A four-parameter negative binomial-Lindley regression model to analyze factors influencing the number of cancer deaths using Bayesian inference

Abstract

In this paper, factors influencing the number of cancer deaths in Thailand that is a heavy-tailed data with overdispersion, were analyzed. A new mixed negative binomial (NB) regression model derived from a four-parameter negative binomial-Lindley (NBL) distribution called a four-parameter NBL regression model was developed, with number of cancer deaths analyzed using different factors. Factor importance affecting the number of cancer deaths was also considered to construct an optimal model describing the number of cancer deaths in Thailand. The four-parameter NBL, NB and Poisson regression models were used to describe the data, with parameters in each model estimated using the Bayesian approach. Results showed that the four-parameter NBL model had the highest efficiency compared to the NB and Poisson models. The number of cancer deaths in Thailand was influenced by population size in each province at midyear 2021, province population per doctor, percentage of poor people in each province, number of deaths from cancer caused by smoking behavior from age 15 years and over and number of deaths from cancer as a result of drinking behavior from age 15 years and over.