Global Conference on Mathematics and Applications (GCMA)

Accurately estimating the dependence structure between paired survival times subject to right-censoring is a fundamental problem in biomedical research, reliability engineering, and actuarial modeling. Classical inference methods such as Pseudo-Maximum Likelihood (PML) rely on copula densities, which frequently suffer from numerical non-convergence and computational instability under heavy bivariate right-censoring. In this paper, we present a complete empirical application of the recently formulated Conditional Copula L-Moments (CCLM) methodology to the benchmark Diabetic Retinopathy Study (DRS) dataset (n = 197 patients). In this study, the time to severe visual loss in laser-treated and untreated control eyes is subject to substantial right-censoring (72.6% and 48.7%, respectively). We investigate the inter-eye survival association using Archimedean copula families (Gumbel, Clayton, and the two-parameter transformed Gumbel BB1 copula) via the empirical survival copula and the conditional Kendall distribution. While CCLM and conventional Conditional Copula Moments (CCM) naturally coincide for single-parameter models matching the first moment (tau = 0.595 with 95% bootstrap CI of [0.273, 0.705] for Gumbel, and 0.491 for Clayton), the decisive advantage of CCLM emerges in multi-parameter modeling (BB1). There, CCM's raw quadratic moment induces variance inflation (SE = 0.612), whereas CCLM's orthogonal Legendre weighting ensures stable, bounded estimation with reduced standard error (SE = 0.541) and superior goodness-of-fit (Sn = 0.2359 vs. 0.2371). Goodness-of-fit assessment confirms the fidelity and stability of CCLM as a dependable, density-free tool for practical survival analysis.