A mathematical model for determining age-specific diabetes incidence and prevalence using body mass index

Few models have been developed specifically for the epidemiology of diabetes. Diabetes incidence is critical in predicting diabetes prevalence. However, reliable estimates of disease incidence rates are difficult to obtain. The aim of this study was to propose a mathematical framework for predicting diabetes prevalence using incidence rates estimated within the model using body mass index (BMI) data.

A generic mechanistic model was proposed considering birth, death, migration, aging, and diabetes incidence dynamics. Diabetes incidence rates were determined within the model using their relationships with BMI represented by the Hill equation. The Hill equation parameters were estimated by fitting the model to National Health and Nutrition Examination Survey (NHANES) 1999-2010 data and used to predict diabetes prevalence pertaining to each NHANES survey year. The prevalences were also predicted using diabetes incidence rates calculated from the NHANES data themselves. The model was used to estimate death rate parameters and to quantify sensitivities of prevalence to each population dynamic.

The model using incidence rate estimates from the Hill equations successfully predicted diabetes prevalence of younger, middle-aged, and older adults (prediction error, 20.0%, 9.64%, and 7.58% respectively). Diabetes prevalence was positively associated with diabetes incidence in every age group, but the associations among younger adults were stronger. In contrast, diabetes prevalence was more sensitive to death rates in older adults than younger adults. Both diabetes incidence and prevalence were strongly sensitive to BMI at younger ages, but sensitivity gradually declined as age progressed. Younger and middle aged adults diagnosed with diabetes had at least a two-fold greater risk of death than their nondiabetic counterparts. Nondiabetic older adults were found to be under slightly higher death risk (0.079) than those diagnosed with diabetes (0.073).

The proposed model predicts diagnosed diabetes incidence and prevalence reasonably well using the link between BMI and diabetes development risk. Ethnic group and gender-specific model parameter estimates could further improve predictions. Model prediction accuracy and applicability need to be comprehensively evaluated with independent data sets.