A General Linear Mixed Effect Model to Infer Biomarker Correlations by Bridging Retrospectively Measured Data Across...

A major challenge in biomedical research is that large sample sizes are necessary for sufficient statistical power to detect subtle but potentially important associations between biomarkers and clinical outcomes. Large sample sizes can be achieved by combining biomarker data from multiple studies, but because fluid biomarker platforms and imaging protocols often vary across studies, data from different studies must be bridged or harmonized. We conceptualize that, for a biomarker measured by different studies, a true and latent biomarker exists and underlies the different versions of the observed biomarker through a measurement error model. We then examine the true biological correlation of the latent biomarker with a standard clinical outcome by leveraging biomarker values from a subset of "bridging" samples or scans across studies. Because the true biological correlation with the clinical outcome is related to the correlations of the observed versions of the biomarker with the same clinical outcome and the intraclass correlation coefficient (ICC) of the biomarker across studies, we propose a general linear mixed effects model to estimate the true biological correlation by integrating these correlations estimated across the studies and the bridging cohorts. Our proposed model accounts for study heterogeneity through a random effect and allows both study-specific and the test-retest biomarker data in a joint model to estimate and infer on the true biological correlation. We apply the model to a real world multi-center biomarker study in Alzheimer disease to correlate concentrations of cerebrospinal fluid biomarkers with a standard functional and cognitive outcome. Our simulations and real world applications indicate that the proposed meta-analytic model leads to a bias of no more than 0.03 in the estimated biological correlation of a biomarker with a clinical outcome, even with small to mediocre ICC. When the ICC is large, only 10% of bridging samples may be needed to obtain unbiased estimates to the correlation with close to the nominal level of coverage from the proposed 95% CI estimates. Our proposed methodologies hence provide a novel approach to harmonize retrospectively obtained biomarker data across studies, offer guidance on size of the bridging samples when ICCs are known, and may also be used in a single study to account for batch effects.