Ridge regression for longitudinal biomarker data

Technological advances facilitating the acquisition of large arrays of biomarker data have led to new opportunities to understand and characterize disease progression over time. This creates an analytical challenge, however, due to the large numbers of potentially informative markers, the high degrees of correlation among them, and the time-dependent trajectories of association. We propose a mixed ridge estimator, which integrates ridge regression into the mixed effects modeling framework in order to account for both the correlation induced by repeatedly measuring an outcome on each individual over time, as well as the potentially high degree of correlation among possible predictor variables. An expectation-maximization algorithm is described to account for unknown variance and covariance parameters. Model performance is demonstrated through a simulation study and an application of the mixed ridge approach to data arising from a study of cardiometabolic biomarker responses to evoked inflammation induced by experimental low-dose endotoxemia.