Considerable debate has been generated in recent literature on whether non-confounding covariates should be adjusted for in the analysis of case-control data through logistic regression, and limited theoretical results are available regarding this problem. Zhang et al. (2018) proposed a constrained maximum likelihood approach that is seemingly more powerful than the approaches with or without adjusting for non-confounding covariates in logistic regression, but no theoretical justification was provided regarding this empirical finding. We provide rigorous justification for the relative performances of the above three approaches through Pitman's asymptotic relative efficiencies. Specifically, the constrained maximum likelihood approach is proved to be uniformly most powerful. On the other hand, the relative performance of the other two approaches heavily depends on disease prevalence, that is, adjust for non-confounding covariates can lead to power loss when the disease prevalence is low, but this is not the case otherwise.
翻译:最近的一些文献就以下问题进行了大量辩论:在分析案件控制数据时,是否应该通过后勤回归调整非中央化的共变体,是否应该调整非中央化的共变体,以及这一问题的理论结果有限。张等人(2018年)提出了一种似乎比在后勤回归方面非中央化的共变体更强大的有限最大可能性办法,但对这一经验结论没有提供理论上的理由。我们通过Pitman的消毒相对效率,为上述三种办法的相对表现提供了严格的理由。具体地说,限制的最大可能性办法被证明是最为有力的。另一方面,其他两种办法的相对表现在很大程度上取决于疾病的流行程度,也就是说,在非中央化的共变体中进行调整,在疾病流行程度低的情况下可能导致权力丧失,但情况并非如此。