# Two-Step Estimation Procedure for Parametric Copula-Based Regression Models for Semi-Competing Risks Data

## TL;DR

This paper introduces a new two-step method for analyzing complex data involving non-terminal and terminal events using copula-based regression.

## Contribution

A novel two-step algorithm combined with BOBYQA is proposed for robust estimation in semi-competing risks regression models.

## Key findings

- The proposed method effectively reduces the influence of initial values in complex copula structures.
- Simulation results confirm the method's performance improvements.
- Application to the Amsterdam Cohort Study showed practical improvements.

## Abstract

Non-terminal and terminal events in semi-competing risks data are typically associated and may be influenced by covariates. We employed regression modeling for semi-competing risks data under a copula-based framework to evaluate the effects of covariates on the two events and the association between them. Due to the complexity of the copula structure, we propose a new method that integrates a novel two-step algorithm with the Bound Optimization by Quadratic Approximation (BOBYQA) method. This approach effectively mitigates the influence of initial values and demonstrates greater robustness. The simulations validate the performance of the proposed method. We further applied our proposed method to the Amsterdam Cohort Study (ACS) real data, where some improvements could be found.