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Alzheimers Dement (Amst). 2019 Dec 5;11:797-808. doi: 10.1016/j.dadm.2019.08.003. eCollection 2019 Dec.

Nonlinear Z-score modeling for improved detection of cognitive abnormality.

Author information

1
UCSF, San Francisco, CA, USA.
2
Mayo Clinic Rochester, Rochester, MN, USA.
3
Oregon Health and Science University, Portland, OR, USA.
4
University of Michigan, Ann Arbor, MI, USA.
5
Northwestern University, Chicago, IL, USA.
6
Florida Atlantic University, Boca Raton, FL, USA.
7
Case Western Reserve University, Cleveland, OH, USA.
8
Department of Psychiatry, David Geffen School of Medicine, UCLA, Los Angeles, CA, USA.
9
University of Pennsylvania, Philadelphia, PA, USA.
10
Tau Consortium, Rainwater Charitable Foundation, Fort Worth, TX, USA.
11
University of Washington, Seattle, WA, USA.
12
Harvard University/MGH, Boston, MA, USA.
13
Association for Frontotemporal Degeneration, Radnor, PA, USA.
14
National Cell Repository for Alzheimer's Disease (NCRAD), Indiana University, Indianapolis, IN, USA.
15
University of North Carolina, Chapel Hill, NC, USA.
16
Johns Hopkins University, Baltimore, MD, USA.
17
University of Toronto, Toronto, Ontario, Canada.
18
Washington University, St. Louis, MO, USA.
19
Columbia University, New York, NY, USA.
20
Mayo Clinic, Jacksonville, FL, USA.
21
National Institute on Aging (NIA), Bethesda, MD, USA.
22
University of British Columbia, Vancouver, British Columbia, Canada.
23
UTSW, Dallas, TX, USA.
24
National Alzheimer Coordinating Center (NACC), University of Washington, Seattle, WA, USA.
25
UCSD, San Diego, CA, USA.
26
National Institute of Neurological Disorders and Stroke (NINDS), Bethesda, MD, USA.
27
University of Alabama at Birmingham, Birmingham, AL, USA.
28
Bluefield Project to Cure FTD, San Francisco, CA, USA.
29
Laboratory of Neuroimaging (LONI), USC, Los Angeles, CA, USA.

Abstract

Introduction:

Conventional Z-scores are generated by subtracting the mean and dividing by the standard deviation. More recent methods linearly correct for age, sex, and education, so that these "adjusted" Z-scores better represent whether an individual's cognitive performance is abnormal. Extreme negative Z-scores for individuals relative to this normative distribution are considered indicative of cognitive deficiency.

Methods:

In this article, we consider nonlinear shape constrained additive models accounting for age, sex, and education (correcting for nonlinearity). Additional shape constrained additive models account for varying standard deviation of the cognitive scores with age (correcting for heterogeneity of variance).

Results:

Corrected Z-scores based on nonlinear shape constrained additive models provide improved adjustment for age, sex, and education, as indicated by higher adjusted-R2.

Discussion:

Nonlinearly corrected Z-scores with respect to age, sex, and education with age-varying residual standard deviation allow for improved detection of non-normative extreme cognitive scores.

KEYWORDS:

Generalized additive models; Heterogenous variance modeling; Neuropsychological testing scores; Nonlinear Z-score correction; Shape constrained additive models

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