We consider the problem of comparing cumulative incidence functions of non-mortality events in the presence of informative coarsening. We extend frequentist-based hypothesis tests previously developed for non-informative coarsening. Estimation uses the EM algorithm. The data structure and analysis goal are exemplified by the AIDS Link to the Intravenous Experience (ALIVE) study, where researchers aim to compare incidence of human immunodeficiency virus seroconversion by risk behavior categories. Coarsening in the forms of interval and right censoring in ALIVE are thought to be informative, thus we perform a sensitivity analysis by incorporating elicited expert information about the relationship between seroconversion and censoring into the model.