Survival Analysis of Recurrent Events: an Application to Diabetes Mellitus Patients in The Case of Menellik li Referral Hospital

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Addis Abeba university


Diabetes mellitus is a group of metabolic diseases characterized by elevated blood glucose levels (hyperglycemia) resulting from defects in insulin discharge, insulin action or both. Recovery to normal blood sugar level in DM patients often is recurrent and correlation between events needs to be taken into account during analysis of such data. The main objectives of this research were to analysis time to recovery of DM patients and make a comparison between standard Cox-proportional Hazard (PH) and Frailty models. To achieve the objectives of the study, a retrospective data were obtained from Menellik II Referral Hospital chronic patient’s clinic. All diabetes patients of over 15 years of age and who were under treatment between 2009 and 2015 were included in the study. Unmeasured shared similarities due to the impact of multiple events were modeled using a random effect (Frailty) term. The Likelihood Cross Validation (LCV) criteria were used for comparison between the Standard Cox PH and Frailty model. Shared Log- Normal Frailty model had a minimum value of LCV than the Cox PH and shared Gamma Frailty models. Hence, the shared log-normal Frailty model was chosen for analysis of the recurrent event of time to recovery of DM patients in Menellik II Referral Hospital. The median recovery time of DM patients was 32 weeks. The patient’s sex and Regimen groups at baseline were significantly associated with recurrent event of time to recovery of DM patients. Key Words: Recurrent events, Frailty, Gamma, Log-normal, LCV, Penalized Marginal Likelihood



Recurrent Events, Frailty, Gamma, Log-Normal, LCV, Penalized Marginal Likelihood