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协变量误分类和测量误差的逻辑回归
- 研究问题
- 连续协变量有测量误差、分类协变量有误分类时，如何结合主研究与验证研究估计潜在真实协变量的逻辑回归关系？
- 方法与思路
- 作者以多元正态描述连续误差，以链式逻辑回归描述误分类，联合最大化两类研究的似然，同时估计回归与误差模型参数。
- 材料陈述的贡献
- 摘要称，常见验证样本规模下没有单一方案表现满意；扩大验证样本后渐近性质更明显，所设分析对条件模型链顺序误设较稳健。
- 阅读关注点
- 应核对验证研究的代表性与测量准确性、误差模型条件、链式分解，以及验证样本规模如何影响偏差和区间覆盖率。
- 阅读边界
- 依据 OpenAlex 索引摘要，稿件版本未注明；摘要未说明验证抽样机制和具体误差结果，链顺序稳健性不能推广到所有模型误设。
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.