A Comparison of Survival Analysis, Threshold Regression and Linear Mixed Models in a Longitudinal Diabetes Clinic Study (2009 – 2013) at Kalafong Hospital with Nephropathy as Outcome

Abstract

Background: This study compares three methodologies appropriate for the analysis of longitudinal time-to-event data. The Cox model is well researched and frequently used. Threshold regression, however, is relatively new and there are few articles describing its application in biomedical statistics. A linear mixed model provides an alternative interpretation of a continuous outcome rather than time to an event. A longitudinal study of the time to onset of diabetic nephropathy, a common complication of Diabetes Mellitus, is used to compare the three models with respect to their explanatory and predictive abilities and utilitarian value to researchers. Methods: The study entails a secondary data analysis of 1160 retrospective patient records, collected at a diabetic clinic at Kalafong Hospital, Pretoria. Model selection was based on current literature, backward elimination of insignificant variables (p>0.2) and the Akaike and Bayesian Information Criterion. Survival and hazard functions and ratios were determined for the survival data. Risk categories in the Cox model evaluated discrimination, while threshold regression predicted survival probabilities for specific patient profiles. The linear mixed model predicted albumin-creatinine ratio values, a marker for the diagnosis of diabetic nephropathy. Results: The Cox model, stratified by glucose control, gender, hypertension, type of diabetes and smoking status, had an AIC of 81 and was the most parsimonious model. Threshold regression, with an AIC of 1428, indicated duration of diabetes as a significant factor in the process of health deterioration. Individual variation in weight and total cholesterol amongst patients was accounted for by the linear mixed model, with an AIC of 3755. Conclusion: All three regression models provided valuable insight into underlying risk factors of diabetic nephropathy and should form part of a multi-faceted approach to analysing longitudinal survival data.