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Survival analysis is a statistical method used to analyze time-to-event data, often employed in fields such as medicine, engineering, and social sciences. One of the key challenges in survival analysis is dealing with incomplete data, a phenomenon known as "censoring." Censoring occurs when the event of interest (such as death, relapse, or system failure) has not occurred for some individuals by the end of the study period or is otherwise unobservable, and it might have many different...
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Survival models analyze the time until one or more events occur, such as death in biological organisms or failure in mechanical systems. These models are widely used across fields like medicine, biology, engineering, and public health to study time-to-event phenomena. To ensure accurate results, survival analysis relies on key assumptions and careful study design.
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Establishing a Competing Risk Regression Nomogram Model for Survival Data
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Deep partially linear transformation model for right-censored survival data.

Junkai Yin1, Yue Zhang2, Zhangsheng Yu2

  • 1Department of Statistics, Shanghai Jiao Tong University, Shanghai 200240, PR China.

Biometrics
|October 30, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a deep partially linear transformation model for survival data analysis, offering a flexible alternative when the Cox proportional hazards assumption fails. The method effectively handles high-dimensional data while maintaining covariate interpretability.

Keywords:
deep learningminimax lower boundmonotone splinespartially linear transformation modelssemiparametric efficiency

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Area of Science:

  • Statistics
  • Biostatistics
  • Machine Learning

Background:

  • The Cox proportional hazards (PH) model is a standard for survival data analysis.
  • The PH assumption is not always valid in real-world applications.
  • Semiparametric transformation models offer a broader framework extending the Cox model.

Purpose of the Study:

  • Introduce a deep partially linear transformation model for analyzing right-censored survival data.
  • Provide a flexible regression framework that addresses the curse of dimensionality.
  • Retain interpretability for key covariates.

Main Methods:

  • Developed a deep partially linear transformation model.
  • Derived convergence rates for maximum likelihood estimators.
  • Established minimax lower bounds for nonparametric deep neural network estimators.
  • Proved asymptotic normality and semiparametric efficiency for parametric estimators.

Main Results:

  • The proposed model demonstrates impressive estimation accuracy in simulations.
  • The method shows strong predictive power for survival data.
  • Theoretical analysis provides guarantees on estimator performance.

Conclusions:

  • The deep partially linear transformation model is a powerful and flexible tool for survival data analysis.
  • The approach effectively handles high-dimensional data and maintains interpretability.
  • Simulation studies and real-world data application validate the method's performance.