Branching process models to identify risk factors for infectious disease transmission

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 2003-2009. 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.