An introduction to mixed models and joint modeling: analysis of valve function over time.

An important target of many clinical studies is to identify biomarkers, including risk scores, with strong prognostic capabilities. While biomarker evaluations are commonly utilized to predict the progress of the disease at single time points, appropriate statistical tools to assess the prognostic value of serial biomarker evaluation are rarely used. The goal of this paper is to demonstrate flexible and appropriate statistical methodology to assess the predictive capability of serial echocardiographic measurements of allograft aortic valve function. Moreover, the concept of joint modeling of longitudinal and survival data to optimally utilize the relationship between repeated valve function measurements and time-to-death or time-to-reoperation, is introduced and illustrated. Optimal and suboptimal methods are illustrated using a prospective cohort of patients who survived aortic valve or root replacement with an allograft valve and who were followed clinically and echocardiographically over time.