A bivariate power generalized Weibull distribution: A flexible parametric model for survival analysis

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• Flexible parametric survival analysis is crucial for understanding time-to-event data.
• The power generalized Weibull distribution offers adaptability for univariate survival data.
• Bivariate survival data analysis requires models that capture dependencies between event times.

Purpose of the Study:

• To propose a novel bivariate shared frailty model with adapted power generalized Weibull marginal distributions.
• To leverage the frailty relationship within the power generalized Weibull family for bivariate modeling.
• To demonstrate the practical utility of the proposed bivariate model using real-world data.

Main Methods:

• Utilizing an adapted power generalized Weibull distribution for marginal modeling.
• Employing a BB9 (power variance function) copula to link marginal distributions.
• Developing a bivariate shared frailty model incorporating these components.
• Analyzing a retinopathy dataset to illustrate model implementation and interpretability.

Main Results:

• A novel bivariate adapted power generalized Weibull model was developed.
• The model effectively links marginal distributions using a natural copula choice.
• Theoretical properties of the bivariate model were derived.
• The model proved straightforward to implement and yielded informative results for the retinopathy data.

Conclusions:

• The bivariate adapted power generalized Weibull model is a flexible and powerful tool for analyzing bivariate survival data.
• The proposed model offers a novel combination of existing statistical components.
• The model's practical application is demonstrated, highlighting its informativeness and ease of use in biostatistical research.