In this paper response curves of patients with chronic myeloid leukemia are modeled using one and two-level censored models. Two-level models (also called mixed models) allow random effects and censored models are used to account for the large amount of values too small to be detected. The curves are observed from start of medication to a maximum of 36 months (9 measurement points). The data set is divided into two: "excellent responders" and "other". The "excellent responders" are modeled with a simple cubic censored model, and only one of the background variables measured at time zero ("blasts"), is found to be significant in explaining variation in the change curves, and even this with certain reservations. "Other" are modeled with a cubic two-level censored model and hemoglobin and eosinophile levels, as well as amount of blasts, are significant in explaining variation in this group.