Temporal trends of biomarkers and between‐biomarker associations
We are interested in the temporal trends of biomarkers that are related to disease progression, especially the association between two temporal trends. When biological mechanisms are lacking, no parametric forms of the temporal trends are theoretically justified. In this work, we adopt joint non‐parametric local linear mixed effects modelling. By local linear regression, each temporal trend is represented by its magnitude and slope (the primary interest in medical studies) which both change with time. By mixed effects modelling, we take care of data sparsity within each subject and the large subject‐to‐subject variability. The association between two temporal trends is evaluated by the correlation coefficient matrix, assessing association in terms of both the magnitude and the slope. The joint modelling enables evaluation of the association as a continuous function of time, even if one or neither biomarker is observed at some specific time points. We apply the method proposed to a study of human immunodeficiency virus patients following anti‐retroviral therapy until viral suppression. We find that associations between some biomarkers change over time, reflecting potentially changing stages of disease.
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