A COPULA-BASED SEMIPARAMETRIC BIVARIATE SURVIVAL MODEL WITH YANG–PRENTICE MARGINALS: ESTIMATION AND SIMULATION STUDY

Abstract

This study proposed a semiparametric bivariate survival model that combines Yang–Prentice marginals with Archimedean copulas (Clayton, Frank, and Gumbel) to jointly address non-proportional hazards and dependence between paired survival times. Parameters were estimated via a two-stage inference-functions-for-margins approach with BFGS optimization, with performance evaluated through a Monte Carlo simulation study (R = 500 replications) across sample sizes of n = 300 and 500 and censoring rates of 10% and 40%. Results showed that baseline hazard parameters were estimated with near-zero bias across all scenarios, while regression coefficients exhibited increased variability under higher censoring rates. The Gumbel copula yielded the most stable dependence parameter estimates, the Frank copula produced the smallest bias, and the Clayton copula delivered balanced and consistent performance with well calibrated coverage probabilities. Overall, the proposed framework offers a numerically reliable basis for analyzing correlated, censored survival outcomes. The results imply that practitioners should choose the copula family according to whether lower-tail, symmetric, or upper-tail dependence best matches their data, since this choice directly affects the precision of the estimated dependence structure.