A HIERARCHICAL BAYESIAN-APPROACH TO THE BACK-CALCULATION OF NUMBERS OF HIV-INFECTED SUBJECTS

In a recent paper, Commenges and Etcheverry (1993) propose a two-stage back-calculation method in order to estimate numbers of HIV-infected subjects from the number of incident cases. As is usual in back-calculation, the distribution of the incubation time is supposed to be known, but instead of estimating the parameters of the intensity density function l(s), the incidence itself is modelled as a stochastic process which specifies a correlation structure between numbers of infected in consecutive periods and whose distribution is governed by a hyper-paramater lambda which controls the smoothness of the incidence curve. As the classical approach of integrating out lambda proves technically unfeasible, Commenges and Etcheverry rely on an empirical Bayesian technique by estimating the numbers of infected for given lambda and choosing the 'best' lambda by a normal approximation of the marginal likelihood. We present here a full Bayesian treatment of this model by specifying a hyper-prior for lambda and implementing Markov chain Monte Carlo methods. The first results show a decreasing trend for the incidence of infection in the US as early as 1985.