# Reconciling Binary Replicates: Beyond the Average

## TL;DR

This paper explores better ways to analyze repeated binary medical data, showing that new methods like Bayesian approaches can improve diagnostic accuracy over traditional averaging.

## Contribution

Proposes and evaluates three alternative methods to averaging for analyzing binary replicates, emphasizing Bayesian approaches with uncertainty.

## Key findings

- Bayesian methods outperform averaging in diagnostic accuracy and provide credible intervals.
- Simulations and real datasets show practical benefits of the proposed methods.
- Incorporating uncertainty improves disease prevalence estimation.

## Abstract

Binary observations are often repeated to improve data quality, creating technical replicates. Several scoring methods are commonly used to infer the actual individual state and obtain a probability for each state. The common practice of averaging replicates has limitations, and alternative methods for scoring and classifying individuals are proposed. Additionally, an indecisive response might be wiser than classifying all individuals based on their replicates in the medical context, where 1 indicates a particular health condition. Building on the inherent limitations of the averaging approach, three alternative methods are examined: the median, maximum penalized likelihood estimation, and a Bayesian algorithm. The theoretical analysis suggests that the proposed alternatives outperform the averaging approach, especially the Bayesian method, which incorporates uncertainty and provides credible intervals. Simulations and real‐world medical datasets are used to demonstrate the practical implications of these methods for improving diagnostic accuracy and disease prevalence estimation.