Regression analysis of discrete time survival data under heterogeneity

Area of Science:

• Biostatistics
• Epidemiology
• Survival Analysis

Background:

• Discrete time survival data presents challenges in heterogeneous populations.
• Frailty models are used to account for unobserved heterogeneity.
• Existing methods may not fully capture population-averaged effects.

Purpose of the Study:

• To develop a regression framework for discrete time survival data in heterogeneous populations.
• To integrate frailty models for population-averaged analysis.
• To provide a method for analyzing cardiovascular disease risk factors.

Main Methods:

• Survival time is modeled as a sequence of binary indicators.
• Likelihood is factored into conditional survival probabilities integrated over frailty distribution.
• Population-averaged conditional probabilities are modeled using covariates.
• Binary regression models are fitted for conditional failure probabilities.

Main Results:

• The likelihood factorization justifies treating failure indicators as independent Bernoulli trials.
• Regression coefficients represent population-averaged, not subject-specific, parameters.
• The method is applicable to real-world epidemiological studies.

Conclusions:

• The proposed method simplifies the analysis of discrete survival data with heterogeneity.
• It enables robust modeling of population-averaged risks.
• The approach is validated using cardiovascular disease data from the Framingham Heart Study.