An Active Set Algorithm to Estimate Parameters in Generalized Linear Models with Ordered Predictors

TL;DR

This paper introduces an active set algorithm for efficiently estimating parameters in generalized linear models with ordered predictors, improving inference in biomedical studies with ordinal variables.

Contribution

It presents a novel active set algorithm for monotonicity-constrained estimation in generalized linear models with ordered predictors, including a solution characterization.

Findings

Efficient algorithm for constrained parameter estimation.

Application to real oncology data demonstrating practical utility.

Enhances likelihood ratio testing in restricted models.

Abstract

In biomedical studies, researchers are often interested in assessing the association between one or more ordinal explanatory variables and an outcome variable, at the same time adjusting for covariates of any type. The outcome variable may be continuous, binary, or represent censored survival times. In the absence of precise knowledge of the response function, using monotonicity constraints on the ordinal variables improves efficiency in estimating parameters, especially when sample sizes are small. An active set algorithm that can efficiently compute such estimators is proposed, and a characterization of the solution is provided. Having an efficient algorithm at hand is especially relevant when applying likelihood ratio tests in restricted generalized linear models, where one needs the value of the likelihood at the restricted maximizer. The algorithm is illustrated on a real life data set from oncology.