Modeling Time to Kidney Failure of the Patients at Adama Hospital Medical College: Application of Copula Model

Abstract

Background: Kidney failure is an irreversible disease in which one or both kidneys are unable to adequately filter waste products from the blood. Bi-variate time to event endpoints may be correlated as they come from the same subject. However, classical survival analysis assumes that survival times of different subjects are independent. Thus, this study aimed to model time to right and left kidney failure of the patient at Adama Hospital Medical College. Methods: The data for this study was the chronic kidney disease patients under follow up at Adama Hospital Medical College fromfrom 1st January 2015 to 30th January 2020 . The copulas are used to join the bi-variate time to event endpoints to the one dimensional marginal distribution functions. The dependence between the time to right and left kidney failure of the patient was quantified using the copula parameter, while the effect of covariates were modeled using the parametric marginal survival model. Akaike information criterion and Bayesian information criterion were used for the models comparison. Results: Of all 431 patients, 170 (39.4%) failed at least one kidney during the follow up period. The Log-logistic marginal distribution with Clayton copula model revealed that sex of patients, hypertension, family history of kidney disease, obesity and age of patients were the most significant factor that associated with time to kidney failure. The dependence parameter was 1.4 (p-value < 0.0001). Conclusions: The Log-logistic marginal distribution with Clayton copula model fit the kidney failure dataset well. Being male, older adult, obese, hypertensive and having family history of kidney disease were the most risk factors that leads to kidney failure. There is the dependence between the time to right and left kidney failure of the patient.