In comparing the effectiveness of two treatments, suppose that for each patient repeated measurements of an outcome variable are taken at prespecified time points, but some observations may be missing due to the patient's dependent right censoring. In this article, a simple rank estimation procedure, constructed based on an artificial censoring technique, is proposed for the treatment differences over time without imposing a parametric structure on the dependence between the outcome measures and the censoring variable. Our method can be easily implemented and is illustrated by a dataset from an AIDS clinical trial.