| check_data_format | Check the Format of a Data Frame for Multicentre Competing Risks with Frailty |
| compute_M_optimized | Compute the Weight Matrix M (Optimized) |
| create_G_function | Create Step Function for Estimated Survival (G) |
| KaplanMeier_Censoring_vectorized | Kaplan-Meier Estimator for Censoring Distribution (Vectorized) |
| logLikelihood_1 | Log-Likelihood Contribution for Cause 1 |
| logLikelihood_2 | Compute Log-Likelihood Penalty for Random Effects |
| Ml_CompRisk | Maximum Likelihood Estimation for Cause 1 in Competing Risks |
| Ml_Cox | Maximum Likelihood Estimation for the Cox Model (Optimized) |
| Nelson_Censoring_vectorized | Nelson-Aalen Estimator of Censoring Distribution (Vectorized) |
| Parameters_estimation | Unified Interface for Parameter Estimation in (Competing Risks) Frailty Models |
| Reml_CompRisk_frailty | REML Estimation for Cause 1 in a Competing Risks Model with Shared Frailty |
| Reml_Cox_frailty | Cox Model with Random Frailty (REML Estimation) |
| simulate_data | Simulate clustered competing risks data with shared frailty |