Predicting Vitamin D Levels Using Ordinal Logistic Regression, Gaussian Process Regression and ARIMA: A Comparative Study

Edlira Lashi; Klea Lashi; Hasanien K Kuba; Andres Annuk; Ambrozia Itellari; Hussein Alkattan; Mostafa Abotaleb

Authors

Edlira Lashi Faculty of Medical Science, Albanian University, Albania https://orcid.org/0009-0002-5435-6291
Klea Lashi Department of Clinical Biochemistry, Mother Teresa University Hospital Center, Tirana, Albania https://orcid.org/0009-0009-8705-9040
Hasanien K Kuba College of Biomedical Informatics, University of Information Technology and Communications (UoITC), Baghdad, Iraq https://orcid.org/0000-0002-1987-4731
Andres Annuk Institute of Forestry and Engineering, Estonian University of Life Sciences, Tartu, Estonia https://orcid.org/0000-0001-5464-0415
Ambrozia Itellari School of Medicine, Lake Erie College of Osteopathic Medicine, Florida, United States of America https://orcid.org/0009-0009-4293-2344
Hussein Alkattan Department of System Programming, South Ural State University, Chelyabinsk, Russia; Directorate of Environment in Najaf, Ministry of Environment, Najaf, Iraq https://orcid.org/0000-0002-0281-082X
Mostafa Abotaleb Engineering School of Digital Technologies, Yugra State University, Khanty-Mansiysk, Russia https://orcid.org/0000-0002-3442-6865

Abstract

Vitamin D deficiency is a common health condition that increases the risk of metabolic, cardiovascular, and musculoskeletal disorders. Many individuals are unaware of their vitamin D deficiency. In this work, we develop and present three complementary machine learning models to explore Vitamin D levels based on regular healthcare data. The dataset consists of anonymized patient records with demographic features, clinical indicators, and laboratory measurements of serum 25(OH)D. It is taken from a healthcare setting and pre-processed to eliminate absent or inconsistent results. Vitamin D level variables were transformed into ordered, clinical categories: severe deficiency, deficiency, insufficiency, and sufficiency. However, for regression and time-series forecasting, the original continuous concentration, measured in ng/mL, was preserved together with monthly averages. A proportional odds Ordinal Logistic Regression model was used to figure out Vitamin D status. The best overall performance was an accuracy of 0.77, a macro recall of 0.76, and an F2-score of 0.78. Most of the mistakes were made between categories that were next to each other. We utilized Gaussian Process Regression to predict continuous Vitamin D concentration. The results were R² = 0.79, MAE = 2.3 ng/mL, and RMSE = 3.4 ng/mL, which means that the model can get close to laboratory values with clinically acceptable error. To capture temporal dynamics, an ARIMA model was fitted to monthly mean Vitamin D levels and showed the best performance with R² = 0.82, MAE = 2.0 ng/mL and RMSE = 3.1 ng/mL, accurately recreating the observed seasonal pattern.