Active-set algorithms based statistical inference for shape-restricted generalized additive Cox regression models

TL;DR

This paper introduces a shape-restricted inference method for Cox regression models using active-set algorithms, allowing flexible modeling of covariate effects with automatic knot selection, improving nonlinear response recovery.

Contribution

It develops a novel SR-Cox model with active-set optimization, enabling shape-restricted additive functions and automatic knot elimination for better covariate effect estimation.

Findings

Accurate linear covariate effect estimates comparable to traditional methods.

Enhanced nonlinear covariate response recovery.

Automatic knot elimination improves model interpretability.

Abstract

Recently the shape-restricted inference has gained popularity in statistical and econometric literature in order to relax the linear or quadratic covariate effect in regression analyses. The typical shape-restricted covariate effect includes monotonic increasing, decreasing, convexity or concavity. In this paper, we introduce the shape-restricted inference to the celebrated Cox regression model (SR-Cox), in which the covariate response is modeled as shape-restricted additive functions. The SR-Cox regression approximates the shape-restricted functions using a spline basis expansion with data driven choice of knots. The underlying minimization of negative log-likelihood function is formulated as a convex optimization problem, which is solved with an active-set optimization algorithm. The highlight of this algorithm is that it eliminates the superfluous knots automatically. When covariate effects include combinations of convex or concave terms with unknown forms and linear terms, the most interesting finding is that SR-Cox produces accurate linear covariate effect estimates which are comparable to the maximum partial likelihood estimates if indeed the forms are known. We conclude that concave or convex SR-Cox models could significantly improve nonlinear covariate response recovery and model goodness of fit.