Detection of spatial clustering with average likelihood ratio test statistics

TL;DR

This paper introduces an average likelihood ratio (ALR) test for detecting spatial clustering, demonstrating its higher power over traditional methods and providing efficient tail probability approximations to avoid intensive simulations.

Contribution

The paper develops an ALR test statistic for spatial clustering detection and derives accurate tail probability approximations, improving power and computational efficiency over existing methods.

Findings

ALR test has greater power than traditional scan statistics.

Derived tail probability approximations enable faster p-value estimation.

ALR performs well even with covariate adjustments.

Abstract

Generalized likelihood ratio (GLR) test statistics are often used in the detection of spatial clustering in case-control and case-population datasets to check for a significantly large proportion of cases within some scanning window. The traditional spatial scan test statistic takes the supremum GLR value over all windows, whereas the average likelihood ratio (ALR) test statistic that we consider here takes an average of the GLR values. Numerical experiments in the literature and in this paper show that the ALR test statistic has more power compared to the spatial scan statistic. We develop in this paper accurate tail probability approximations of the ALR test statistic that allow us to by-pass computer intensive Monte Carlo procedures to estimate $p$-values. In models that adjust for covariates, these Monte Carlo evaluations require an initial fitting of parameters that can result in very biased $p$-value estimates.