Modeling In-patients with Chronic Non-Communicable Diseases Using Parametric Shared Frailty Models

Background: Non-communicable diseases, known as chronic diseases, are not contagious in their nature. They progress slowly in affecting the health of a person. They are the leading causes of death in all continents except Africa, but current projections indicated that by 2025 the largest increases in the non-communicable diseases deaths will occur in Africa. In Ethiopian about 34% of patients suffered from chronic non communicable diseases and there is a gap of estimating the time-to-death of these patients to manage the diseases progression in earlier. Thus, this study was aimed in estimating the survival outcome (death times) of the retrospective follow-up studies of registered inpatients for three years in three hospitals of Oromiya National Regional State, Ethiopia. Methods To describe the prediction and diseases progression of non-communicable diseases, different types of parametric frailty models were compared. Hospitals of the patients were considered as the unobserved variable in the models. The Exponential, Weibull and log-logistic as baseline hazard functions and the gamma and inverse Gaussian for the frailty distributions were checked for their performance using both AIC criteria and Likelihood ratio test. Results On average death times of chronic diseases was 12 days with the maximum of 40 days. Of 646 chronic non-communicable hospitalized patients about 41.5% were died. The log-logistic model with inverse Gaussian frailty has the minimum AIC and LRT value among the models compared. The hospital of the patient has a significant effect in modeling time-to-death of chronic diseases datasets. Conclusion The log-logistic with inverse Gaussian frailty model fitted better than other distributions for the chronic diseases data sets. Therefore, considering the hospital as random effects has a significant impact on time-to-death for NCDs patients and therefore, it is recommendable to include frailty to act as covariates for capturing any dependency under clustered time-to-event methods.