Estimating heterogeneous transmission with multiple infectives using MCMC methods.

We developed a general procedure for estimating the transmission probability adjusting for covariates when susceptibles are exposed to several infectives concurrently and taking correlation within transmission units into account. The procedure is motivated by a study estimating efficacy of pertussis vaccination based on the secondary attack rate in a rural sub-Saharan community (Niakhar, Senegal) and illustrated with simulations. The procedure is also appropriate to estimate the pairwise transmission probability in transmission studies of live vaccine virus in a collection of transmission units, such as day-care centres or retirement centres. Previously, analyses either excluded transmission units with multiple infectives or ignored co-infectives. Excluding transmission units with multiple infectives is statistically less efficient and ignoring co-infectives can lead to biased estimation. Modelling is carried out by regressing the latent pairwise transmission probability from each infective to a susceptible on covariates and specifying a transmission linkage function linking the latent pairwise transmission probability to the overall transmission probability. Parameters are estimated using Markov chain Monte Carlo methods. Copyright 2003 John Wiley & Sons, Ltd.