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 immunodeficien cy virus (HIV) may or may not become infected by perinatal transmissio n. Unfortunately, passively transferred maternal antibodies make it ha rd to determine the infant's infection status from HIV antibody testin g, because shortly after birth it is not possible to distinguish passi vely transferred maternal antibodies from antibodies produced by an in fected 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 (AI DS). 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 an d biased. In this note, we define a mixture model underlying the onset time of AIDS and then obtain the nonparametric maximum likelihood est imators 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 diff erent groups of infants. Finally, the methods are applied to the Mothe rs 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%).