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Regression Analysis with Response-selective Sampling

Authors Chen, Kani View this author's profile
Lin, Yuanyuan
Yao, Yuan
Zhou, Chaoxu HKUST affiliated (currently or previously).
Issue Date 2017
Source Statistica Sinica , v.27, (4), October 2017
Summary Response-selective sampling, in which samples are drawn from a population according to the values of the response variable, is common in biomedical, epidemiological, economic and social studies. This paper proposes to use transformation models, known as the generalized accelerated failure time model in econo-metrics, for regression analysis with response-selective sampling. With unknown error distribution, the transformation models are broad enough to cover linear regression models, the Cox's model and the proportional odds model as special cases. To the best of our knowledge, except for the case-control logistic regression , there is no report in the literature that a prospective estimation approach can work for biased sampling without any modification. We prove that the maximum rank correlation estimation is valid for response-selective sampling and establish its consistency and asymptotic normality. Unlike the inverse probability methods, the proposed method of estimation does not involve the sampling probabilities, which are often difficult to obtain in practice. Without the need of estimating the unknown transformation function or the error distribution, the proposed method is numerically easy to implement with the Nelder-Mead simplex algorithm, which does not require convexity or continuity. We propose an inference procedure using random weighting to avoid the complication of density estimation when using the plug-in rule for variance estimation. Numerical studies with supportive evidence are presented. Application is illustrated with the Forbes Global 2000 data.
Language English
Format Article
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