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, $p\text{-value}\in [0,0\text{⋅}014]$ (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⋅0 m, 95% BCa CI (14⋅9, 46⋅6), vs 30 m) 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.

头统计 $\tau$使用地理位置和通常的症状发作时间从流行病学数据评估总体时空聚类。通过与开放式麻疹数据集的基线分析进行比较，我们测试了可能影响基于统计的聚类或偏差聚类范围估计值的图形假设检验的不同因素。

通过对这些数据的重新分析，我们发现用于构造tau估计的置信区间和置信区间（CI）类型的空间自举采样方法会偏向聚类范围估计。我们建议，对于tau估计值的不对称样本自举分布，偏差校正和加速（BCa）CI是必不可少的。

我们还发现了没有时空聚类的证据， $p\text{-值}\in [0，0\text{⋅}014]$（全局信封测试）。我们开发了Loh＆Stein空间自举采样方法的tau特定修改，该方法提供了更精确的自举tau估计值，并且比以前发表的估计聚类终点高出20％（36⋅0m，95％BCa CI（14⋅9， 46⋅6），而30 m），则疾病几率升高的聚集区域相应增加了44％。在范围估计中出现的较小的径向偏差在面积尺度上增加了一倍以上，与公共卫生资源成正比。这种差异可能会对控制产生重要影响。

图形摘要中说明了无聚类的假设检验的正确做法以及tau统计量的聚类范围估计。我们提倡正确实施此有用的统计数据，以最终减少疾病聚类分析过程中制定的控制策略决策中的不准确性。