A mathematical model of the Alzheimer’s Disease biomarker cascade demonstrates statistical pitfalls in identifying neurobiological surrogates of cognitive reserve

Introduction In order to investigate neurobiological surrogates of cognitive reserve, statistical interaction analyses have been put forward and used by several studies. However, as these neurobiological surrogates are potentially affected by neurodegeneration as part of the amyloid cascade, which is characterized by chronological time-moderated associations between biomarkers, cross sectional sampling in combination with the disregard of time as a confounder could introduce interaction effects that may be misinterpretabed as cognitive reserve in statistical analyses. Methods We modeled the amyloid cascade with a minimal set of three biomarkers amyloid load, corticospinal fluid tau, hippocampal volume and cognitive outcome using a differential equation system, whose parameters were estimated from empirical data from the ADNI. Interaction effects between pathology markers amyloid and tau with hippocampal volume as potential marker of cognitive reserve were estimated on two simulated data samples. Both samples were calculated from varying amyloid, tau and hippocampal volume for the initial configuration of individual trajectories. For Sample 1, data points were sampled at a fixed time after baseline. For Sample 2, data points were sampled at random time points. Results Regression analyses on Sample 1 yielded estimates for interaction effects of 0. For Sample 2, estimates were -.1692 and -.0807 for amyloid and tau with hippocampal volume, respectively. The interaction effect estimates for Sample 2 decreased several orders of magnitude when taking into account the timepoint of sampling. Conclusion Studies aiming to investigate neurobiological surrogates of cognitive reserve that are affected by Alzheimer’s Disease-related neurodegenerative processes need to consider inter-individually varying sampling time points in the data to avoid misinterpreting interaction effects. ### Competing Interest Statement The authors have declared no competing interest.