On longitudinal prediction with time-to-event outcome: Comparison of modeling options

Long-term follow-up is common in many medical investigations where the interest lies in predicting patients' risks for a future adverse outcome using repeatedly measured predictors over time. A key quantity is the likelihood of developing an adverse outcome among individuals who survived up to time s given their covariate information up to time s. Simple, yet reliable, methodology for updating the predicted risk of disease progression using longitudinal markers remains elusive. Two main approaches have been considered in the literature. One approach, based on joint modeling (JM) of failure time and longitudinal covariate process (Tsiatis and Davidian, 2004), derives such longitudinal predictive probability from the joint probability of a longitudinal marker and an event at a given time. A second approach, the partly conditional (PC) modeling (Zheng and Heagerty, 2005), directly models the predictive probability conditional on survival up to a landmark time and information accrued by that time. In this article, we propose new PC models for longitudinal prediction that are more flexible than joint modeling and improve the prediction accuracy over existing PC models. We provide procedures for making inference regarding future risk for an individual with longitudinal measures up to a given time. In addition, we conduct simulations to evaluate both JM and PC approaches in order to provide practical guidance on modeling choices. We use standard measures of predictive accuracy adapted to our setting to explore the predictiveness of the two approaches. We illustrate the performance of the two approaches on a dataset from the End Stage Renal Disease Study (ESRDS).