We apply parametric empirical Bayes inference of Morris to the estimation of rate of change from incomplete longitudinal studies where the right censoring process is considered informative, that is, the length of time the subjects participate in the study is associated with level of the study variable. Ignoring such an association can result in a biased estimate of rate of change. The proposed method provides estimates of rate of change for individual subjects as well as for the entire group, adjusted for informative right censoring. The method is considered more robust than those based on a specific parametric model for the censoring distribution. Under non-informative right censoring these estimators of slopes are equivalent to the Bayes estimators derived by Fearn. We illustrate the method with an example involving renal transplant data. We evaluate the method's performance through a simulation study.