Background: Multiple longitudinal responses together with time-to-event outcome are common in biomedical studies. There are several instances where the longitudinal responses are correlated with each other and at the same time each longitudinal response is associated with the survival outcome. The main purpose of this study is to present and explore a joint modeling approach for multiple correlated longitudinal responses and a survival outcome. The method will be illustrated using the Jackson Heart Study (JHS), which is one of the largest cardiovascular studies among African Americans.
Methods: Four longitudinal responses, i.e., total cholesterol (TC), high density lipoprotein (HDL) cholesterol, triglyceride (TG) and inflammation measured by high-sensitivity C-reactive protein (hsCRP); and time-to-coronary heart disease (CHD) were considered from the JHS. The repeated lipid and hsCRP measurements from a given subject overtime are likely correlated with each other and could influence the subject's risk for CHD. A joint modeling framework is considered. To deal with the high dimensionality due to the multiple longitudinal profiles, we use a pairwise bivariate model fitting approach that was developed in the context of multivariate Gaussian random effects models. The method is further explored through simulations.
Results: The proposed model performed well in terms of bias and relative efficiency. The JHS data analysis showed that lipid and hsCRP trajectories could exhibit interdependence in their joint evolution and have impact on CHD risk.
Conclusions: We applied a unified and flexible joint modeling approach to analyze multiple correlated longitudinal responses and survival outcome. The method accounts for the correlation among the longitudinal responses as well as the association between each longitudinal response and the survival outcome at once. This helps to explore how the combination of multiple longitudinal trajectories could be related to the survival process.