An empirical bayes approach to the estimation of the incidence curve of HIV infection

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Abstract
A new approach is proposed for estimating the incidence curve of HIV infection and obtaining short term prediction of AIDS incidence. It is based on the method of back calculation which utilizes the fact that AIDS incidence is generated from HIV infection incidence by convolution with the incubation period distribution, but avoids the difficulties associated with approximating the infection incidence curve by a class of step functions. Instead, the infection incidence is modelled as a simple stochastic epidemic process which ensures smoothness of the estimate. We first derive the distribution of AIDS incidence knowing infection incidence. The best linear estimators of infection incidence as well as future AIDS incidence are given; a smoothed past AIDS incidence is also obtained. The parameters of the stochastic infection process can be estimated by maximum likelihood using a normal approximation to the marginal distribution of the AIDS incidence. This approach is applied to AIDS incidence data in the United States up to mid 1987. We find that the epidemic started in mid 1976, peaked at the end of 1983 and dropped afterwards.