Distributions of Aβ42 and Aβ42/40 in the Cerebrospinal Fluid in View of the Probability Theory

Abstract

Amyloid β 42/40 concentration quotient has been empirically shown to improve accuracy of the neurochemical diagnostics of Alzheimer’s Disease (AD) compared to the Aβ42 concentration alone, but this improvement in diagnostic performance has not been backed up by a theoretical argumentation so far. In this report we show that better accuracy of Aβ42/40 compared to Aβ1-42 is granted by fundamental laws of probability. In particular, it can be shown that the dispersion of a distribution of a quotient of two random variables (Aβ42/40) is smaller than the dispersion of the random variable in the numerator (Aβ42), provided that the two variables are proportional. Further, this concept predicts and explains presence of outlying observations, i.e., AD patients with falsely negatively high Aβ42/40 ratio, and non-AD subjects with extremely low, falsely positive, Aβ42/40 ratio.