一种用于估计具有有序预测变量的广义线性模型中参数的积极集算法
An Active Set Algorithm to Estimate Parameters in Generalized Linear Models with Ordered Predictors
AI总结：
本文提出一种积极集算法，用于在有序预测变量上施加单调性约束，高效估计广义线性模型参数，并应用于肿瘤学真实数据。
摘要：
在生物医学研究中，研究人员通常关注评估一个或多个有序解释变量与结果变量之间的关联，同时调整任意类型的协变量。结果变量可以是连续的、二元的，或表示删失生存时间。在缺乏对响应函数的精确了解的情况下，对有序变量使用单调性约束可提高参数估计的效率，尤其是在样本量较小时。本文提出了一种能够高效计算此类估计量的积极集算法，并给出了解的特征刻画。在受限广义线性模型中应用似然比检验时，需要受限最大化点处的似然值，此时拥有一个高效算法尤为重要。该算法在一个来自肿瘤学的真实数据集上进行了说明。
英文摘要：
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.
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