Estimation and comparison of rates of change in repeated-measures studies with planned dropout

Many repeated-measures studies are designed to compare rates of change over time in responses among treatment groups. In such studies, some responses are often censored because some individuals drop out before completing the study. The Vitamin D(3) Trial was a repeated-measures, randomized clinical trial for secondary hyperparathyroidism in hemodialysis patients in which the efficacy of vitamin D(3) infusions for suppressing the secretion of parathyroid hormone (PTH) was compared among four dose groups during dialysis over 12 weeks. In this trial some patients dropped out because the protocol stated that any individual should have been off protocol if his or her serum calcium (Ca) level exceeded 11.5 mg/dL. While the dropout mechanism for the Ca level (secondary response) corresponded to the missing at random (MAR) assumption (because whether patients dropped out or not depended only on their previously recorded Ca level), the MAR assumption for the PTH level (primary response) was not justifiable without taking into account the effect of the Ca level. We consider estimation and comparison of several estimators of mean rate of change in the presence of dropout due to the selection process inherent in a study design like the Vitamin D(3) Trial. Simulation experiments are used to compare the bias and efficiency of several estimators of mean rate of change. The estimators based on a bivariate mixed-effects model outperform all other estimators in the primary response as well as in the secondary response. These estimators are applied to the Vitamin D(3) Trial data.