Timing of human immunodeficiency virus type 1 (HIV-1) transmission from mother to child: bayesian estimation using a mixture.

The timing of mother-to-child HIV transmission is not directly observable but influences the infected child's viral and immune status in the neonatal period. A hierarchical model was developed in a Bayesian framework to 'back-calculate' the timing of HIV-1 transmission from mother to child from the virological and immunological kinetics in the infected infant. Joint evolution of viral markers and immune response was modelled as a continuous time Markov process. The modelling of the period from infection to birth was based on a mixture of three distributions taking into account the various mother-to-child transmission pathways: In utero (early or late in gestation) and intrapartum (during the delivery process), integrating the fact that transmission is a continuum during the pregnancy. Gibbs sampling was used to estimate the marginal posterior distributions of the transition intensities between stages of HIV infection and those of the individual times from infection to birth. We applied our model to data on 135 perinatally HIV-1-infected children included in the French Prospective Study on Pediatric HIV infection. The model suggested that transmission occurred late in utero during the last month of pregnancy and that the day of delivery was a particularly critical time in HIV-1 transmission from mother to child. The paper ends with a discussion of model assumptions and a comparison with results obtained using a non-parametric method.