We analyze adolescent BMI and middle-age systolic blood pressure (SBP) repeatedly measured on women enrolled in the Fels Longitudinal Study (FLS) between 1929 and 2010 to address three questions: Do adolescent-specific growth rates in body mass index (BMI) and menarche affect middle-age SBP? Do they moderate the aging effect on middle-age SBP? Have the effects changed over historical time? To address the questions, we propose analyzing a growth curve model (GCM) that controls for age, birth-year cohort, and historical time. However, several complications in the data make the GCM analysis nonstandard. First, the person-specific adolescent BMI and middle-age SBP trajectories are unobservable. Second, missing data are substantial on BMI, SBP, and menarche. Finally, modeling the latent trajectories for BMI and SBP, repeatedly measured on two distinct sets of unbalanced time points, are computationally intensive. We adopt a bivariate GCM for BMI and SBP with correlated random coefficients. To efficiently handle missing values of BMI, SBP, and menarche assumed missing at random, we estimate their joint distribution by maximum likelihood via the EM algorithm where the correlated random coefficients and menarche are multivariate normal. The estimated distribution will be transformed to the desired GCM for SBP that includes the random coefficients of BMI and menarche as covariates. We demonstrate unbiased estimation by simulation. We find that adolescent growth rates in BMI and menarche are positively associated with, and moderate, the aging effect on SBP in middle age, controlling for age, cohort, and historical time, but the effect sizes are at most modest. The aging effect is significant on SBP, controlling for cohort and historical time, but not vice versa.

中文翻译：

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给定数据 MAR 的青少年肥胖对女性中年健康的影响

我们分析了 1929 年至 2010 年间参加 Fels 纵向研究 (FLS) 的女性反复测量的青少年 BMI 和中年收缩压 (SBP)，以解决三个问题：青少年特定的体重指数 (BMI) 增长率和初潮影响中年收缩压？它们是否可以减轻对中年 SBP 的老化影响？影响是否随着历史时间而改变？为了解决这些问题，我们建议分析控制年龄、出生年份队列和历史时间的生长曲线模型 (GCM)。然而，数据中的一些复杂情况使 GCM 分析变得不标准。首先，个体特定的青少年 BMI 和中年 SBP 轨迹是不可观察的。其次，BMI、SBP 和月经初潮的缺失数据很多。最后，对 BMI 和 SBP 的潜在轨迹进行建模，在两组不同的不平衡时间点上重复测量，计算量很大。我们采用具有相关随机系数的 BMI 和 SBP 的双变量 GCM。为了有效地处理 BMI、SBP 和初潮假设随机丢失的缺失值，我们通过 EM 算法通过最大似然估计它们的联合分布，其中相关的随机系数和初潮是多元正态的。估计的分布将转换为 SBP 所需的 GCM，其中包括 BMI 和初潮的随机系数作为协变量。我们通过模拟展示了无偏估计。我们发现，在控制年龄、队列和历史时间的情况下，BMI 和月经初潮的青少年增长率与中年 SBP 的衰老效应呈正相关，并且呈中等程度，但效应大小至多是适度的。