There is a considerable literature in case-control logistic regression on whether or not non-confounding covariates should be adjusted for. However, only limited and ad hoc theoretical results are available on this important topic. A constrained maximum likelihood method was recently proposed, which appears to be generally more powerful than logistic regression methods with or without adjusting for non-confounding covariates. This note provides a theoretical clarification for the case-control logistic regression with and without covariate adjustment and the constrained maximum likelihood method on their relative performances in terms of asymptotic relative efficiencies. We show that the benefit of covariate adjustment in the case-control logistic regression depends on the disease prevalence. We also show that the constrained maximum likelihood estimator gives an asymptotically uniformly most powerful test.

翻译：在病例-对照逻辑回归中，关于是否应调整非混杂协变量的问题已有大量文献。然而，这一重要议题目前仅有零散且特设的理论结果。近期有研究提出一种约束最大似然方法，该方法在调整或不调整非混杂协变量的逻辑回归方法中普遍表现出更强的统计效力。本文从理论层面阐明了有无协变量调整的病例-对照逻辑回归与约束最大似然方法在渐近相对效率方面的性能差异。研究表明，病例-对照逻辑回归中协变量调整的收益取决于疾病患病率。此外，我们证明约束最大似然估计量能提供渐近一致的最优检验。