Two-phase, response-dependent sampling is often used in regression settings that involve expensive covariate measurements. Conditional maximum likelihood (CML) is an attractive approach in many cases as it avoids modelling of the covariate distribution, unlike full maximum likelihood. Scott & Wild (2011) introduced an augmented CML approach which is semi-parametric efficient in certain settings with a discrete response variable. We consider general regression models and show the Scott–Wild estimator of covariate effects has the same asymptotic efficiency as two empirical likelihood estimators, and that these estimators dominate the CML estimator. We compare the efficiencies of various estimators in simulation studies and illustrate the methodology in a two-phase genetics study.

中文翻译：

---

两阶段研究的经验和条件可能性

两阶段、响应相关抽样通常用于涉及昂贵协变量测量的回归设置。与完全最大似然不同，条件最大似然 (CML) 在许多情况下是一种有吸引力的方法，因为它避免了对协变量分布的建模。Scott & Wild (2011) 介绍了一种增强 CML 方法，该方法在具有离散响应变量的某些设置中是半参数有效的。我们考虑一般回归模型并表明协变量效应的 Scott-Wild 估计量与两个经验似然估计量具有相同的渐近效率，并且这些估计量主导 CML 估计量。我们比较了模拟研究中各种估计器的效率，并说明了两阶段遗传学研究中的方法。