Are amyloid and tau synergistic? How to interpret an amyloid/tau interaction on cognitive decline in clinically normal adults

Abstract

AbstractBackgroundMany recent studies have examined interactions between β‐amyloid (Aβ) and tau‐PET to predict clinical progression. Ab and tau are moderately correlated in clinically‐normal older adults (r∼0.4‐0.5, p<0.001; Figure 3B), which complicates statistical modelling of interactive effects. Multi‐collinearity can result in conflated interactions that reflect nonlinear effects (square of shared variance) rather than true interactions between separate channels of information. Here, we use simulated and real data to examine the extent to which an Aβ and tau interaction reflects ‘true’ synergism vs. conflated shared variance in predicting cognitive decline.MethodWe first ran simulations to illustrate how interactions between collinear variables inflates the association with shared sources of variance: we simulated two collinear independent variables by generating three random sources of variance (one shared variance [v1] and two unique sources of variance [v2 and v3]) (Figure 1). extracted two principal components from these simulated variables (PC1shared and PC2unique) and ran correlations between a PC1*PC2 interaction and different combinations of the simulated v1‐v3 sources of variance (Figure 1). We also examined real data (Aβ‐PET, entorhinal and inferior temporal tau‐PET, and longitudinal PACC) from the Harvard Aging Brain Study (n=224; Agemean=72.0 (sd=7.3), Female=59%) and ADNI (n=291; Agemean=71.8 (sd=6.5), Female=47%), in order to compare the pattern of effects with the simulated results.ResultThe PC1shared, and its square, PC1shared 2, were strongly associated with shared variance and its square (v1 and v1 2; see Figure 2). A Principal Components Analysis (PCA) of Aβ and entorhinal tau in HABS and ADNI cohorts resulted in a PC1shared and PC1shared 2 that closely associated with PACC slopes, mirroring the simulated results showing collinear interactions are more likely to represent conflated shared variance (see Figure 3A). Interactions between Aβ with inferior temporal tau were less extreme, suggesting additional associations between PACC slopes and PC2unique.ConclusionOur results suggest an Aβ and tau interaction should be interpreted with caution, as this may represent the non‐linear effects of shared variance, rather than the interaction of two (Aβ and tau) unique sources of variance. That is, PC1shared can be interpreted as a squared term, e.g. tau2 or Aβ2, rather than reflecting something truly synergistic between the proteinopathies to influence cognitive decline.