Multi-state Transition Models With Censoring in Vertical Transmission of Hiv

Abstract

In this study we have developed multistate models with censoring for vertical transmis- sion of HIV, also refered to as mother to child transmission of HIV. We then use the multistate models developed to derive the forward Kolmogorov di erential equations. Depending on when transmission takes place, whether in-utero, intrapartum or postpar- tum we introduced the aspect of censoring when estimating the transition intensities from the transition probabilities. The study is in two parts, multi-state models for a child born infected where we consider two and three state models and multistate mod- els for a child born healthy where we have three, four and ve state models. In each part we have solved the respective forward Kolmogorov di erential equations using the generator matrix approach to obtain the transition probabilities which are in form of transition intensities. Maximum likelihood estimation method is then used to estimate the transition intensities. From the results we observe that the transition probabilities are exponentialy distributed and that if the number of infected children are maintained at a constant number then the transition intensities will approach zero as time increases.