A STATISTICAL METHOD FOR SURROGATE WEALTH DATA IN AGING

这项研究提出了一种新的统计方法，用于解决老龄化流行病学中二次数据分析中的一个重要问题。研究人员建议开发一种方法，将来自两个独立样本的数据组合在一起，以模拟当y和a不在一个样本中共存时，响应y与协变量a的关系。利益的一般关系是财富(U)和健康(Y)。具体地说，主要数据包含感兴趣的反应y，即生物学或临床健康测量。研究人员使用第三次全国健康和营养检查调查(NHANES)，其中包含基于临床检查的详细数据。然而，NHANES只包含与财富松散相关的标准社会人口学代理变量x，而不是财务状况信息。这些代理变量或替代变量与真实财务状况指标a的关系将使用辅助的外部验证数据集--健康和退休研究--来建模。由此产生的代理模型将在原始数据(NHANES)中用于研究利益关系。这个问题被形式化化为协变量中的误差之一。拟议的研究将调查可行性，并随后制定一种解决这一问题的方法。此外，该方法将通过一个在美国很少受到关注的真实的实质性问题进行演示：骨密度(BMD)或骨量减少(低BMD)的流行与财富之间是否存在关联？这个问题令人感兴趣，因为美国白人髋部骨折的地理模式表明，病理与终身贫困之间可能存在关联。具体目标是：(1)建立和检验多元代理x的均值和方差作为缺失协变量u和其他协变量w的函数的回归模型。使用目标1中开发的模型和协变量中误差的新方法，根据a和w对健康结果y的回归进行建模。

This study proposes a novel statistical methodology for addressing an important problem in secondary data analysis in the epidemiology of aging. The investigators propose to develop a method to combine data from two separate samples to model the relationship of a response y to a covariate a when y and a do not coexist in one sample. The general relationship of interest is wealth (u) and health (y). Specifically, primary data contain the response y of interest, a biological or clinical health measurement. The investigators use the third National Health and Nutrition Examination Survey (NHANES), which contains detailed data based on clinical examination. However, rather than financial status information, NHANES only contains standard sociodemographic proxy variables x which are loosely related to wealth. The relationship of these proxy, or surrogate, variables to the true financial status indicators a is to be modelled using an auxiliary external validation data set, the Health and Retirement Study. The resulting surrogate model will then be used in the primary data (NHANES) to study the relationship of interest. The problem is formalized as one of errors-in-covariates. The proposed study will investigate the feasibility and subsequently develop a method for addressing this problem. Additionally, the method will be demonstrated with a real substantive question which has received little attention in the US: Is there an association between bone mineral density (BMD) or the prevalence of osteopenia (low BMD) and wealth? The question is of interest because the geographic pattern of hip fractures among whites in the US suggests a possible association between pathology and lifelong poverty. Specific aims are: (1.) To develop and test a regression model for the mean and variance of a multivariate surrogate x as a function of the missing covariate u and other covariates w. (2.) To use the model developed in Aim 1 and a new methodology for errors-in-covariates to model the regression of health outcome y in terms of a and w.