We use the framework of coarsened data to motivate performing sensitivity analysis in the presence of incomplete data. To perform the sensitivity analysis, we specify pattern-mixture models to allow departures from the assumption of coarsening at random, a generalization of missing at random and independent censoring. We apply the concept of coarsening to address potential bias from missing data and interval-censored data in a randomized controlled trial of an herbal treatment for acute hepatitis. Computer code using SAS PROC NLMIXED for fitting the models is provided.