The increasing availability of clinical measures (e.g., electronic medical records) leads to collecting different types of information. This information includes multiple longitudinal measurements, and sometimes, also survival outcomes. The motivation comes from several clinical applications. In particular, patients after a heart valve replacement have a higher risk of dying or requiring a reoperation. These patients are followed echocardiographically, where several biomarkers are collected. Another example comes from patients after stroke, where measurements to assess recovery are taken over time.
Each outcome of interest is mainly analyzed separately, although it is biologically relevant to study them together. Previous work has focused on investigating the association between longitudinal and survival outcomes; however, less work has been done to examine the association between multiple longitudinal outcomes. In that case, it is common to assume a multivariate normal distribution for the corresponding random effects. This approach, nevertheless, will not measure the strength of association between the outcomes. Including longitudinal outcomes, as time-dependent covariates, in the model of interest would allow us to investigate the strength of the association between different outcomes.
Several challenges arise in both the analysis of multiple longitudinal data and longitudinal-survival data. In particular, different characteristics of the patients’ longitudinal profiles could influence the outcome(s) of interest. Using extensions of multivariate mixed-effects models and joint models of longitudinal and survival outcomes, we investigate how different features (underlying value, slope, area under the curve) of the longitudinal predictors are associated with the primary outcome(s).
We obtain a strong association between death/reoperation with the underlying value and rate of change of the aortic valve gradient (difference in pressure on each side of the valve). Moreover, there is a strong association between the limb functioning with the rate of change in body function impairments for patients after stroke. Further results from simulations studies show important bias when not using the appropriate characteristic of the longitudinal profile. In this new era of rich medical data sets, it is often challenging to decide how to analyze all the available data appropriately.