### Abstract

The two-test two-population model, originally formulated by Hui and Walter, for estimation of test accuracy and prevalence estimation assumes conditionally independent tests, constant accuracy across populations and binomial sampling. The binomial assumption is incorrect if all individuals in a population e.g. child-care centre, village in Africa, or a cattle herd are sampled or if the sample size is large relative to population size. In this paper, we develop statistical methods for evaluating diagnostic test accuracy and prevalence estimation based on finite sample data in the absence of a gold standard. Moreover, two tests are often applied simultaneously for the purpose of obtaining a 'joint' testing strategy that has either higher overall sensitivity or specificity than either of the two tests considered singly. Sequential versions of such strategies are often applied in order to reduce the cost of testing. We thus discuss joint (simultaneous and sequential) testing strategies and inference for them. Using the developed methods, we analyse two real and one simulated data sets, and we compare 'hypergeometric' and 'binomial-based' inferences. Our findings indicate that the posterior standard deviations for prevalence (but not sensitivity and specificity) based on finite population sampling tend to be smaller than their counterparts for infinite population sampling. Finally, we make recommendations about how small the sample size should be relative to the population size to warrant use of the binomial model for prevalence estimation.

Original language | English (US) |
---|---|

Pages (from-to) | 2237-2255 |

Number of pages | 19 |

Journal | Statistics in Medicine |

Volume | 23 |

Issue number | 14 |

DOIs | |

State | Published - Jul 30 2004 |

### Fingerprint

### Keywords

- Bayesian approach
- Gibbs sampling
- Hypergeometric distribution
- Prevalence
- Sensitivity
- Specificity

### ASJC Scopus subject areas

- Epidemiology
- Statistics and Probability

### Cite this

*Statistics in Medicine*,

*23*(14), 2237-2255. https://doi.org/10.1002/sim.1809

**Diagnostic test accuracy and prevalence inferences based on joint and sequential testing with finite population sampling.** / Su, Chun Lung; Gardner, Ian; Johnson, Wesley O.

Research output: Contribution to journal › Article

*Statistics in Medicine*, vol. 23, no. 14, pp. 2237-2255. https://doi.org/10.1002/sim.1809

}

TY - JOUR

T1 - Diagnostic test accuracy and prevalence inferences based on joint and sequential testing with finite population sampling

AU - Su, Chun Lung

AU - Gardner, Ian

AU - Johnson, Wesley O.

PY - 2004/7/30

Y1 - 2004/7/30

N2 - The two-test two-population model, originally formulated by Hui and Walter, for estimation of test accuracy and prevalence estimation assumes conditionally independent tests, constant accuracy across populations and binomial sampling. The binomial assumption is incorrect if all individuals in a population e.g. child-care centre, village in Africa, or a cattle herd are sampled or if the sample size is large relative to population size. In this paper, we develop statistical methods for evaluating diagnostic test accuracy and prevalence estimation based on finite sample data in the absence of a gold standard. Moreover, two tests are often applied simultaneously for the purpose of obtaining a 'joint' testing strategy that has either higher overall sensitivity or specificity than either of the two tests considered singly. Sequential versions of such strategies are often applied in order to reduce the cost of testing. We thus discuss joint (simultaneous and sequential) testing strategies and inference for them. Using the developed methods, we analyse two real and one simulated data sets, and we compare 'hypergeometric' and 'binomial-based' inferences. Our findings indicate that the posterior standard deviations for prevalence (but not sensitivity and specificity) based on finite population sampling tend to be smaller than their counterparts for infinite population sampling. Finally, we make recommendations about how small the sample size should be relative to the population size to warrant use of the binomial model for prevalence estimation.

AB - The two-test two-population model, originally formulated by Hui and Walter, for estimation of test accuracy and prevalence estimation assumes conditionally independent tests, constant accuracy across populations and binomial sampling. The binomial assumption is incorrect if all individuals in a population e.g. child-care centre, village in Africa, or a cattle herd are sampled or if the sample size is large relative to population size. In this paper, we develop statistical methods for evaluating diagnostic test accuracy and prevalence estimation based on finite sample data in the absence of a gold standard. Moreover, two tests are often applied simultaneously for the purpose of obtaining a 'joint' testing strategy that has either higher overall sensitivity or specificity than either of the two tests considered singly. Sequential versions of such strategies are often applied in order to reduce the cost of testing. We thus discuss joint (simultaneous and sequential) testing strategies and inference for them. Using the developed methods, we analyse two real and one simulated data sets, and we compare 'hypergeometric' and 'binomial-based' inferences. Our findings indicate that the posterior standard deviations for prevalence (but not sensitivity and specificity) based on finite population sampling tend to be smaller than their counterparts for infinite population sampling. Finally, we make recommendations about how small the sample size should be relative to the population size to warrant use of the binomial model for prevalence estimation.

KW - Bayesian approach

KW - Gibbs sampling

KW - Hypergeometric distribution

KW - Prevalence

KW - Sensitivity

KW - Specificity

UR - http://www.scopus.com/inward/record.url?scp=3242777025&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3242777025&partnerID=8YFLogxK

U2 - 10.1002/sim.1809

DO - 10.1002/sim.1809

M3 - Article

C2 - 15236428

AN - SCOPUS:3242777025

VL - 23

SP - 2237

EP - 2255

JO - Statistics in Medicine

JF - Statistics in Medicine

SN - 0277-6715

IS - 14

ER -