Tests for time-invariant correlation of longitudinally measured biomarkers

Our work is motivated by a study that longitudinally measured serum biomarkers and levels of bacterial pathogens in the oral cavity with the intent of testing if the correlation between each biomarker and each pathogen is homogeneous over time. To address this question, we propose a model for the joint distribution of the serial biomarker measures and the serial pathogen measures and use the variance of this distribution to derive the asymptotic distribution of the sample correlation coefficient of a biomarker and a pathogen at each time point. We use both a Wald test based upon Fisher's Z-transformation and an F-test with an estimated degrees of freedom in order to produce a test with valid size. We examine the performance of both tests via Monte Carlo simulation in a variety of settings defined by the number of subjects, the number of time points, and the range of the true correlation coefficients.