A meta-analysis of estimates of the AIDS incubation distribution

Information from 12 studies is combined to estimate the AIDS incubation distribution with greater precision than is possible from a single study. The analysis uses a hierarchy of parametric models based on a four-parameter generalized F distribution. This general model contains four standard two-parameter distributions as special cases. The cases are the Weibull, gamma, log-logistic, lognormal distributions. These four special cases subsume three distinct asymptotic hazard behaviors. As time increases beyond the median of approximately 10 years, the hazard can increase to infinity (Weibull), can plateau at some constant level (gamma), or can decrease to zero (log-logistic and lognormal). The Weibull, gamma and 'log-logistic distributions' which represent the three distinct asymptotic hazard behaviors, all fit the data as well as the generalized F distribution at the 25 percent significance level. Hence, we conclude that incubation data is still too limited to ascertain the specific hazard assumption that should be utilized in studies of the AIDS epidemic. Accordingly, efforts to model the AIDS epidemic (e.g., back-calculation approaches) should allow the incubation distribution to take several forms to adequately represent HIV estimation uncertainty. It is recommended that, at a minimum, the specific Weibull, gamma and log-logistic distributions estimated in this meta-analysis should all be used in modeling the AIDS epidemic, to reflect this uncertainty.