Symbolic Regression for Discovery of Medical Equations: A Case Study on Glomerular Filtration Rate Estimation Equations

Symbolic Regression (SR) is a sub-field of machine learning that attempts to find a concise closed-form equation for regression tasks. The main strength of SR is in discovering new equations which are explainable and interpretable, in contrast to many black-box machine learning models. Thus, SR has become a first-class algorithm in various fields, including physics and engineering, and more recently healthcare. In this paper, we utilize and evaluate recent state-of-the-art (SOTA) SR methods and introduce our new proposed SR methods to the problem of estimating Glomerular Filtration Rate (GFR). GFR is a key indicator of kidney health and is an important determinant in certain diagnoses, such as Chronic Kidney Disease (CKD). As measuring GFR directly is expensive, the common practice for healthcare professionals is to use medical equations to estimate GFR from other biomarkers. However, most of these equations are built on specific populations and are potentially inaccurate for other populations. Additionally, there has been a growing need to tailor equations for cohorts with unique properties (e.g., young children, renal transplant patients). To address these issues, we propose to use SR to discover new equations to better estimate GFR for new populations or new cohorts. First, we utilize SOTA SR methods to discover equations that achieve better estimation performance than existing equations. Then, we introduce our novel method of taking existing GFR medical estimation equations as prior knowledge and evolving them via Constrained Genetic Perturbation (CGP). The prior knowledge used drastically reduces the search space and also discovers equations that closely resemble the functional forms familiar to medical professionals. We also introduce a variant that enables the equation to be modified with newly obtained features. Finally, we show that equations discovered by our methods demonstrate the best performance among all equations.