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In biomedical studies, researchers are often interested in assessing theassociation between one or more ordinal explanatory variables and an outcomevariable, at the same time adjusting for covariates of any type. The outcomevariable may be continuous, binary, or represent censored survival times. Inthe absence of precise knowledge of the response function, using monotonicityconstraints on the ordinal variables improves efficiency in estimatingparameters, especially when sample sizes are small. An active set algorithmthat can efficiently compute such estimators is proposed, and acharacterization of the solution is provided. Having an efficient algorithm athand is especially relevant when applying likelihood ratio tests in restrictedgeneralized linear models, where one needs the value of the likelihood at therestricted maximizer. The algorithm is illustrated on a real life data set fromoncology.

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