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Combined estimating equation approaches for semiparametric transformation models with length-biased survival data. (English) Zbl 1299.62093
Summary: Survival data are subject to length-biased sampling when the survival times are left-truncated and the underlying truncation time random variable is uniformly distributed. Substantial efficiency gains can be achieved by incorporating the information about the truncation time distribution in the estimation procedure [M.-Ch. Wang, J. Am. Stat. Assoc. 84, No. 407, 742–748 (1989; Zbl 0677.62037); Biometrika 83, No. 2, 343–354 (1996; Zbl 0864.62080)]. Under the semiparametric transformation models, the maximum likelihood method is expected to be fully efficient, yet it is difficult to implement because the full likelihood depends on the nonparametric component in a complicated way. Moreover, its asymptotic properties have not been established. In this article, we extend the martingale estimating equation approach and the pseudo-partial likelihood approach for semiparametric transformation models with right-censored data to handle left-truncated and right-censored data. In the same spirit of the composite likelihood method [Ch.-Y. Huang and J. Qin, J. Am. Stat. Assoc. 107, No. 499, 946–957 (2012; Zbl 1299.62123)], we further construct another set of unbiased estimating equations by exploiting the special probability structure of length-biased sampling. Thus the number of estimating equations exceeds the number of parameters, and efficiency gains can be achieved by solving a simple combination of these estimating equations. The proposed methods are easy to implement as they do not require additional programming efforts. Moreover, they are shown to be consistent and asymptotically normally distributed. A data analysis of a dementia study illustrates the methods.

MSC:
62N02 Estimation in survival analysis and censored data
62P10 Applications of statistics to biology and medical sciences; meta analysis
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