A statistical framework for comparing epidemic forests

TL;DR

This paper introduces a statistical framework using chi-square and PERMANOVA tests to compare multiple plausible epidemic transmission trees, aiding in understanding outbreak dynamics despite limited data.

Contribution

It presents the first formal statistical method to compare epidemic forests, improving robustness over existing approaches.

Findings

PERMANOVA outperforms chi-square in sensitivity across various epidemic sizes.

Both methods achieve perfect specificity with large forests (100+ trees).

The framework is implemented in the R package mixtree.

Abstract

Inferring who infected whom in an outbreak is essential for characterising transmission dynamics and guiding public health interventions. However, this task is challenging due to limited surveillance data and the complexity of immunological and social interactions. Instead of a single definitive transmission tree, epidemiologists often consider multiple plausible trees forming \textit{epidemic forests}. Various inference methods and assumptions can yield different epidemic forests, yet no formal test exists to assess whether these differences are statistically significant. We propose such a framework using a chi-square test and permutational multivariate analysis of variance (PERMANOVA). We assessed each method's ability to distinguish simulated epidemic forests generated under different offspring distributions. While both methods achieved perfect specificity for forests with 100+ trees, PERMANOVA consistently outperformed the chi-square test in sensitivity across all epidemic and forest sizes. Implemented in the R package \textit{mixtree}, we provide the first statistical framework to robustly compare epidemic forests.