A scan statistic for continuous data based on the normal probability model

TLDR

Scan statistics are widely used to detect disease clusters without prior assumptions, typically applied to count data but also relevant for continuous variables such as lead levels or low birth weight. The study proposes a scan statistic for continuous data that computes likelihoods via the normal probability model. The method extends to other distributions while preserving type‑I error, and is applied to identify low birth‑weight clusters in New York City.

Abstract

Temporal, spatial and space-time scan statistics are commonly used to detect and evaluate the statistical significance of temporal and/or geographical disease clusters, without any prior assumptions on the location, time period or size of those clusters. Scan statistics are mostly used for count data, such as disease incidence or mortality. Sometimes there is an interest in looking for clusters with respect to a continuous variable, such as lead levels in children or low birth weight. For such continuous data, we present a scan statistic where the likelihood is calculated using the the normal probability model. It may also be used for other distributions, while still maintaining the correct alpha level. In an application of the new method, we look for geographical clusters of low birth weight in New York City.