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Partially Linear Additive Quantile Regression: Theory and Applications to Breast Cancer Patients' Survival.

Xinyi Zhao1, Maozai Tian1

  • 1Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing, China.

Statistics in Medicine
|February 27, 2026
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Summary

This study introduces a new method for predicting breast cancer patient survival, improving treatment decisions. The novel approach effectively handles censored survival data and identifies key prognostic factors for personalized care.

Keywords:
group SCADpartially linear additive quantile regressionright‐censored datasurvival predictionvariable selection

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Area of Science:

  • Biostatistics
  • Medical Informatics
  • Oncology

Background:

  • Accurate breast cancer patient life expectancy prediction is crucial for effective treatment planning.
  • Existing methods for censored survival data often rely on complex data imputation or weighting techniques.
  • There is a need for robust statistical models that can accurately estimate survival and identify significant predictors in the presence of censoring.

Purpose of the Study:

  • To develop a novel statistical method for estimating survival and selecting variables in partially linear additive quantile regression models with right-censored data.
  • To introduce an adapted loss function to address data censoring, moving beyond traditional synthetic data or weighting approaches.
  • To enhance prediction accuracy through variable selection using a group smoothly clipped absolute deviation (SCAD) penalty.

Main Methods:

  • Utilized a partially linear additive quantile regression framework.
  • Employed B-splines to approximate non-parametric additive components within the model.
  • Implemented an adapted loss function to effectively handle right-censored survival times.
  • Applied a group smoothly clipped absolute deviation (SCAD) penalty for variable selection in non-parametric components.
  • Developed a block-wise majorize-minimize (MM) algorithm for method implementation.
  • Established asymptotic properties for the derived estimators.

Main Results:

  • The proposed method demonstrated superior finite sample performance compared to alternative approaches in numerical simulations.
  • The adapted loss function effectively managed censored survival data.
  • The group SCAD penalty successfully identified significant variables influencing survival.
  • The block-wise MM algorithm provided an effective means for implementing the complex model.
  • Asymptotic properties of the estimators were theoretically established.

Conclusions:

  • The developed method offers a robust and accurate approach for predicting breast cancer patient life expectancy with censored survival data.
  • This novel technique enhances personalized treatment strategies by identifying key prognostic factors.
  • The study provides a valuable tool for oncologists and researchers utilizing SEER data for breast cancer research and patient care.