The obesity epidemic represents an important public health issue in the United States. Studying obesity trends across age groups over time helps to identify crucial relationships between the disease and medical treatment allowing for the development of effective prevention policies. We aim to define subgroups of age and cohort effects in obesity prevalence over time by considering an optimization approach applied to the age-period-cohort (APC) model. We consider a heterogeneous regression problem where the regression coefficients are age dependent and belong to subgroups with unknown grouping information. Using the APC model, we apply the alternating direction method of multipliers (ADMM) algorithm to develop a two-step algorithm for (1) subgrouping of cohort effects based on similar characteristics and (2) subgrouping age effects over time. The proposed clustering approach is illustrated for the United States population, aged 18-79, during the period 1990-2017.

中文翻译：

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确定肥胖患病率中年龄和队列效应的亚组

肥胖流行是美国一个重要的公共卫生问题。随着时间的推移研究不同年龄组的肥胖趋势有助于确定疾病与医疗之间的重要关系，从而制定有效的预防政策。我们的目标是通过考虑应用于年龄-周期-队列 (APC) 模型的优化方法来定义年龄和队列对肥胖患病率随时间的影响的亚组。我们考虑一个异构回归问题，其中回归系数依赖于年龄并且属于具有未知分组信息的子组。使用 APC 模型，我们应用乘数交替方向法 (ADMM) 算法来开发两步算法，用于 (1) 基于相似特征的队列效应子分组和 (2) 随着时间的推移对年龄效应进行子分组。