Screening and surveillance are routinely used in medicine for early detection of disease and close monitoring of progression. Motivated by a study of patients who received a human tissue valve in the aortic position, in this work we are interested in personalizing screening intervals for longitudinal biomarker measurements. Our aim in this paper is 2-fold: First, to appropriately select the model to use at the time point the patient was still event-free, and second, based on this model to select the optimal time point to plan the next measurement. To achieve these two goals, we combine information theory measures with optimal design concepts for the posterior predictive distribution of the survival process given the longitudinal history of the subject.