Abstract
There is a desire to tap into aspects of Magnetic Resonance Imaging (MRI) data of the brain that pertain to the temporal-order of cause and effect. Intuitively, such information can only be derived from longitudinal observations. Current approaches to longitudinal designs, such as repeated-measures ANOVA or mixed effects modeling, can be dauntingly convoluted and often fail to capture the mechanistic changes that describe dynamics between variables in a system. Differentiation, the method of difference ratios between quantities, is used to derive a series of new quantities known as derivatives from the observed variables. The derivatives used in the present demonstration are known as time-derivatives because of how derivatives are calculated with respect to their denominator. Each time-derivative contains information describing the variable's direction and rate of change over a window of time. Integration, the method of summing over the derivatives within a window of the denominator, compacts the information from each derivative into a single quantity. The new quantity includes the components of variance found in raw variables in addition to components of variance contributed from time-derivatives, which contain information pertaining to the mechanics of a system. Time-derivative variables have an edge over the simpler base variables because of the increases in their information content and a relative decrease in their random noise. Our method of multivariate time-derivatives reduces the computational complexity of large, multivariate datasets observed longitudinally. Additionally, a researcher's power to discern is enhanced with time-derivative variables relative to untransformed variables. Variables produced by this method have refined, high-resolution multivariate distribution spaces resulting from having delineated temporal boundaries and differentiating between cases with accreting or depleting quantities. Time-derivative variables maximize the efficiency of a variable, increasing its efficacy, information content, resolution, and ease of deployment in multivariate models. The intricacies of longitudinal big data may appear computationally immutable, but the method of time-derivatives makes quick work of this phenomenon by reducing entire datasets into cross-section-like variables. Importantly, time-derivative variables also incorporate novel information, including components of variance that characterize system dynamics in addition to the standard components available from an analysis of population characteristics.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Alzheimer's & Dementia: The Journal of the Alzheimer's Association
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.