Comparison of ordinary logistic regression and robust logistic regression models in modeling of pre-diabetes risk factors

Regarding the increased risk of developing type 2 diabetes in pre-diabetic people, identifying pre-diabetes and determining of its risk factors seems so necessary. In this study, it is aimed to compare ordinary logistic regression and robust logistic regression models in modeling pre-diabetes risk factors. This is a cross-sectional study and conducted on 6460 people, over 30 years old, who have participated in the screening of diabetes plan in Mashhad city that it was done by Mashhad University of Medical Sciences from October to December 2010. According to the fasting blood sugar criteria, 5414 individuals were identified as healthy and 1046 individuals were identified as pre-diabetic. Age, gender, body mass index, systolic blood pressure, diastolic blood pressure and waist-to-hip ratio were measured for every participant. The data was entered into the Microsoft Excel 2013 (Microsoft Corp., Redmond, WA, USA) and then analysis of the data was done in R Project for Statistical Computing, Version R 3.1.2 (www.r-project.org). Ordinary logistic regression model was fitted on the data. The outliers were identified. Then Mallow, WBY and BY robust logistic regression models were fitted on the data. And then, the robust models were compared with each other and with ordinary logistic regression model according to goodness of fit and prediction ability using Pearson's chi-square and area under the receiver operating characteristic (ROC) curve respectively. Among the variables that were included in the ordinary logistic regression model and three robust logistic models, age, body mass index and systolic blood pressure were statistically significant (P< 0.01) but waist-to-hip ratio was not statistically significant (P> 0.1). There were 552 outliers with misclassification error in the ordinary logistic regression model. Pearson's chi-square value and area under the ROC curve value in the Mallow model were almost the same as for ordinary logistic regression model. But it was relatively higher in BY and WBY models. Based on results of this study age, overweight and hypertension are risk factors of prediabetes. Also, WBY and BY models were better than ordinary logistic regression model, according to goodness of fit criteria and prediction ability