School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona.
School of Mathematical and Natural Sciences, Arizona State University, Glendale, Arizona.
Stat Med. 2019 May 30;38(12):2171-2183. doi: 10.1002/sim.8099. Epub 2019 Jan 30.
Correlation is inherent in longitudinal studies due to the repeated measurements on subjects, as well as due to time-dependent covariates in the study. In the National Longitudinal Study of Adolescent to Adult Health (Add Health), data were repeatedly collected on children in grades 7-12 across four waves. Thus, observations obtained on the same adolescent were correlated, while predictors were correlated with current and future outcomes such as obesity status, among other health issues. Previous methods, such as the generalized method of moments (GMM) approach have been proposed to estimate regression coefficients for time-dependent covariates. However, these approaches combined all valid moment conditions to produce an averaged parameter estimate for each covariate and thus assumed that the effect of each covariate on the response was constant across time. This assumption is not necessarily optimal in applications such as Add Health or health-related data. Thus, we depart from this assumption and instead use the Partitioned GMM approach to estimate multiple coefficients for the data based on different time periods. These extra regression coefficients are obtained using a partitioning of the moment conditions pertaining to each respective relationship. This approach offers a deeper understanding and appreciation into the effect of each covariate on the response. We conduct simulation studies, as well as analyses of obesity in Add Health, rehospitalization in Medicare data, and depression scores in a clinical study. The Partitioned GMM methods exhibit benefits over previously proposed models with improved insight into the nonconstant relationships realized when analyzing longitudinal data.
由于对受试者进行了重复测量，以及研究中存在时间相关的协变量，因此纵向研究中存在相关性。在国家青少年到成人健康纵向研究（Add Health）中，数据在四个波次中对 7-12 年级的儿童进行了重复收集。因此，在同一青少年身上获得的观察结果是相关的，而预测因子与当前和未来的结果（如肥胖状况和其他健康问题）相关。以前提出的方法，如广义矩方法（GMM），已被用于估计时间相关协变量的回归系数。然而，这些方法将所有有效的矩条件结合起来，为每个协变量生成一个平均参数估计，因此假设每个协变量对响应的影响在整个时间内是恒定的。这种假设在 Add Health 或与健康相关的数据等应用中不一定是最优的。因此，我们背离了这个假设，而是使用分区 GMM 方法根据不同的时间段为数据估计多个系数。这些额外的回归系数是通过对每个相关关系的矩条件进行分区来获得的。这种方法提供了对每个协变量对响应的影响的更深入的理解和欣赏。我们进行了模拟研究，以及对 Add Health 中的肥胖、医疗保险数据中的再住院和临床研究中的抑郁评分的分析。分区 GMM 方法在分析纵向数据时，表现出优于以前提出的模型的优势，对非恒定关系有了更深入的了解。
