Habeeb Abolaji Bashir^*1, George Paul Komolafe², John Olusegun Okunade³

¹Department of Statistics and Data Science, University of Kentucky, Kentucky, USA, ORCID: 0009-0008-2881-2154

 ²Department of Computer Science, Boston University. Massachusetts, USA, ORCID: 0009-0001-0413-241X

 ³Department of Environment and Sustainability, University of Michigan, Ann Arbor, Michigan, USA, ORCID: 0000-0002-4392-9130

Corresponding Author: Habeeb Abolaji Bashir, Department of Statistics and Data Science, University of Kentucky, Kentucky, USA, ORCID: 0009-0008-2881-2154

Citation: Habeeb Abolaji Bashir, George Paul Komolafe, John Olusegun Okunade (2024) Optimizing Diabetes Treatment Using High Dimensional Single Index Quantile Regression. Int J Diabetes Case Rep, 2(1);1-13.

Copyrights: © 2024, Habeeb Abolaji Bashir, et al., This is an open-access article distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution and reproduction in any medium, provided the original author and source are credited.

Abstract:

Diabetes poses a massive global health burden, affecting hundreds of millions and leading to severe complications if not optimally managed. Traditional one size fits all treatment approaches often yield suboptimal glycemic control; fewer than half of patients achieve recommended HbA1c targets under standard care. There is growing interest in data driven, individualized therapy guided by advanced statistical models. We aimed to improve personalized diabetes treatment by developing a high dimensional single index quantile regression model. This semiparametric approach captures how patient features combine into a single risk index and influence the entire distribution of outcomes (not just the mean), thereby identifying heterogeneity in treatment response. We assembled a dataset of type 2 diabetes patients (clinical, demographic, genetic, and treatment variables; p >> n). A single index quantile regression model was formulated: the conditional outcome quantile $Q_Y(\tau|X)$ is modeled as $g_\tau(\beta^T X)$, with $\beta$ a sparse high dimensional coefficient vector. We employed ℓ₁-penalization and adaptive algorithms to handle dimensionality. Model tuning used cross validation, and we assessed performance against standard linear regression. Key features (e.g., baseline HbA1c, medication dose, and a genotype treatment interaction) were selected into the index. The single index model revealed a nonlinear relationship: outcome improvements plateaued at higher risk index values. Importantly, the model captured variability across quantiles e.g., baseline HbA1c had a larger effect on higher quantile outcomes than on medians. Compared to ordinary regression, our quantile model reduced prediction error for poorly controlled patients and provided well calibrated prediction intervals. High dimensional single index quantile regression effectively identified patient specific factors and their heterogeneous effects on glycemic outcomes. This approach can guide clinicians in tailoring therapies for individuals at different risk levels, advancing the paradigm of precision diabetes management.

Keywords: Diabetes, Quantile regression, High dimensional data, Single index model, Personalized treatment, Precision medicine.