title: Testing for clustering at many ranges inflates family-wise error rate (FWE).
abstract: BACKGROUND
  Testing for clustering at multiple ranges within a single dataset is a common practice in spatial epidemiology. It is not documented whether this approach has an impact on the type 1 error rate.
  
  
  METHODS
  We estimated the family-wise error rate (FWE) for the difference in Ripley's K functions test, when testing at an increasing number of ranges at an alpha-level of 0.05. Case and control locations were generated from a Cox process on a square area the size of the continental US (≈3,000,000 mi2). Two thousand Monte Carlo replicates were used to estimate the FWE with 95% confidence intervals when testing for clustering at one range, as well as 10, 50, and 100 equidistant ranges.
  
  
  RESULTS
  The estimated FWE and 95% confidence intervals when testing 10, 50, and 100 ranges were 0.22 (0.20 - 0.24), 0.34 (0.31 - 0.36), and 0.36 (0.34 - 0.38), respectively.
  
  
  CONCLUSIONS
  Testing for clustering at multiple ranges within a single dataset inflated the FWE above the nominal level of 0.05. Investigators should construct simultaneous critical envelopes (available in spatstat package in R), or use a test statistic that integrates the test statistics from each range, as suggested by the creators of the difference in Ripley's K functions test.
authors.affiliation: Department of Biostatistics, University of Alabama at Birmingham, 1665 University Boulevard, RPHB 327, 35294 Birmingham, Alabama, USA. loop2@uab.edu.
authors.forename: Matthew Shane
authors.initials: MS
authors.lastname: Loop
authors.forename: Leslie A
authors.initials: LA
authors.lastname: McClure
mesh_terms: D016022:Case-Control Studies; D016000:Cluster Analysis; D015331:Cohort Studies; D006801:Humans; D015233:Models, Statistical; D012107:Research Design / Q000706:statistics & numerical data