Data and projections of HIV/AIDS cases in Portugal: an unstoppable epidemic?

The size of the affected population with HIV/AIDS is a vital question asked by healthcare providers. A statistical procedure called Back-calculation has been the most widely used method to answer that question. Recent discussions suggest that this method is gradually becoming less appropriate for reliable incidence and prevalence estimates, as it does not take into account the effect of treatment. In spite of this, in the current paper that method and a worst-case scenario are used to assess the quality of previous projections and obtain new ones. The first problem faced was the need to account for reporting delays, no reporting and underreporting. The adjusted AIDS incidence data were then used to obtain lower bounds on the size of the AIDS epidemic, using the back-calculation methodology. A Weibull and Gamma distribution was considered for the latency period distribution. The EM algorithm was applied to obtain maximum likelihood estimates of the HIV incidence. The density of infection times was parameterized as a step function. The methodology is applied to AIDS incidence in Portugal for four different transmission categories (injecting drug users, heterosexual, homo/bisexual and other) to obtain short-term projections (2002–2005) and an estimate of the minimum size of the epidemic.