Wang C Y, Huang Yijian
Division of Public Health Sciences, Fred Hutchinson Cancer Research Center, P.O. Box 19024, Seattle, WA 98109-1024, U.S.A.
Stat Med. 2003 Aug 30;22(16):2577-90. doi: 10.1002/sim.1435.
We consider regression analysis of a disease outcome in relation to longitudinal data which are observations from a random effects model. The covariate variables of interest are the values of the underlying trajectory at some time points, which may be fixed or subject-specific. Because the underlying random coefficients are unknown, the covariates to the primary model are generally unobserved. In addition, measurements are often not observed at the time points of interest. A motivating example to our model is the effects of age at adiposity rebound and the associated body mass index on the risk of adult obesity. The adiposity rebound is a time point at which the trajectory of a child's body fatness declines to a minimum. This general error in timing problem may be applied to an analysis when time-dependent marker variables follow a polynomial model in which the effect of a local maximum or minimum point may be of interest. It can be seen that directly applying estimated covariates, possibly obtained from estimated time points, may lead to bias. Estimation procedures based on expected estimating equations, regression calibration and simulation extrapolation are applied to this problem.
我们考虑对疾病结局与纵向数据进行回归分析，这些纵向数据是来自随机效应模型的观测值。感兴趣的协变量是基础轨迹在某些时间点的值，这些时间点可能是固定的，也可能是个体特定的。由于基础随机系数未知，主模型的协变量通常是未观测到的。此外，在感兴趣的时间点通常无法观测到测量值。我们模型的一个激励性例子是肥胖反弹年龄及其相关体重指数对成人肥胖风险的影响。肥胖反弹是儿童体脂轨迹下降到最小值的时间点。当随时间变化的标记变量遵循多项式模型时，这种一般的时间误差问题可应用于分析，其中局部最大值或最小值点的影响可能是感兴趣的。可以看出，直接应用可能从估计时间点获得的估计协变量可能会导致偏差。基于期望估计方程、回归校准和模拟外推的估计程序被应用于此问题。
