Efficient Estimation Methods for the QR Distribution with Type-II Censored Data: An Empirical Validation on Lung...

Area of Science:

• Statistics
• Survival Analysis
• Reliability Engineering

Background:

• The QR distribution is a recent advancement for modeling lifetime data, particularly under Type-II censoring.
• Effective estimation techniques are crucial for its application in survival and reliability analysis.
• Existing methods require comprehensive evaluation for complex censored data.

Purpose of the Study:

• To conduct the first comprehensive evaluation of modern estimation techniques for the QR distribution under Type-II censoring.
• To compare the performance of classical, Bayesian, and machine learning-based methods.
• To assess parameter estimation accuracy, computational efficiency, and convergence behavior.

Main Methods:

• Maximum Likelihood Estimation (MLE)
• Stochastic Gradient Descent (SGD) variants (Momentum, Adam)
• Bayesian methods (MAP, MCMC, Variational Inference)
• Machine learning-integrated methods (amortized neural network inference)
• Evaluation using synthetic data and the Veterans' Administration Lung Cancer dataset.

Main Results:

• Optimization-based, Bayesian, and neural network approaches demonstrate significant strengths.
• These modern methods exhibit practical utility in handling complex censored survival data.
• The QR distribution is validated for its effectiveness in capturing survival dynamics.

Conclusions:

• Modern estimation techniques, particularly Bayesian and neural approaches, are highly effective for the QR distribution under Type-II censoring.
• These methods offer valuable insights for clinical applications in survival analysis.
• Further methodological improvements for censored data modeling are identified.