A simulation study to explore the dangers of ignoring competing

Abstract

Abstract This study investigates the consequences of incorrectly handling competing risks in survival analysis, particularly applied to simulated customer churn and multimorbidity data. Traditional survival analysis methods often neglect competing risks, potentially leading to biased estimations and inaccurate conclusions. This research aims to evalu- ate the impact of neglecting competing risks using comprehensive simulation studies, addressing a significant gap in practical methodological validation. To achieve this, synthetic datasets representing customer churn scenarios and multi- morbidity contexts were generated, encompassing varying sample sizes of 1,000, 2,000, and 3,000.The Churn data was simulated to be linear and the multimorbidity data was simulated to be non-linear. Four competing risks survival models Cause Specific Cox, Random Survival Forest (RSF), DeepHit, and the Fine-Gray model were employed and rigorously compared. Each model was implemented to evaluate discriminative per- formance, calibration accuracy, and predictive consistency using key metrics: C-index, Brier score, and ROC AUC, with five-fold cross-validation applied to ensure robustness. The results indicated significant variations in model performance and clearly demon- strated the implications of ignoring competing risks. In the customer churn scenar- ios, the Cox proportional hazards model consistently exhibited superior discriminative performance (C-index and ROC AUC values generally above 0.8) and superior calibra- tion (Brier scores around 0.1) across all dataset sizes (N = 1000, 2000, 3000). This can be attributed to the churn data being simulated to be linear and the presence of competing risk being negligible. Random Survival Forest (RSF) and DeepHit models performed comparably well, though without substantial gains from increased sample sizes, whereas the Fine-Gray model consistently showed the weakest performance, with lower discriminative abilities (C-index and ROC AUC around 0.6) and poorer calibra- tion (Brier scores around 0.2). In multimorbidity scenarios, RSF and DeepHit emerged as the best performing models, achieving high discrimination (C-index and ROC AUC around or exceeding 0.8) and excellent calibration (Brier scores close to 0.1), particularly with larger dataset sizes. Traditional methods (Cox and Fine-Gray) displayed moderate to low performance, par- ticularly for Disease B (C-index around 0.4-0.6 and higher Brier scores around 0.2-0.3), indicating limited effectiveness in complex health scenarios when compared to machine learning methods. The study underscores the substantial risks of neglecting competing events in survival analysis, clearly showing that failure to properly account for competing risks can inflate event probabilities and distort predictive accuracy. This research reaffirms the need to carefully select analytical approaches aligned with the specific aims and available data in real-world applications. In conclusion, accurately modeling competing risks is crucial across domains such as business analytics and clinical research. This work provides empirical evidence to guide researchers and practitioners in adopting appro- priate competing-risk methodologies, ultimately promoting more precise, reliable, and domain-specific survival analyses.