Developments in statistical inference when assessing spatiotemporal disease clustering with the tau statistic.

The tau statistic $\tau$ uses geolocation and, usually, symptom onset time to assess global spatiotemporal clustering from epidemiological data. We test different factors that could affect graphical hypothesis tests of clustering or bias clustering range estimates based on the statistic, by comparison with a baseline analysis of an open access measles dataset. From re-analysing this data we find that the spatial bootstrap sampling method used to construct the confidence interval for the tau estimate and confidence interval (CI) type can bias clustering range estimates. We suggest that the bias-corrected and accelerated (BCa) CI is essential for asymmetric sample bootstrap distributions of tau estimates. We also find evidence against no spatiotemporal clustering, $p$-value $\in$ [0,0.014] (global envelope test). We develop a tau-specific modification of the Loh & Stein spatial bootstrap sampling method, which gives more precise bootstrapped tau estimates and a 20% higher estimated clustering endpoint than previously published (36.0m; 95% BCa CI (14.9, 46.6), vs 30m) and an equivalent increase in the clustering area of elevated disease odds by 44%. What appears a modest radial bias in the range estimate is more than doubled on the areal scale, which public health resources are proportional to. This difference could have important consequences for control. Correct practice of hypothesis testing of no clustering and clustering range estimation of the tau statistic are illustrated in the Graphical abstract. We advocate proper implementation of this useful statistic, ultimately to reduce inaccuracies in control policy decisions made during disease clustering analysis.