Joint frailty models for over time modeling recurrent events and a final event using penalized likelihood estimation method and its application in medical data

Repeated events in cohort studies can be terminated by loss to follow-up, end-of-study, or a major failure event such as death or stable disease. In this regard, the major failure event can be correlated with recurrent events, thus the usual assumption (no-informative censoring of the recurrent event process by death) required by most statistical analyses, can be violated. Joint modeling as an appropriate way of analysis for this kind of data, can investigating two processes, simultaneously and leads to unbiased and efficient parameter estimations. In the present study, joint frailty model with maximum penalized likelihood method is introduced and used for analyzing real clinical data of cohort study was included first-degree relatives (FDR) of type 2 diabetes patients who attending to Isfahan endocrine and metabolism research center. The R-software (version 2.15.2) was used to fit the models. The hazard ratios adjusted by energy intake showed that pre-diabetes recurrent rate is 3.48 times higher in Individual with carbohydrate greater than 65 percent energy intake, than Individual with lower than 40 percent energy intake. The hazards for terminal events as diabetes adjusted by energy intake indicated that the rate of diabetes 0.19 times higher in individual with protein 12-15 percent energy intake than individuals with protein lower than 12 percent energy intake and 0.19 times higher in individuals with protein greater than 15 percent energy intake than individual with protein lower than 12 percent energy intake. Adjusting life style through the nutritional status and anthropometric measure adjustments can effect on the prevalence of diabetes between FDRs who have genetics risk factors.