Transmission of Pneumococcal Carriage in Families: A Latent Markov Process Model for Binary Longitudinal Data

Abstract

We present a Bayesian data augmentation model to estimate acquisition and clearance rates of carriage of Streptococcus pneumoniae (Pnc) bacteria. The panel observation data comprise 10 measurements of Pnc carriage (carrier/noncarrier of the bacteria) in all members of 97 families with young children over a period of 2 years. Using natural conditional independence assumptions, a transmission model is constructed for the unobserved dependent binary processes of the augmented data. The model explicitly considers carriage transmission within the family and carriage acquisition from the surrounding community. The joint posterior of the model parameters and the augmented data is explored by Markov chain Monte Carlo sampling. The analysis shows that in young children the rate of acquiring carriage of three common Pnc serotypes increases with age. In children less than 2 years old, the duration of carriage is longer than in older family members. Asymptomatic Pnc carriage is found highly transmittable between members of the same family. In young children, the estimated rate of acquiring carriage from a family member carrying Pnc is more than 20-fold to that from acquiring it from the community.

Key Words:

• Bayesian analysis
• Conditional independence modeling
• Data augmentation
• Markov chain Monte Carlo
• Recurrent infection