Generalized Statistical Modeling Maternal Infant HIV Transmission with Constant Hazard Rate

Knowledge of the timing of perinatal transmission of Human Immunodeficiency Virus (HIV) would be valuable for the determination and evaluation of preventive treatments. Effective strategies are urgently needed to reduce mother to infant perinatal HIV transmission. Various ongoing or planned trials and studies concentrate on mode of infant feeding or antiretroviral therapy to the infant over the breastfeeding period. It is essential to determine the risk of perinatal HIV transmission. Further it is also essential to observe when the perinatal transmission takes place in infant. The main idea of modeling is to estimate the probabilities of positive polymerase chain reaction (PCR). The transmission of HIV from a HIV-positive mother to her child during pregnancy, labour, delivery or breastfeeding is called perinatal transmission.  It results from fetal exposure to the maternal fluids or infected maternal secretions. The present article proposes the generalized statistical models that simultaneously estimate the risks of perinatal transmission together with the sensitivity of the screening tests for HIV infection. The article aims at brief overview of exponential and geometric distribution as lag time distributions. The methods are illustrated with the data from a randomized control study, conducted in South Africa.