specificity and sensitivity of a test and an estimate of the base rate of a disorder, Bayes' theorem can be used to provide a post-test probability for the presence of the disorder given a positive test result (and a post-test probability for the absence of a disorder given a negative result). However, in the standard application of Bayes' theorem the three quantities (sensitivity, specificity, and the base rate) are all treated as fixed, known quantities. This is very unrealistic as there may be considerable uncertainty over these quantities and therefore even greater uncertainty over the post-test probability. Methods of obtaining interval estimates on the specificity and sensitivity of a test are set out. In addition, drawing and extending upon work by Mossman and Berger (2001), a Monte Carlo method is used to obtain interval estimates for post-test probabilities. All the methods have been implemented in a computer program, which is described and made available (www.abdn.ac.uk/similar to psy086/dept/BayesPTP.htm). When objective data on the base rate are lacking (or have limited relevance to the case at hand) the program elicits opinion for the pre-test probability.

AB - Most neuropsychologists are aware that, given the specificity and sensitivity of a test and an estimate of the base rate of a disorder, Bayes' theorem can be used to provide a post-test probability for the presence of the disorder given a positive test result (and a post-test probability for the absence of a disorder given a negative result). However, in the standard application of Bayes' theorem the three quantities (sensitivity, specificity, and the base rate) are all treated as fixed, known quantities. This is very unrealistic as there may be considerable uncertainty over these quantities and therefore even greater uncertainty over the post-test probability. Methods of obtaining interval estimates on the specificity and sensitivity of a test are set out. In addition, drawing and extending upon work by Mossman and Berger (2001), a Monte Carlo method is used to obtain interval estimates for post-test probabilities. All the methods have been implemented in a computer program, which is described and made available (www.abdn.ac.uk/similar to psy086/dept/BayesPTP.htm). When objective data on the base rate are lacking (or have limited relevance to the case at hand) the program elicits opinion for the pre-test probability.

KW - post-test probabilities

KW - Bayesian methods

KW - diagnostic testing

KW - interval estimates

KW - quantitative methods

KW - test score

KW - distributions

KW - confidence

KW - limits

U2 - 10.1080/13854040802524229

DO - 10.1080/13854040802524229

M3 - Article

VL - 23

SP - 624

EP - 644

JO - Clinical Neuropsychologist

JF - Clinical Neuropsychologist

SN - 1385-4046

IS - 4

ER -