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Estimation and variable selection for semiparametric transformation models with length-biased survival data.

Jih-Chang Yu1, Yu-Jen Cheng2

  • 1Department of Statistics, National Taipei University, New Taipei, Taiwan. jcyu@gm.ntpu.edu.tw.

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Summary

This study introduces a more efficient method for analyzing length-biased survival data using semiparametric transformation models. The approach improves variable selection and estimation by utilizing the full likelihood, offering better performance than existing techniques.

Keywords:
Model selectionOne step estimatorSurvivalTransformation model

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Area of Science:

  • Statistics
  • Biostatistics
  • Survival Analysis

Background:

  • Length-biased survival data presents unique challenges due to sampling bias.
  • Existing methods like conditional likelihood and martingale estimating equations may lack efficiency.
  • These methods often rely on partial information, limiting their effectiveness.

Purpose of the Study:

  • To develop a more efficient estimation and variable selection method for semiparametric transformation models with length-biased survival data.
  • To address the limitations of conventional methods by utilizing the full likelihood.
  • To introduce a unified approach for improved statistical analysis in relevant fields.

Main Methods:

  • A full-likelihood approach under the semiparametric transformation model framework.
  • Development of a nonparametric maximum likelihood estimator (NPMLE).
  • Incorporation of an adaptive least absolute shrinkage and selection operator (ALASSO) penalty for variable selection.

Main Results:

  • The proposed NPMLE offers a unified and more efficient estimator.
  • The one-step ALASSO estimator, initialized with NPMLE, achieves oracle properties.
  • Theoretical properties are rigorously established using empirical process techniques.

Conclusions:

  • The proposed full-likelihood approach and ALASSO penalty provide an efficient method for semiparametric transformation models with length-biased data.
  • The methods demonstrate strong performance in simulations and a real-world data application.
  • This work offers advancements for statistical modeling in social sciences and clinical trials.