Flexible two-piece distributions for right censored survival data

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• Censored data presents challenges due to incomplete observations.
• Asymmetric distributions and maximum likelihood estimation are established for complete data.
• Flexible modeling of survival data with censoring is crucial.

Purpose of the Study:

• To develop flexible quantile-based asymmetric distributions for right censored survival data.
• To enable characterization of various hazard function shapes (constant, increasing, decreasing, bathtub, unimodal).
• To establish statistical inference methods for these distributions.

Main Methods:

• Utilizing quantile-based asymmetric distributions with symmetric distributions and monotonic link functions.
• Employing maximum likelihood estimation by optimizing a non-differentiable likelihood function.
• Establishing asymptotic properties of the parameter estimators.

Main Results:

• Demonstrated the flexibility of the proposed distributions for modeling censored survival data.
• Showcased the location parameter's role as an index-parameter quantile.
• Confirmed the suitability for modeling diverse hazard function shapes.
• Established asymptotic properties of the estimators and investigated finite-sample performance via simulations.

Conclusions:

• The proposed quantile-based asymmetric distributions provide a flexible framework for survival data analysis with right censoring.
• The method allows for accurate parameter estimation and characterization of complex hazard functions.
• The methodology is validated through simulations and real-world data applications.