A parametric survival model with an interval-censored covariate.

We present a parametric survival model whose particularity consists in the inclusion of an interval-censored covariate. The methodology is motivated by a study on injecting drug users in Badalona (Spain), most of whom suffered HIV infection as a result of their drug addiction. The study aims to examine the possible association between the elapsed time from first injecting drug use until HIV infection and the subsequent AIDS incubation period. Whereas the moment of HIV infection cannot be observed exactly and is therefore interval-censored, time until AIDS onset is doubly-censored. For the maximization of the resulting likelihood function, we use a numerical solver. Maximization is carried out by means of the mathematical programming language AMPL.