AI 中文总结
针对稀疏匹配病例对照研究中条件逻辑回归估计量偏差与收缩控制不足问题，提出log-F惩罚条件逻辑回归方法，其在模拟中表现出与Firth方法相当的置信区间覆盖率，且均方误差更低。
AI 中文摘要
我们研究条件逻辑回归中用于估计和推断的惩罚似然方法。已知在小型或稀疏匹配病例对照研究中，标准条件最大似然估计量存在远离零的偏差。一种广泛使用的补救方法是Firth惩罚似然方法，该方法具有良好的频率论操作特性，但对单个回归系数施加的收缩程度控制有限。我们通过使用独立的log-F分布惩罚条件似然来开发点估计量和区间估计量。这种log-F惩罚方法允许分析人员使用关于合理效应量的可解释先验假设来校准收缩程度。我们还提供了校准收缩量的实用指导，并表明该方法可通过使用标准条件逻辑回归软件的数据增广来实现。我们使用两类数据说明该方法：（i）母亲暴露于己烯雌酚与女儿阴道癌风险的研究数据；（ii）2型糖尿病的遗传关联研究数据。随后我们在模拟研究中将log-F惩罚方法与Firth惩罚似然方法进行比较。在模拟中，log-F惩罚估计量的置信区间覆盖率与Firth方法相当，均方误差更低，且具有相似的1类错误率和功效。这些结果支持将log-F惩罚条件逻辑回归用于稀疏匹配和分层研究的推断。
英文摘要
We investigate penalized likelihood methods for estimation and inference in conditional logistic regression. The standard conditional maximum likelihood estimator is known to be biased away from zero in small or sparse matched case-control studies. A widely used remedy is Firth's penalized likelihood approach, which has good frequentist operating characteristics but provides limited control over the degree of shrinkage applied to individual regression coefficients. We develop point and interval estimators by penalizing the conditional likelihood with independent log-$F$ distributions. The log-\(F\)-penalized approach allows analysts to calibrate shrinkage using interpretable prior assumptions about plausible effect sizes. We also provide practical guidance for calibrating the amount of shrinkage and show that the method can be implemented through data augmentation using standard conditional logistic regression software. We illustrate the methods using data from (i) a study of maternal exposure to diethylstilbestrol and the risk of vaginal cancer in daughters, and (ii) a genetic association study of type 2 diabetes. We then compare the log-$F$-penalized approach with Firth's penalized likelihood method in a simulation study. In simulations, the log-$F$-penalized estimators had confidence-interval coverage comparable to that of Firth's method and lower mean squared error, with similar type~1 error rates and power. These results support the use of log-$F$-penalized conditional logistic regression for inference in sparse matched and stratified studies.
Comments21 pages, 5 figures
