Long-term Dagum-power variance function frailty regression model: Application in health studies

Area of Science:

• Epidemiology
• Biostatistics
• Survival Analysis

Background:

• Long-term survival models are crucial in epidemiology for analyzing data with immune and susceptible patient groups.
• Estimating unobservable heterogeneity due to unmeasured factors is essential.
• Hazard functions can exhibit non-monotonic shapes, such as unimodal patterns.

Purpose of the Study:

• To propose a novel long-term survival model.
• To incorporate a defective Dagum distribution with a power variance function frailty term.
• To address unobservable heterogeneity and non-monotonic hazard functions in survival data.

Main Methods:

• Utilized a defective Dagum distribution.
• Incorporated a power variance function frailty term for heterogeneity.
• Reparameterized the distribution for cure fraction and used a logit link for covariates.

Main Results:

• The proposed model accommodates survival data with cure fractions and non-monotonic hazards.
• Covariate effects on the cure fraction are directly interpretable.
• Maximum likelihood estimation was employed and validated via Monte Carlo simulations.

Conclusions:

• The developed model provides a flexible framework for analyzing complex survival data in epidemiology.
• It effectively handles unobservable heterogeneity and non-monotonic hazard functions.
• Demonstrated applicability in analyzing severe COVID-19 and malignant skin neoplasm data.