ORIGINAL RESEARCH article
Front. Appl. Math. Stat.
Sec. Statistics and Probability
Volume 11 - 2025 | doi: 10.3389/fams.2025.1617381
Modelling Longitudinal Cognitive Test Data with Ceiling Effects and Left Skewness
Provisionally accepted
- 1GATE Institute, Sofia University, Sofia, Bulgaria
- 2Faculty of Mathematics and Informatics, Sofia University St. Kliment Ohridski, Sofia, Sofia City, Bulgaria
- 3Institute of Mathematics and Informatics, Bulgarian Academy of Sciences (BAS), Sofia, Bulgaria
- 4Department of Biostatistics, School of Public Health, Yale University, New Haven, Connecticut, United States
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Cognitive tests such as the Mini Mental State Examination (MMSE) may result in data with discrete and skewed distributions that necessitate proper statistical models for valid inference. We review different longitudinal approaches to model cognitive decline data in older individuals and provide recommendations for model choice and result interpretation. We used data from Alzheimer's Disease Neuroimaging Initiative study and focused on MMSE scores as response variable collected on up to four visits over a two-year period in older individuals (mean age 73 years). At baseline individuals were classified as having Alzheimer's disease (AD), early or late mild cognitive impairment, subjective memory concern, or being cognitively normal. We considered generalized additive models for location, scale and shape (GAMLSS) with binomial/beta-binomial response distribution and parametric/non-parametric random effects, selected the best model and used graphs for illustration. Binomial model with non-parametric random intercept and slope fit the data the best according to the Bayesian Information Criterion. The three-way interaction between time, age and diagnostic group was statistically significant suggesting that AD individuals had the steepest cognitive decline among all groups, especially in younger individuals. Furthermore, males and APOE4 carriers had worse cognitive performance, while more educated people had better cognitive performance compared to less educated. Various plots are used to illustrate and aid in interpretation of the results. GAMLSS are an appropriate class of models providing interpretable results for repeatedly measured cognitive test data. We recommend that they are used more widely, accompanied by effect estimation, statistical testing and visualizations for illustration.
Keywords: Generalized Additive Models for Location, scale and shape (gamlss), longitudinal data, cognitive test, Ceiling effect, Binomial models, random effects
Received: 24 Apr 2025; Accepted: 28 Jul 2025.
Copyright: © 2025 Grigorova, Palejev and Guerguieva. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Denitsa Grigorova, GATE Institute, Sofia University, Sofia, Bulgaria
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