Modeling longitudinal data and its impact on survival in observational nephrology studies: tools and considerations

Abstract

Nephrologists and kidney disease researchers are often interested in monitoring how patients' clinical and laboratory measures change over time, what factors may impact these changes, and how these changes may lead to differences in morbidity, mortality, and other outcomes. When longitudinal data with repeated measures over time in the same patients are available, there are a number of analytical approaches that could be employed to describe the trends and changes in these measures, and to explore the associations of these changes with outcomes. Researchers may choose a streamlined and simplified analytic approach to examine trajectories with subsequent outcomes such as estimating deltas (subtraction of the last observation from the first observation) or estimating per patient slopes with linear regression. Conversely, they could more fully address the data complexity by using a longitudinal mixed model to estimate change as a predictor or employ a joint model, which can simultaneously model the longitudinal effect and its impact on an outcome such as survival. In this review, we aim to assist nephrologists and clinical researchers by reviewing these approaches in modeling the association of longitudinal change in a marker with outcomes, while appropriately considering the data complexity. Namely, we will discuss the use of simplified approaches for creating predictor variables representing change in measurements including deltas and patient slopes, as well more sophisticated longitudinal models including joint models, which can be used in addition to simplified models based on the indications and objectives of the study as warranted.

Keywords: change analysis; joint models; longitudinal; mixed-effects models; repeated measures.