# A Dirichlet‐Multinomial Gibbs Algorithm for Assessing the Accuracy of Binary Tests in the Absence of a Gold Standard

## TL;DR

This paper introduces a statistical method to evaluate the accuracy of multiple binary tests for a disease when no perfect diagnostic test exists.

## Contribution

A novel Dirichlet-multinomial Gibbs algorithm is proposed to estimate test accuracy with conditional independence across test groups.

## Key findings

- The model successfully estimated sensitivity and specificity for four Chlamydia tests.
- The method handled missing data effectively by treating 10% of the data as randomly missing.
- Conditional independence between test groups improved the accuracy of the estimates.

## Abstract

Each patient is simultaneously given several binary tests for a disease. The tests are partitioned into disjoint groups, assumed to be conditionally independent between groups, but allowed to have arbitrary dependence within a group. The groups are intended to capture similar biological features of the tests. A Dirichlet‐multinomial model is employed with a Gibbs Sampler to estimate the sensitivity and specificity of the tests. The model is exemplified by data on four tests for Chlamydia, both with complete data and with a random 10% of the data treated as missing.