A Sparse Regression Framework for a Predictive Nomogram of Severe Low Anterior Resection Syndrome: Mathematical Foundations
Autores: Coral Leonor Blíe Magaña
Tipo: Short Note
Número: Volume 1, Issue 1
Fecha de publicación: 2026-11-12
Recibido: 2026-11-10
Aceptado: 2026-11-11
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Resumen
Severe low anterior resection syndrome (LARS) is a major functional sequel of colorectal cancer treatment, and current clinical practice lacks predictive models that allow early stratification of patients at risk. This note argues that the appropriate mathematical framework is not a hand-crafted risk score but a sparse logistic regression with structured regularization. We formalize the problem as the estimation of a sparse coefficient vector in a generalized linear model and identify the mathematical objects involved: a design matrix with block-structured covariates, a logistic loss with an l1 or l1/l2 penalty, and a nomogram as a monotone transformation of the fitted linear predictor. We prove a proposition establishing that, under the weighting w_g = sqrt(|g|) and singleton blocks, the group-Lasso formulation reduces to the standard Lasso, thereby unifying the two regularization paths and justifying the use of block penalties for clinically meaningful covariate groups. The framework is instantiated on a retrospective cohort of colorectal cancer patients treated at the Instituto Nacional de Cancerologia (INCan) in Mexico City, with clinically defined covariate blocks (neoadjuvant therapy, radiotherapy, type of surgery, hip adductor strength, continence status, time since surgery). The result provides a rigorous foundation for the nomogram as a calibrated decision tool in multidisciplinary prehabilitation.