Estimation and Inference for Logistic Regression with Covariate Misclassification and Measurement Error in Main Study/Validation Study Designs
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主研究与验证研究设计下含误分类和测量误差的 Logistic 回归推断
- 研究问题
- 连续协变量存在测量误差、分类协变量存在误分类时，如何结合主研究和验证样本估计潜在真实协变量的 Logistic 回归关系？
- 方法与思路
- 作者以多元正态误差和链式 Logistic 误分类模型构建联合似然，同时估计回归、测量误差及分类校正参数。
- 材料陈述的贡献
- 摘要提出联合似然方法，并报告通常验证样本规模下没有一种推断方案表现满意；扩大验证样本后渐近最优特征更明显。
- 阅读关注点
- 应核对验证样本的选取与可比性、误差模型的验证方式、有限样本推断方案，以及链式模型排序稳健性的证据范围。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要，不能推断刊本变化；样本规模和稳健性结论来自所述实例与模拟，不能视为通用保证。
原文摘要
In epidemiological studies, continuous covariates often are measured with error and categorical covariates often are misclassified. Using the logistic regression model to represent the relationship between the binary outcome and the perfectly measured and classified covariates, the model for the observed main study data is derived. This derivation relies on the assumption that the error in the continuous covariates is multivariate normally distributed and uses a chain of logistic regression models to describe the misclassification processes. These model assumptions are empirically verified in the validation study, where the misclassified and mismeasured covariates are validated using perfectly measured and classified data. The full data likelihood, including contributions from both the main study and the validation study, is maximized to obtain the maximum likelihood estimates for the parameters of the underlying logistic regression model and of the measurement error model and reclassification models simultaneously. Standard asymptotic theory is applied. An example of this methodology is presented from the Nurses' Health Study investigating the relationship between cumulative incidence of breast cancer and saturated fat, total energy, and alcohol intake. A detailed simulation study was conducted to investigate the small-sample properties of these likelihood-based estimates and inferential quantities. No single estimation/inference option performed satisfactorily when the main study/validation study size was representative of that typically encountered in practice. When the validation size was twice or larger than from the usual one, features of asymptotic optimality were more apparent. By example and through simulation, the procedures appeared to be robust to misspecification of the order of the chain of conditional measurement error/reclassification models.