A simple Bayesian model to estimate proportions and ratios from count data with a hierarchical error structure with an application to droplet digital PCR experiments

2023/05/04 by Elyas Mouhou, Mouhou, Elyas, Vincent Audigier +3
Biochemistry, Genetics and Molecular Biology · Decision Sciences · Mathematics · #Applications (stat.AP) #FOS: Computer and information sciences #Gene expression and cancer classification #Optimal Experimental Design Methods #Statistical Methods in Clinical Trials

paper · pdf · doi:10.48550/arxiv.2305.02700

openalex publication_date 2023/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Experimental designs with hierarchically-structured errors are pervasive in many biomedical areas; it is important to take into account this hierarchical architecture in order to account for the dispersion and make reliable inferences from the data. This paper addresses the question of estimating a proportion or a ratio from positive or negative count data akin to those generated by droplet digital polymerase chain reaction experiments when the number of biological or technical replicates is limited. We present and discuss a Bayesian framework, for which we provide and implement a Gibbs sampler in R and compare it to a random effect model.

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