A nonparametric analysis of the transmission rate of human immunodeficiency virus from mother to infant

Infants born to mothers who are infected with the human immunodeficiency virus (HIV) may or may not become infected by perinatal transmission. Unfortunately, passively transferred maternal antibodies make it hard to determine the infant's infection status from HIV antibody testing, because shortly after birth it is not possible to distinguish passively transferred maternal antibodies from antibodies produced by an infected infant. Usually, the infection status is unobservable for each infant, unless the infant reaches the age of 15 months or develops an HIV-related disease such as the acquired immunodeficiency syndrome (AIDS). Traditionally, statistical analyses of the perinatal transmission rate of HIV are based on infants who had been born at least 15 months before the date of analysis. Such analyses can be both inefficient and biased. In this note, we define a mixture model underlying the onset time of AIDS and then obtain the nonparametric maximum likelihood estimators of the HIV transmission rate and of the distribution function of AIDS onset time for infected infants. Nonparametric tests are also derived for detecting differences in HIV transmission rates among different groups of infants. Finally, the methods are applied to the Mothers and Infants Cohort Study in New York City. The transmission rate of HIV from infected mothers to their infants was estimated to be 30.0% with 95% confidence interval (22.3%, 39.1%).