An Overdispersion and Inflated Zeros Model for the Spatial Scan Statistic

• Activity Number: 183
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Luiz Duczmal*+ and Max Sousa de Lima and José Cardoso Neto and Leticia Pereira Pinto
• Companies: Universidade Federal de Minas Gerais and Universidade Federal do Amazonas and Universidade Federal do Amazonas and Universidade Federal de Minas Gerais
• Keywords: Spatial scan statistics ; Zero inflation ; Overdispersion ; Double Poisson ; Expectation-Maximization ; Fast Double Bootstrap

Abstract

The Spatial Scan Statistic is the most popular method for the detection and inference of spatial disease clusters. Disease case counts frequently present excess of zeroes and/or overdispersion, resulting in the violation of the commonly used Poisson or binomial models, thus increasing type I error occurrence.

This work describes a modification of the Spatial Scan Statistic with the Zero Inflated Double Poisson (ZIDP) model to reduce type I error, accommodating simultaneously the excess of zeroes and overdispersion. The null and alternative model parameters are estimated by the Expectation-Maximization algorithm and the p-value is obtained through the Fast Double Bootstrap Test.

Numerical simulations where conducted in several scenarios. The ZIDP model reduces substantially the probability of type I error, compared to the Poisson, overdispersed Poisson, and zero inflated Poisson, which have been shown to be inadequate in the presence of excess of zeroes and overdispersion. The proposed algorithm is computationally fast.

A detailed application is presented for Hanseniasis data in the Brazilian Amazon.