Branching Process Models to Identify Risk Factors for Infectious Disease Transmission

• Published in: Journal of computational and graphical statistics Vol. 31; no. 2; pp. 529 - 540
• Main Authors: Gallagher, Shannon K., Follmann, Dean
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 03-04-2022; Taylor & Francis Ltd
• Subjects: Algorithms; Branching (mathematics); Branching process; Clusters; Disease transmission; Infectious diseases; Markov processes; Maximum likelihood estimates; Monte Carlo sampling; Risk analysis; Risk factors; Transmission trees; Trees; Tuberculosis; Unobserved transmission
• ISSN: 1061-8600; 1537-2715
• DOI: 10.1080/10618600.2021.2000871

Simple branching processes for infectious disease transmission assume all individuals are homogeneous, which means that risk factors that may inhibit or increase transmission are unable to be identified. In this work, we develop a branching process model that allows for identification of risk factors by assuming the probability of onward transmission is determined by the individual's covariates. Because enumerating the transmission trees is infeasible for large clusters, we develop an algorithm to sample transmission trees to compute approximate maximum likelihood estimates. We then discuss how our model can be extended to account for cases that are undetected but are part of the true transmission tree. We use our method to investigate individual characteristics that are associated with transmission of Tuberculosis using clusters of detected cases in Maryland from 2003 to 2009. We find that later detection within a cluster is associated with an increased probability of onward transmission (OR = 1.41 [95% CI: 1.31, 1.52]). We show some of most likely transmission trees from our model, and results can be reproduced via our R package InfectionTrees. Supplementary files for this article are available online.