A theoretical discussion on modeling the number of COVID-19 death cases using penalized spline negative binomial regression approach

Abstract

The Covid-19 pandemic that has occurred since the end of 2019 has changed almost the entire order of the world community, including Indonesia, in terms of health, economic, social and cultural arrangements. Based on the initial study, it is known that the number of Covid-19 deaths in East Java in 2020 has a high variance in each district/city which will cause an over dispersion problem, to overcome this, regression can be used assuming the response variable has a negative binomial distribution. Therefore, in this study we determine theoretically a model estimate of the number of cases of Covid-19 deaths in East Java due to comorbidities using a nonparametric negative binomial regression (NNBR) model approach based on a penalized spline estimator which is applied to generalized additive model (GAM). In this study, we provided steps for a local scoring algorithm to estimate NNBR model based on penalized spline estimator. In the future, the theoretical results of this study can be applied to the real data namely the number of Covid-19 death cases affected by comorbidities such as percentage of diabetes mellitus patients, percentage of hypertension over 15 years old patients, and percentage of tuberculosis patients.