Modeling of Tuberculosis Cases in Sumatera Region using Poisson Inverse Gaussian Regression

Abstract

In the Sumatra Region, tuberculosis (TB) is a disease that needs special attention because it tends to increase every year. Based on health theory, there are many factors that cause TB, but it is not easy to determine which factors have a significant effect. Therefore, in this study an analysis was carried out that could model, predict, and determine the factors causing TB disease in the Sumatra Region. The data used is data on TB cases in the Sumatra Region in 2018 taken from the Publication of the Central Statistics Agency. Poisson regression is an analysis that is suitable for modeling count data such as TB disease data. The assumption of Poisson regression is that the mean and variance of the response variables must be equal (equidispersion). However, the TB case data in the Sumatra Region in 2018 has an average value that is smaller than the variance (overdispersion) so it cannot be solved by Poisson regression. To overcome this problem, we need a method that can overcome overdispersion, namely Poisson Inverse Gaussian (PIG) ​​regression. From the results of the analysis using PIG regression, it can be concluded that the factors that have a significant effect on TB cases in the Sumatra Region are the percentage of the male population (X₁), the percentage of the productive age population (X₂), the percentage of households with a floor area of ≤ ​​19m² (X₃), and the percentage of households that have access to proper sanitation (X₄), where the model formed is 

Based on the model, the predicted results of TB cases in the Sumatra Region had an average of 596.04178 where the lowest cases occurred in Pringsewu of 154.8943 and the highest cases occurred in Bukittinggi of 2719.59400.