Rosner B, Spiegelman D, Willett W C
Channing Laboratory, Harvard Medical School, Boston, MA 02115.
Am J Epidemiol. 1992 Dec 1;136(11):1400-13. doi: 10.1093/oxfordjournals.aje.a116453.
Frequently, covariates used in a logistic regression are measured with error. The authors previously described the correction of logistic regression relative risk estimates for measurement error in one or more covariates when a "gold standard" is available for exposure assessment. For some exposures (e.g., serum cholesterol), no gold standard exists, and one must assess measurement error via a reproducibility substudy. In this paper, the authors present measurement error methods for logistic regression when there is error (possibly correlated) in one or more covariates and one has data from both a main study and a reproducibility substudy. Confidence intervals from this procedure reflect error in parameter estimates from both studies. These methods are applied to the Framingham Heart Study, where the 10-year incidence of coronary heart disease is related to several coronary risk factors among 1,731 men disease-free at examination 4. Reproducibility data are obtained from the subgroup of 1,346 men seen at examinations 2 and 3. Estimated odds ratios comparing extreme quintiles for risk factors with substantial error were increased after correction for measurement error (serum cholesterol, 2.2 vs. 2.9; serum glucose, 1.3 vs. 1.5; systolic blood pressure, 2.8 vs. 3.8), but were generally decreased or unchanged for risk factors with little or no error (body mass index, 1.6 vs. 1.6; age 65-69 years vs. 35-44 years, 4.3 vs. 3.8; smoking, 1.7 vs. 1.7).
在逻辑回归中使用的协变量常常存在测量误差。作者之前描述了在暴露评估有“金标准”时，对一个或多个协变量测量误差进行逻辑回归相对风险估计的校正方法。对于某些暴露因素（如血清胆固醇），不存在金标准，必须通过重复性子研究来评估测量误差。在本文中，作者提出了一种逻辑回归的测量误差方法，该方法适用于一个或多个协变量存在误差（可能相关）且同时拥有主要研究和重复性子研究数据的情况。此方法得到的置信区间反映了两项研究中参数估计的误差。这些方法应用于弗雷明汉心脏研究，在该研究中，1731名在第4次检查时无疾病的男性中，冠心病的10年发病率与多种冠心病风险因素相关。重复性数据来自在第2次和第3次检查时观察的1346名男性亚组。校正测量误差后，比较存在大量误差的风险因素的极端五分位数的估计比值比有所增加（血清胆固醇，从2.2增至2.9；血清葡萄糖，从1.3增至1.5；收缩压，从2.8增至3.8），但对于几乎没有误差或无误差的风险因素，估计比值比通常降低或不变（体重指数，1.6比1.6；65 - 69岁与35 - 44岁，4.3比3.8；吸烟，1.7比1.7）。
