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 a precise knowledge of the response function, using monotonicity constraints on the ordinal variables improves efficiency in estimating parameters, especially when sample sizes are small. In this article, we show that an active set algorithm can efficiently compute such estimators, and we provide a characterization of the solution. 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. We illustrate the algorithm on a real life data set from oncology.
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