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@ARTICLE{Lewczuk:163548,
      author       = {Lewczuk, Piotr and Wiltfang, Jens and Kornhuber, Johannes
                      and Verhasselt, Anneleen},
      title        = {{D}istributions of {A}β42 and {A}β42/40 in the
                      {C}erebrospinal {F}luid in {V}iew of the {P}robability
                      {T}heory.},
      journal      = {Diagnostics},
      volume       = {11},
      number       = {12},
      issn         = {2075-4418},
      address      = {Basel},
      publisher    = {MDPI},
      reportid     = {DZNE-2022-00304},
      pages        = {2372},
      year         = {2021},
      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.},
      keywords     = {Alzheimer’s disease (Other) / amyloid β (Other) /
                      distribution of a random variable (Other) / probability
                      theory (Other)},
      cin          = {AG Wiltfang},
      ddc          = {610},
      cid          = {I:(DE-2719)1410006},
      pnm          = {353 - Clinical and Health Care Research (POF4-353)},
      pid          = {G:(DE-HGF)POF4-353},
      typ          = {PUB:(DE-HGF)16},
      pubmed       = {pmid:34943609},
      pmc          = {pmc:PMC8700661},
      doi          = {10.3390/diagnostics11122372},
      url          = {https://pub.dzne.de/record/163548},
}