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A Unified Approach to Semiparametric Transformation Models Under General Biased Sampling Schemes
- Kim, Jane Paik, Lu, Wenbin, Sit, Tony, Ying, Zhiliang
- Journal of the American Statistical Association 2013 v.108 no.501 pp. 217-227
- data collection, equations, models, variance
- We propose a unified estimation method for semiparametric linear transformation models under general biased sampling schemes. The new estimator is obtained from a set of counting process-based unbiased estimating equations, developed through introducing a general weighting scheme that offsets the sampling bias. The usual asymptotic properties, including consistency and asymptotic normality, are established under suitable regularity conditions. A closed-form formula is derived for the limiting variance and the plug-in estimator is shown to be consistent. We demonstrate the unified approach through the special cases of left truncation, length bias, the case-cohort design, and variants thereof. Simulation studies and applications to real datasets are presented.