Department of Mathematical Sciences, University of Bath, Bath, UK.
Stat Med. 2023 May 30;42(12):1888-1908. doi: 10.1002/sim.9703. Epub 2023 Mar 12.
Age-period-cohort (APC) models are frequently used in a variety of health and demographic-related outcomes. Fitting and interpreting APC models to data in equal intervals (equal age and period widths) is nontrivial due to the structural link between the three temporal effects (given two, the third can always be found) causing the well-known identification problem. The usual method for resolving the structural link identification problem is to base a model on identifiable quantities. It is common to find health and demographic data in unequal intervals, this creates further identification problems on top of the structural link. We highlight the new issues by showing that curvatures which were identifiable for equal intervals are no longer identifiable for unequal data. Furthermore, through extensive simulation studies, we show how previous methods for unequal APC models are not always appropriate due to their sensitivity to the choice of functions used to approximate the true temporal functions. We propose a new method for modeling unequal APC data using penalized smoothing splines. Our proposal effectively resolves the curvature identification issue that arises and is robust to the choice of the approximating function. To demonstrate the effectiveness of our proposal, we conclude with an application to UK all-cause mortality data from the Human mortality database.
年龄-时期-队列（APC）模型常用于各种健康和人口相关的结果。由于三个时间效应之间存在结构联系（给定两个，第三个总是可以找到），因此在等间隔（相等的年龄和时期宽度）下拟合和解释 APC 模型是很复杂的，这会导致众所周知的识别问题。解决结构联系识别问题的常用方法是基于可识别的量来构建模型。在不相等的间隔中找到健康和人口数据是很常见的，这在结构联系的基础上又增加了进一步的识别问题。我们通过展示在等间隔下可识别的曲率在不等间隔数据下不再可识别，突出了新的问题。此外，通过广泛的模拟研究，我们表明由于之前用于不等 APC 模型的方法对用于近似真实时间函数的函数选择的敏感性，它们并不总是合适的。我们提出了一种使用惩罚平滑样条对不等 APC 数据进行建模的新方法。我们的建议有效地解决了出现的曲率识别问题，并且对近似函数的选择具有鲁棒性。为了证明我们建议的有效性，我们以应用于人类死亡率数据库中的英国全因死亡率数据为例。
