Non-parametric analysis of transfusion-related HIV and AIDS incidence data

The method for making non-parametric inferences about the probability distribution of the incubation period for AIDS from transfusion-related AIDS data is extended to include data on individuals who have tested positive for HIV but do not have AIDS at the time of analysis. The method is illustrated with data on individuals infected by transfusion in Australia. The shape of the incubation distribution, as represented by the truncated distribution function, can be estimated, but the additional data contribute very little to the estimation of this shape. With a general non-parametric form for the incubation distribution the additional data do not overcome the identifiability problem that exists for non-parametric estimation of this distribution from AIDS data alone. If quarterly rates for HIV testing are specified, the additional data make it possible to estimate the cumulative distribution function for the incubation period. This is also possible when a simple parametric form, with one or two unknown parameters, is used for the testing rates. However, the additional data do not allow effective estimation of the HIV testing rates. The estimated shape of the incubation distribution indicates a higher proportion of short incubation periods than an earlier estimate based on U.S. data. Estimates for the incubation distribution itself do not vary much over a plausible range of HIV testing rates.