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Estimation and Inference of Quantile Regression for Survival Data Under Biased Sampling
Gongjun Xu1,2, Tony Sit3, Lan Wang1
1School of Statistics, University of Minnesota, Minneapolis, MN.
Journal of the American Statistical Association
|August 7, 2018
Summary
This study introduces a unified method for statistical inference in quantile regression with survival data, addressing biased sampling common in medical and economic research. The new resampling technique offers accurate covariance estimation without repeated equation solving.
Area of Science:
- Statistics
- Biostatistics
- Econometrics
Background:
- Biased sampling is prevalent in economics, epidemiology, and medical studies, often leading to inaccurate statistical inference.
- Common biased sampling schemes include length-biased sampling and case-cohort designs.
Purpose of the Study:
- To propose a unified estimation procedure for quantile regression with survival data under general biased sampling.
- To develop a computationally fast resampling method for statistical inference.
- To provide a convenient tool for analyzing data from various biased sampling designs.
Main Methods:
- A unified estimation procedure for quantile regression with survival data.
- A computationally fast resampling method that avoids repeatedly solving estimating equations.
- Investigation of efficient estimation using the generalized method of moments.
Main Results:
- The proposed estimator is established to have uniform consistency and weak convergence.
- Asymptotic normality is derived for efficient estimation.
- The resampling method is proven to consistently estimate the asymptotic covariance matrix.
Conclusions:
- The unified framework offers a practical tool for researchers analyzing data from biased sampling schemes.
- The proposed methods enhance the accuracy and efficiency of statistical inference in survival data analysis.
- Simulation studies and real-world applications demonstrate the utility of the approach.
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