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

Timothy M Pollington,Michael J Tildesley,T Déirdre Hollingsworth,Lloyd A.C Chapman

doi:10.1016/j.spasta.2020.100438

Timothy M Pollington, Michael J Tildesley + Show 2 more

Open Access

https://doi.org/10.1016/j.spasta.2020.100438

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Abstract

The tau statisticτ uses geolocation and, usually, symptom onset time to assess global spatiotemporal clustering from epidemiological data. We test different methods that could bias the clustering range estimate based on the statistic or affect its apparent precision, by comparison with a baseline analysis of an open access measles dataset.From re-analysing this data we find evidence against no clustering and no inhibition, p-value∈[0,0⋅022] (global envelope test). We develop a tau-specific modification of the Loh & Stein spatial bootstrap sampling method, which gives bootstrap tau estimates with 24% lower sampling error and a 110% higher estimated clustering endpoint than previously published (61⋅0 m vs. 29 m) and an equivalent increase in the clustering area of elevated disease odds by 342%. These differences could have important consequences for control efforts.Correct practice of graphical hypothesis testing of no clustering and clustering range estimation of the tau statistic are illustrated in the online Graphical abstract. We advocate proper implementation of this useful statistic, ultimately to reduce inaccuracies in control policy decisions made during disease clustering analysis.

Highlights

Assessing if spatiotemporal clustering is present and measuring its magnitude and range is informative for epidemiologists working to control infectious diseases
We develop a tau-specific modification of the Loh & Stein spatial bootstrap sampling method, which gives bootstrap tau estimates with 24% lower sampling error and a 110% higher estimated clustering endpoint than previously published (61·0 m vs. 29 m) and an equivalent increase in the clustering area of elevated disease odds by 342%
The tau statistic is non-unique as it depends on the distance band set chosen (Pollington et al, 2019a), so the potential variation in τ estimates from this choice is of interest; we explore this briefly in a non-systematic way

Summary

Introduction

Assessing if spatiotemporal clustering is present and measuring its magnitude and range is informative for epidemiologists working to control infectious diseases. The tau statistic (Section 2) is more appropriate than most statistics for this task as it measures spatiotemporal rather than just spatial clustering, produces non-parametric estimates (without process assumptions) and, unlike the K function (Gabriel and Diggle, 2009), offers a relative magnitude in the difference of risk, rate or odds of disease versus the background level (Section 2.1) (Lessler et al, 2016; Pollington et al, 2019a). This study is motivated by a review of its use that found that its current implementation inflates type I errors (incorrectly rejecting a true null hypothesis) when testing for no clustering and no inhibition, and may bias estimates of the range of clustering (Pollington et al, 2019a) We investigate these aspects by analysing a well-studied open access measles dataset containing household geolocations and symptom onset times of cases (Section 3.1). It represents a spatially discrete process since infection is only recorded and can only occur at discrete household locations, so the (statistical) support is not spatially continuous (Diggle et al, 2010)

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