ABSTRACT

A mixture of a distribution of responses from untreated patients and a shift of that distribution is a useful model for the responses from a group of treated patients. The mixture model accounts for the fact that not all the patients in the treated group will respond to the treatment and consequently their responses follow the same distribution as the responses from untreated patients. The treatment effect in this context consists of both the fraction of the treated patients that are responders and the magnitude of the shift in the distribution for the responders. In this article, we investigate asymptotic properties of method of moment estimators for the treatment effect based on a semi-supervised two-component mixture model. From these properties, we develop asymptotic confidence intervals and demonstrate their superior statistical inference performance compared to the computationally intensive bootstrap intervals and their Bias-Corrected versions.

摘要

来自未治疗患者的反应分布和该分布的变化的混合是来自一组治疗患者的反应的有用模型。混合模型解释了这样一个事实，即并非治疗组中的所有患者都会对治疗产生反应，因此他们的反应遵循与未治疗患者的反应相同的分布。在这种情况下，治疗效果既包括作为反应者的治疗患者的比例，也包括反应者分布变化的幅度。在本文中，我们研究了基于半监督二元混合模型的处理效果矩估计法的渐近性质。从这些属性中，