Bayesian Analysis of Prevalence of Diabetes Mellitus by Age among Patients of University Health Centre, University of Ibadan

The prevalence of Diabetes Mellitus (DM) in Nigeria continues to rise and remains a major concern for public health. This study investigates the age distribution of patients diagnosed with DM at the University Health Centre, University of Ibadan. Using Bayesian inference, the study compares five candidate distributions—Normal, Log-Normal, Weibull, Gamma, and Log-Logistic—to determine the model that best fits the data. The Akaike Information Criterion (AIC), log-likelihood values, and posterior distribution summaries were used to evaluate model performance. Results indicate that the Log-Normal distribution provides the best fit among the models considered. Posterior diagnostics, including trace plots, autocorrelation plots, and probability density plots, confirm the adequacy of the Bayesian estimation procedure. Findings reveal that patients aged 45–74 years have the highest probability of being diagnosed with DM. The study highlights the usefulness of Bayesian methods for understanding disease prevalence and underscores the importance of targeted public health interventions for at-risk age groups.