  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.
