Hybrid Robust Beta Regression Based on Support Vector Machines and Iterative Reweighted Least Squares

Abstract

In this paper, we examine and compare the performance of several beta regression approaches for response variables constrained to the (0,1) interval, focusing on robustness in the presence of outliers and nonlinear relationships. Since the beta distribution is well suited for modeling proportions, it is used here to describe the rate of tumor response to cancer therapy. Four modeling strategies are considered: standard beta regression estimated via maximum likelihood; robust beta regression using the IRLS-Huber procedure; support vector regression (SVR) followed by a beta transformation; and a hybrid beta regression model that combines SVR with Huber-based robustness. The models are assessed using a simulated dataset generated under controlled levels of contamination and varying sample sizes, as well as a quasi-real tumor response dataset in which age is the primary covariate. The simulation results indicate that although classical least squares (CLS) and robust beta regression can provide adequate predictions under ideal conditions, their performance deteriorates when outliers are present and the relationship is nonlinear. While SVR better captures nonlinear patterns and therefore outperforms the other individual methods, it also lacks robustness to contaminated data. Across all conditions, the hybrid model achieves higher accuracy and greater robustness, reflecting strong generalization capability and adaptability. When applied to the real tumor response data, the hybrid method again emerges as the preferred model, effectively accommodating outliers and delivering the most stable and precise predictions. Overall, the hybrid SVR-Huber beta regression framework proves to be a valuable and powerful tool for medical research and other applied fields that must analyze noisy, bounded real-world data.