Maternal-to-infant transmission of the human immunodeficiency virus (HI V) accounts for most cases of acquired immune deficiency syndrome (AIDS) in children. In New York City more than 500 cases of AIDS attributed to such transmission were reported before the end of 1989; this accounts for 80% of the cases of pediatric AIDS in the United States. In addition to surveillance of AIDS cases, the New York State Health Department instituted a program to screen the blood of newborns for presence of HIV antibodies in December 1987. Such antibodies imply that the mother, although not necessarily the child, is infected with HIV. The new methods we propose in this article allow us to combine the two types of information to estimate the risk of AIDS for the first 10 years of life. They also make it possible to estimate the number of children born to infected mothers since the start of the epidemic and to project the future number of cases of pediatric AIDS. From these projections it appears that the case load and the average age at diagnosis will increase steadily throughout the early 1990s. The statistical problem that we address concerns making inferences about processes of infection, disease, and reporting for which realizations are right- (and perhaps left-) truncated. Further complication arises from the fact that the reporting delay distribution appears to be changing over chronologic time.