Diabetes mellitus is a global chronic health problem affecting over 400 million people. The study focused on the commonest type of Diabetes-Type II diabetes. The disease is associated with morbidity and mortality. Bayesian survival model may be utilized to assess the risk factors associated with Diabetes. The study utilized secondary data from 532 diabetic patients from two General Hospital facilities in Nasarawa State, Nigeria. The aim of the paper was to apply a Bayesian survival model on diabetic dataset to assess some risk factors pertaining to the disease. This Bayesian model was modified to Diabetic Additive Models (DAMS) and further extended to the Diabetic Additive Constant Hazard Model (DACHM), the coded version C. DACHM (when all metrical covariates were coded) and Diabetic Additive Accelerated Failure Time Model (DAAFTM). The results show that C.DACHM outperforms the other model with least values of Watanabe Akaike Information Criterion (WAIC), Deviance Information Criterion (DIC), and a large predictive power measured by the Log Pseudo Maximum Likelihood (LPML). The C.DACH model suggests that; good management of type II diabetes patients aged 40 years and above in both hospitals reduced the risk of death. Considerably, low Body Mass Index (BMI) increased the risk of death of patients with the disease. Body Mass Index, BMI greater than 24.9 (overweight) are 5.41E-17 times at risk of death from diabetes than those of normal weight. High Systolic Blood Pressure, SBP, greater than 140 (high) increases the risk of dying from the diseases by 1.51 times than those of normal SBP. High Diastolic Blood Pressure, DBP, greater than or equal to 90 (high) increases the risk of dying from the diseases by 7.81 times than those of normal DBP. Male patients were 1.28 times at risk of death from diabetes than their female patients. Patients of General Hospital Keffi experience are 1.02 times at risk of death than those of the General Hospital Nasarawa. The research recommends patients’ drug compliance especially for patients above 40 years, maintenance of a healthy body mass index and maintenance of a healthy blood pressure.

Survival analysis involve the set of statistical techniques or procedures used to study time until an event occurs, these techniques are not without some conditions. One of the basic assumptions is that, to enable a straight forward interpretation of hazard rates of subject’s covariate(s) on some reference categories or in situations where variables are continuous in nature, the hazard rates must be constant through time “also known as the proportional hazard assumption” for cox regression. This assumption is often violated in medical practice where subject’s vital statistics or measures are often time varying, as their medical situations changes with time. This paper under study a modification of Piece wise survival model, where three levels of Weibull distribution were assumed for baseline hazards, the sensitivity of the baselines were assessed under four (4) censoring percentages (0%, 25%, 50%, & 75%) and sample sizes (n=100, n=500 & n=1000), for when models were Single parametric (SPM) and when partitioned – Piece wise Parametric Model (PPM). A Piece-wise Bayesian hazard model with structured additive predictors in which the functional form of time varying covariate was incorporated in a non-proportional hazards framework was developed, capable of incorporating complex situations in a more flexible framework. Analysis was done utilizing MCMC simulation technique. Results revealed on comparison that the PPM outperformed the SPM with smaller DIC values and larger predictive powers with the LPML criterion and consistently so throughout all simulations.

Spatial effects are often simultaneously investigated with non-linear effects of continuous covariates and the usual linear effect. In this work the performance of models with and without spatial dependence in partitioned (PM) and non-partitioned models (NPM) for four (4) censoring percentages, three(3) levels of Weibull baseline variances (WBV), and sample sizes 100, 500 & 1000 were investigated. Hazard models were adapted to the generalized additive predictors and analyses were carried out via MCMC simulation technique. The performances of the models were again assessed when fitted to the diabetic data set. Results suggest that; partition models outperformed the non-partition ones. Models with spatial dependence perform better than models without spatial dependence in denser event times and when WBVs are low. The partition models perform better with spatial dependence than the Non-partitioned models. For the diabetic data set, it is seen that covariates Age and Blood Sugar level (BSL) violates the proportionality assumptions upon test. Further assessment from the graph of coefficient against time; suggest that Age be put to cut-points while BSL was estimated for models with and without Penalized splines for the sake of comparison, since the graph shows just a slight deviation from proportionality. Hazard rates for the time varying Age; indicate that as the time of study rolls by, the hazard of experiencing the event death from the disease increases steadily between intervals but constant within each time interval. A unit change in hazard rate for BSL indicates a decrease for PM implemented for with and without penalized splines. The model without penalized splines was however, seen to be better with smaller DIC (Deviance Information Criteria) value. Marriage is seen to be significant in the management of the disease in comparison to single patients. In addition patients are advised to visit their physicians on a regular basis to run a routine check to keep their BSL in good range. The study provides a means of moving out of non-linear ruts in survival data analysis. Intervals increase sample sizes (pseudoobservations), which in turn improves the modified Partitioned model when they are with or without spatial dependence.