A Semi-stationary Copula Model Approach for Bivariate Survival Data with Interval Sampling

Area of Science:

• Biostatistics
• Epidemiology
• Survival Analysis

Background:

• Disease registries often collect bivariate survival data using interval sampling, where initial events (e.g., HIV infection) occur within a specific timeframe.
• This sampling method can introduce bias, as first failure times are doubly truncated and second failure times may be informatively right censored.

Purpose of the Study:

• To develop and evaluate statistical methods for analyzing bivariate survival data collected under interval sampling, accounting for associated biases.
• To assess the association between disease progression times and to incorporate covariates into survival models.

Main Methods:

• Utilized copula models to estimate the association between bivariate survival times under interval sampling, assuming a semi-stationary condition.
• Developed bias-corrected estimators for marginal survival functions and employed a two-stage procedure to estimate the copula model's association parameter.
• Incorporated covariates using proportional hazards models to allow the association measure to depend on covariates.

Main Results:

• Proposed methods provide bias-corrected estimators for survival functions and association parameters in the presence of interval sampling.
• Demonstrated the ability to incorporate covariates, allowing for a more nuanced understanding of survival time associations.
• The approach was successfully applied to an AIDS registry, investigating the relationship between age at HIV infection and residual lifetime.

Conclusions:

• The developed copula-based methods effectively address biases inherent in interval sampling for bivariate survival data.
• The methodology allows for covariate adjustment, providing more robust inferences on survival time associations.
• The application to an AIDS study highlights the practical utility of these methods in epidemiological research.