Nonlinear Z-score modeling for improved detection of cognitive abnormality

John Kornak, Julie Fields, Walter Kremers, Sara Farmer, Hilary W Heuer, Leah Forsberg, Danielle Brushaber, Amy Rindels, Hiroko Dodge, Sandra Weintraub, Lilah Besser, Brian Appleby, Yvette Bordelon, Jessica Bove, Patrick Brannelly, Christina Caso, Giovanni Coppola, Reilly Dever, Christina Dheel, Bradford Dickerson, Susan Dickinson, Sophia Dominguez, Kimiko Domoto-Reilly, Kelley Faber, Jessica Ferrall, Ann Fishman, Jamie Fong, Tatiana Foroud, Ralitza Gavrilova, Deb Gearhart, Behnaz Ghazanfari, Nupur Ghoshal, Jill Goldman, Jonathan Graff-Radford, Neill Graff-Radford, Ian M Grant, Murray Grossman, Dana Haley, John Hsiao, Robin Hsiung, Edward D Huey, David Irwin, David Jones, Lynne Jones, Kejal Kantarci, Anna Karydas, Daniel Kaufer, Diana Kerwin, David Knopman, Ruth Kraft, Joel Kramer, Walter Kukull, Maria Lapid, Irene Litvan, Peter Ljubenkov, Diane Lucente, Codrin Lungu, Ian Mackenzie, Miranda Maldonado, Masood Manoochehri, Scott McGinnis, Emily McKinley, Mario Mendez, Bruce Miller, Namita Multani, Chiadi Onyike, Jaya Padmanabhan, Alexander Pantelyat, Rodney Pearlman, Len Petrucelli, Madeline Potter, Rosa Rademakers, Eliana Marisa Ramos, Katherine Rankin, Katya Rascovsky, Erik D Roberson, Emily Rogalski-Miller, Pheth Sengdy, Les Shaw, Adam M Staffaroni, Margaret Sutherland, Jeremy Syrjanen, Carmela Tartaglia, Nadine Tatton, Joanne Taylor, Arthur Toga, John Trojanowski, Ping Wang, Bonnie Wong, Zbigniew Wszolek, Brad Boeve, Adam Boxer, Howard Rosen, ARTFL/LEFFTDS Consortium, John Kornak, Julie Fields, Walter Kremers, Sara Farmer, Hilary W Heuer, Leah Forsberg, Danielle Brushaber, Amy Rindels, Hiroko Dodge, Sandra Weintraub, Lilah Besser, Brian Appleby, Yvette Bordelon, Jessica Bove, Patrick Brannelly, Christina Caso, Giovanni Coppola, Reilly Dever, Christina Dheel, Bradford Dickerson, Susan Dickinson, Sophia Dominguez, Kimiko Domoto-Reilly, Kelley Faber, Jessica Ferrall, Ann Fishman, Jamie Fong, Tatiana Foroud, Ralitza Gavrilova, Deb Gearhart, Behnaz Ghazanfari, Nupur Ghoshal, Jill Goldman, Jonathan Graff-Radford, Neill Graff-Radford, Ian M Grant, Murray Grossman, Dana Haley, John Hsiao, Robin Hsiung, Edward D Huey, David Irwin, David Jones, Lynne Jones, Kejal Kantarci, Anna Karydas, Daniel Kaufer, Diana Kerwin, David Knopman, Ruth Kraft, Joel Kramer, Walter Kukull, Maria Lapid, Irene Litvan, Peter Ljubenkov, Diane Lucente, Codrin Lungu, Ian Mackenzie, Miranda Maldonado, Masood Manoochehri, Scott McGinnis, Emily McKinley, Mario Mendez, Bruce Miller, Namita Multani, Chiadi Onyike, Jaya Padmanabhan, Alexander Pantelyat, Rodney Pearlman, Len Petrucelli, Madeline Potter, Rosa Rademakers, Eliana Marisa Ramos, Katherine Rankin, Katya Rascovsky, Erik D Roberson, Emily Rogalski-Miller, Pheth Sengdy, Les Shaw, Adam M Staffaroni, Margaret Sutherland, Jeremy Syrjanen, Carmela Tartaglia, Nadine Tatton, Joanne Taylor, Arthur Toga, John Trojanowski, Ping Wang, Bonnie Wong, Zbigniew Wszolek, Brad Boeve, Adam Boxer, Howard Rosen, ARTFL/LEFFTDS Consortium

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.

© 2019 Published by Elsevier Inc. on behalf of the Alzheimer's Association.

Figures

Fig. 1
Fig. 1
(A) shows a plot of Trail Making Test B scores versus age in years (based on males with 10, 15, and 20 years of education), and (B) shows Trail Making Test B scores versus education level measured in years (based on males of age 50, 60, 70, and 80). The small difference between ages 50 and 60 in the education plot lines reflects the nonlinearity in the age plot where the lines are relatively flat at younger ages. The sex effects were very small in comparison with age and education. Plots showing sex differences are given in Supplementary Materials.
Fig. 2
Fig. 2
Plot of SD of residuals for Trail Making Test B model versus age in years. Blue line shows raw SD curve based on sample SD estimates within the 11-year window centered on each point. The red line shows the corresponding SCAM model fit. Abbreviations: SCAM, shape constrained additive model; SD, standard deviation.
Fig. 3
Fig. 3
(A) shows a plot of Category fluency–animals versus age in years (based on males with 10, 15, and 20 years of education), and (B) shows Category fluency–animals versus education level measured in years (based on males of age 50, 60, 70, and 80). The sex effects were small in comparison with age and education. Plots showing sex differences are given in Supplementary Materials.
Fig. 4
Fig. 4
Plot of SD of residuals for Category fluency–animals versus age in years. Blue line shows raw SD curve based on sample SD estimates within the 11-year window centered on each point. The red line shows the corresponding SCAM model fit. Abbreviations: SCAM, shape constrained additive model; SD, standard deviation.

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Source: PubMed

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