Kaplan-Meier Bivariate Survival and Cox Copula Regression: A Case Study on Cataract Patients at Undaan Hospital

This study investigates the dependence between the timing of cataract surgeries in both eyes using a copula-based bivariate Cox regression model. A total of 520 patients with bilateral cataracts were analyzed, with survival times defined as the duration from diagnosis to surgery for each eye. The Gumbel copula model was identified as the best fit, with the highest Kendall's tau (0.929) and the lowest AIC value among the copula models evaluated. This strong positive dependence suggests that the timing of surgery in one eye is closely related to the timing in the other, reflecting clinical practices in bilateral cataract management. The analysis also explored the influence of clinical factors such as hypertension, diabetes, and gender. Although these covariates did not show statistically significant effects in the marginal models, clinical literature indicates that comorbidities often lead to delayed surgeries due to preoperative requirements. These include the need for blood pressure stabilization, glucose level monitoring, and systemic evaluations to ensure patient readiness. As such, prolonged waiting times are more reflective of precautionary medical decision-making rather than disease progression. The findings emphasize the importance of accounting for dependence in bilateral event data and highlight the clinical implications of comorbid conditions in surgical timing.