Reweighting estimators for the transformation models with length-biased sampling data and missing covariates

Abstract

Length-biased sampling data are commonly observed in cross-sectional surveys and epidemiological cohort studies. Due to study design or accident, some components of the covariate vector are often missing. This article considers the statistical inference for the transformation models with length-biased sampling data and missing covariates. The reweighting estimating procedures are proposed for the unknown regression parameters when the selection probability is known, estimated non parametrically, or estimated parametrically. The large sample properties of the resulting estimators are studied. Simulation studies are presented to demonstrate the utility and efficiency of the proposed methods.

Keywords:

• Length-biased sampling
• missing covariate data
• transformation models
• weighted estimating equation

Acknowledgments

The authors thank the Co-Editor, the Associate Editor and the anonymous reviewers for their constructive comments and suggestions which help improve the article substantially.

Additional information

Funding

Qiu's research is supported by the MOE (Ministry of Education in China) Project of Humanities and Social Sciences (Grant No. 19YJC910004), and the Scientific Research Funds of Huaqiao University (17BS425). Ma’s research is sponsored by the National Natural Science Foundation of China (11901200, 71931004), Shanghai Pujiang Program (19PJ1403400), and the Fundamental Research Funds for the Central Universities. Shi’s research is supported by Fujian Key Laboratory of Data Science and Statistics (Minnan Normal University) (2020L0703, 2020L0704), Natural Science Foundation of Fujian Province (2019Y3007), China.