This method uses a Bayesian approach and Gibbs sampling to estimate the true animal-level prevalence of infection based on testing of individual (not pooled) samples using a test with imperfect sensitivity and/or specificity. As for the Bayesian method for pooled sampling, the analysis requires prior estimates of true prevalence, test sensitivity and test specificity as Beta probability distributions, and outputs posterior distributions for prevalence, sensitivity and specificity. This method is preferable to the conventional (Rogan-Gladen) method for estimating true prevalence, because it allows for uncertainty about the true values for sensitivity and specificity when calculating probability limits for the true prevalence estimate, which are not routinely included in the conventional approach. It also allows incorporation of prior information on the likely true prevalence based on pre-existing estimates or expert opinion.

For this analysis, the original values for stool sampling
for *Strongyloides* infection in Cambodian refugees from Joseph et al. (1996) were used, as listed in the table
below, and 95% probability limits were calculated about the estimated prevalence.

Input | Value |
---|---|

Number tested | 162 |

Number test + ve | 40 |

Prior prevalence alpha | 1 |

Prior prevalence beta | 1 |

Prior Se alpha | 4.44 |

Prior Se beta | 13.31 |

Prior Sp alpha | 71.25 |

Prior Sp beta | 3.75 |

Iterations | 25000 |

Discard | 5000 |

True pos start | 35 |

False neg start | 35 |

The prior Beta distributions defined above are equivalent to:

Distribution | Alpha value | Beta value | 2.5% percentile | Median | 97.5% percentile | Mean | Mode | Standard deviation |
---|---|---|---|---|---|---|---|---|

Prevalence | 1 | 1 | 0.025 | 0.5 | 0.975 | 0.5 | 0.2887 | |

Sensitivity | 4.44 | 13.31 | 0.0843 | 0.2406 | 0.469 | 0.2501 | 0.2184 | 0.1 |

Specificity | 71.25 | 3.75 | 0.8909 | 0.954 | 0.9868 | 0.95 | 0.9623 | 0.025 |

The simulation was run for 25,000 iterations, with 5,000 iterations discarded to allow for convergence. Posterior probability distributions for prevalence, sensitivity, specificity and other parameters from the analysis are summarised below.

Prevalence | Sensitivity | Specificity | PPV | NPV | LR for positive | LR for negative | True positives | False negatives | |
---|---|---|---|---|---|---|---|---|---|

Minimum | 0.171 | 0.135 | 0.8 | 0.197 | 0.243 | 1 | 0.32 | 7 | 7 |

0.025 | 0.393 | 0.212 | 0.882 | 0.665 | 0.336 | 2.4 | 0.54 | 29 | 33 |

Median | 0.738 | 0.307 | 0.951 | 0.883 | 0.538 | 6.4 | 0.73 | 38 | 82 |

0.975 | 0.985 | 0.484 | 0.986 | 0.969 | 0.786 | 24.4 | 0.85 | 40 | 120 |

Maximum | 1 | 0.697 | 0.998 | 0.994 | 0.907 | 157.8 | 1 | 40 | 122 |

Mean | 0.728 | 0.316 | 0.948 | 0.871 | 0.544 | 7.5 | 0.72 | 38 | 81 |

SD | 0.165 | 0.07 | 0.027 | 0.08 | 0.124 | 6.4 | 0.08 | 3 | 25 |

Iterations | 20000 | 20000 | 20000 | 20000 | 20000 | 20000 | 20000 | 20000 | 20000 |

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