Estimating the Relative Probability of Direct Transmission between Infectious Disease Patients

Van Ness, Sarah E.; Lee, Robyn; Sebastiani, Paola; Horsburgh, Charles R.; Jenkins, Helen E.; White, Laura F.

Estimating infectious disease parameters such as the serial interval (time between symptom onset in primary and secondary cases) and reproductive number (average number of secondary cases produced by a primary case) are important to understand infectious disease dynamics. Many estimation methods require linking cases by direct transmission, a difficult task for most diseases. Using a subset of cases with detailed genetic or contact investigation data to develop a training set of probable transmission events, we build a model to estimate the relative transmission probability for all case pairs from demographic, spatial and clinical data. Our method is based on naive Bayes, a machine learning classification algorithm which uses the observed frequencies in the training dataset to estimate the probability that a pair is linked given a set of covariates. In simulations we find that the probabilities estimated using genetic distance between cases to define training transmission events are able to distinguish between truly linked and non-linked pairs with high accuracy (area under the receiver operating curve value of 95%). Additionally only a small subset of the cases, 10% - 40% depending on sample size, need to have detailed genetic data for our method to perform well. We show how these probabilities can be used to estimate the average effective reproductive number and apply our method to a tuberculosis outbreak in Hamburg, Germany. Our method is a novel way to infer transmission dynamics in any dataset when only a subset of cases have rich contact investigation and/or genetic data.