Schmid C H, Rosner B
Center for Health Services Research and Study Design, New England Medical Center, Boston, MA.
Stat Med. 1993 Jun 30;12(12):1141-53. doi: 10.1002/sim.4780121204.
To estimate the parameters in a logistic regression model when the predictors are subject to random or systematic measurement error, we take a Bayesian approach and average the true logistic probability over the conditional posterior distribution of the true value of the predictor given its observed value. We allow this posterior distribution to consist of a mixture when the measurement error distribution changes form with observed exposure. We apply the method to study the risk of alcohol consumption on breast cancer using the Nurses Health Study data. We estimate measurement error from a small subsample where we compare true with reported consumption. Some of the self-reported non-drinkers truly do not drink. The resulting risk estimates differ sharply from those computed by standard logistic regression that ignores measurement error.
当预测变量存在随机或系统性测量误差时，为估计逻辑回归模型中的参数，我们采用贝叶斯方法，并在给定预测变量观测值的情况下，对其真实值的条件后验分布上的真实逻辑概率进行平均。当测量误差分布随观察到的暴露情况而改变形式时，我们允许这种后验分布由混合分布组成。我们应用该方法，利用护士健康研究数据来研究饮酒与乳腺癌的风险。我们从小子样本中估计测量误差，在该小子样本中我们将真实饮酒量与报告的饮酒量进行比较。一些自我报告的不饮酒者实际上真的不饮酒。由此得到的风险估计值与忽略测量误差的标准逻辑回归计算出的结果有很大差异。
