Estimation of the infection time and latency distribution of AIDS with doubly censored data

We consider the nonparametric estimation of the time to infection with HIV and the latency period between infection and the onset of AIDS in data where both the events of infection and AIDS are not directly observed. The methods use self-consistency equations that are more easily and quickly solvable than the nonparametric estimators proposed by De Gruttola and Lagakos (1989, Biometrics 45, 1-11). The techniques are illustrated with data on hemophiliacs who became infected through contamination of the blood factor they were given to control their hemophilia.