Louis T A, Robins J, Dockery D W, Spiro A, Ware J H
J Chronic Dis. 1986;39(10):831-9. doi: 10.1016/0021-9681(86)90085-8.
Data from longitudinal studies may be analyzed both cross-sectionally and longitudinally. Discrepancies between estimates obtained from these analyses pose questions about the validity of cross-sectional estimates of change. In some cases these discrepancies are the result of period effects, cohort effects, or selective dropout. In others, they are the result of incomplete modeling of the process and are spurious rather than substantive. In this report, we show that when the true relation between a dependent variable and age is non-linear (e.g. quadratic), but is modeled as linear, the estimated age effect will be a function of the age distribution. In a continuous-time idealization, if the age distribution is Gaussian, the estimated age effects agree. If the age distribution is symmetric and the non-linearity is quadratic, cross-sectional and longitudinal results agree. Otherwise they do not. We illustrate these points by analysis of the relation between aging and pulmonary function in middle and old age using data from a large, prospective, longitudinal study.
纵向研究的数据既可以进行横断面分析，也可以进行纵向分析。从这些分析中获得的估计值之间的差异，引发了关于变化的横断面估计值有效性的问题。在某些情况下，这些差异是时期效应、队列效应或选择性失访的结果。在其他情况下，它们是过程建模不完整的结果，是虚假的而非实质性的。在本报告中，我们表明，当因变量与年龄之间的真实关系是非线性的（例如二次函数关系），但却被建模为线性关系时，估计的年龄效应将是年龄分布的一个函数。在连续时间理想化情况下，如果年龄分布是高斯分布，估计的年龄效应是一致的。如果年龄分布是对称的且非线性是二次函数关系，横断面和纵向结果是一致的。否则则不一致。我们使用一项大型前瞻性纵向研究的数据，通过分析中老年人群衰老与肺功能之间的关系来说明这些要点。
