Zhou Haibo, You Jinhong, Qin Guoyou, Longnecker Matthew P
University of North Carolina at Chapel Hill, USA.
J R Stat Soc Ser C Appl Stat. 2011 Aug;60(4):559-574. doi: 10.1111/j.1467-9876.2010.00756.x.
The outcome dependent sampling scheme has been gaining attention in both the statistical literature and applied fields. Epidemiological and environmental researchers have been using it to select the observations for more powerful and cost-effective studies. Motivated by a study of the effect of in utero exposure to polychlorinated biphenyls on children's IQ at age 7, in which the effect of an important confounding variable is nonlinear, we consider a semi-parametric regression model for data from an outcome-dependent sampling scheme where the relationship between the response and covariates is only partially parameterized. We propose a penalized spline maximum likelihood estimation (PSMLE) for inference on both the parametric and the nonparametric components and develop their asymptotic properties. Through simulation studies and an analysis of the IQ study, we compare the proposed estimator with several competing estimators. Practical considerations of implementing those estimators are discussed.
结果依赖抽样方案在统计文献和应用领域中都受到了关注。流行病学和环境研究人员一直在使用它来选择观测值，以进行更具效力和成本效益的研究。受一项关于子宫内接触多氯联苯对儿童7岁时智商影响的研究的启发，其中一个重要混杂变量的影响是非线性的，我们考虑一个半参数回归模型，用于来自结果依赖抽样方案的数据，其中响应变量和协变量之间的关系仅部分参数化。我们提出一种惩罚样条最大似然估计（PSMLE），用于对参数和非参数成分进行推断，并推导它们的渐近性质。通过模拟研究和对智商研究的分析，我们将所提出的估计量与几种竞争估计量进行比较。还讨论了实施这些估计量的实际考虑因素。
