Modeling transmission of multitype infectious agents: application to carriage of Streptococcus pneumoniae

We describe a novel Bayesian approach to estimate acquisition and clearance rates for many competing subtypes of a pathogen in a susceptible-infected-susceptible model. The inference relies on repeated measurements of the current status of being a non-carrier (susceptible) or a carrier (infected) of one of the n(q)  > 1 subtypes. We typically collect the measurements with sampling intervals that may not catch the true speed of the underlying dynamics. We tackle the problem of incompletely observed data with Bayesian data augmentation, which integrates over possible carriage histories, allowing the data to contain intermittently missing values, complete dropouts of study subjects, or inclusion of new study subjects during the follow-up. We investigate the performance of the described method through simulations by using two different mixing groups (family and daycare) and different sampling intervals. For comparison, we describe crude maximum likelihood-based estimates derived directly from the observations. We apply the estimation algorithm to data about transmission of Streptococcus pneumonia in Bangladeshi families. The computationally intensive Bayesian approach is a valid method to account for incomplete observations, and we found that it performs generally better than the simple crude method, in particular with large amount of missing data.