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[P4–229]: METHOD OF MULTIVARIATE TIME‐DERIVATIVES: MODELING NEURAL DEGENERATION AND ITS ETIOLOGIES
Author(s) -
Klinedinst Brandon Skylar,
Willette Auriel A.,
Maitra Ranjan
Publication year - 2017
Publication title -
alzheimer's and dementia
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.713
H-Index - 118
eISSN - 1552-5279
pISSN - 1552-5260
DOI - 10.1016/j.jalz.2017.06.2097
Subject(s) - multivariate statistics , variance (accounting) , variables , variable (mathematics) , random variable , derivative (finance) , second derivative , mathematics , statistics , computer science , econometrics , mathematical analysis , accounting , economics , financial economics , business
Background:There is a desire to tap into aspects of Magnetic Resonance Imaging (MRI) data of the brain that pertain to the temporalorder 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.Methods: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.Results:Ourmethod ofmultivariate 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. Conclusions:Timederivative 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.