Comparison of Soft Indicator and Poisson Kriging for the Noise-Filtering and Downscaling of Areal Data: Application to Daily COVID-19 Incidence Rates

This paper addresses two common challenges in analyzing spatial epidemiological data, specifically disease incidence rates recorded over small areas: filtering noise caused by small local population sizes and deriving estimates at different spatial scales. Geostatistical techniques, including Poisson kriging (PK), have been used to address these issues by accounting for spatial correlation patterns and neighboring observations in smoothing and changing spatial support. However, PK has a limitation in that it can generate unrealistic rates that are either negative or greater than 100%. To overcome this limitation, an alternative method that relies on soft indicator kriging (IK) is presented. The performance of this method is compared to PK using daily COVID-19 incidence rates recorded in 2020-2021 for each of the 581 municipalities in Belgium. Both approaches are used to derive noise-filtered incidence rates for four different dates of the pandemic at the municipality level and at the nodes of a 1 km spacing grid covering the country. The IK approach has several attractive features: (1) the lack of negative kriging estimates, (2) the smaller smoothing effect, and (3) the better agreement with observed municipality-level rates after aggregation, in particular when the original rate was zero.