Modeling the Number of Multibacillary Leprosy Using Negative Binomial Regression to Overcome Overdispersion in Poisson Regression

Abstract

Poisson regression is used on discrete data (count) for the formation of the model. There is often a violation in Poisson regression analysis assumptions i.e., overdispersion, which means the average value of the data is smaller than the value of the variance. The number of multibacillary leprosy (MB) in 31 Surabaya districts orderly from 2015 to 2017 has increased as many as 127 cases, 140 cases, and 158 cases. This study aimed to model the number of MB leprosy in Surabaya in 2017 with a Negative Binomial regression in overdispersion. This was quantitative research with a descriptive method that uses secondary data. The data sourced from Surabaya City Health Profile in 2017. The independent variables studied include BCG immunization coverage, the percentage of healthy houses, the percentage of Households with Clean and Healthy Behavior (HCHB), the percentage of the male population, and the population density level. MB leprosy incidence modeling with Poisson regression proved to be overdispersed so that the Negative Binomial regression was used to overcome it. The variable that influenced the MB leprosy incidence with a Negative Binomial regression analysis was the percentage of healthy houses (p = 0.019). MB leprosy occurence will decrease if the percentage of healthy houses increases. The percentage of healthy houses in Surabaya was 86.99%, which increased compared to the previous year with an increase of 1.78%. Public awareness about healthy houses is required to reduce the number of MB leprosy in Surabaya.