  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.
