Joint Modeling of All-Cause Mortality and Longitudinally Measured Serum Albumin

In clinical studies, longitudinal and survival data are often obtained simultaneously from the same individual. Linear mixed effects models are widely used for analyzing longitudinal continuous outcome data, while survival models are used for analyzing time-to-event data. It is a common practice to analyze these longitudinal and time-to-event data separately. However, when multivariate outcomes are obtained from a given individual, they can be correlated by nature, and one can attain considerable gain in efficiency by jointly analyzing the outcomes. An objective of this study is to analyze such multivariate data by jointly modeling longitudinally measured continuous outcomes and time-to-event data. In this joint modeling, we formulate a joint likelihood function for both outcomes and use the maximum likelihood method to estimate the parameters in the two sub-models (longitudinal and survival models). We demonstrate the merits of joint modeling by considering a joint analysis of longitudinally measured serum albumin (biomarker) and time-to-all-cause mortality data obtained from a hemodialysis (HEMO) study. This HEMO study was a large NIH (National Institute of Health) sponsored multicenter clinical trial contrasting the effects of dialysis dose and dialysis membrane permeability in end-stage renal disease patients receiving hemodialysis. We find that the parameter estimates obtained under joint modeling of HEMO data are more efficient than those obtained under separate modeling of the outcome variables.