# A functional-model-adjusted spatial scan statistic

## TL;DR

This paper presents a novel spatial scan statistic that adjusts for longitudinal confounders using functional models, improving cluster detection accuracy in spatial epidemiology.

## Contribution

It introduces a functional-model-adjusted spatial scan statistic based on generalized functional linear models, applicable to various probability models, enhancing covariate adjustment in cluster detection.

## Key findings

- Method is equivalent to conventional spatial scan with covariate adjustment in Poisson models.
- Simulation shows improved accuracy over existing methods.
- Applied to mortality data with unemployment rate as confounder.

## Abstract

This paper introduces a new spatial scan statistic designed to adjust cluster detection for longitudinal confounding factors indexed in space. The functional-model-adjusted statistic was developed using generalized functional linear models in which longitudinal confounding factors were considered to be functional covariates. A general framework was developed for application to various probability models. Application to a Poisson model showed that the new method is equivalent to a conventional spatial scan statistic that adjusts the underlying population for covariates. In a simulation study with univariate and multivariate models, we found that our new method adjusts the cluster detection procedure more accurately than other methods. Use of the new spatial scan statistic was illustrated by analysing data on premature mortality in France over the period from 1998 to 2013, with the quarterly unemployment rate as a longitudinal confounding factor.