Cuzick and Edward's test

  • spatial
  • global
  • point-based
    • Indications/Recommendations for use: When cases are clustered the nearest neighbor to a case will tend to be another case, and the test statistic will be large (more).
    Description: A case-control test for spatial clustering
    Test statistic: Count of the number of cases whose nearest neighbors are cases and not controls.
    Null Hypothesis: Cases and controls are sampled from a common spatial distribution.
    where N is the sample population size and

    where N0 is the number of cases.
    Alternative Hypothesis: The cases are spatially clustered relative to the controls.
    GeoMed Inputs: Spatial locations of cases and controls.
    GeoMed Outputs: Results table, for which the

    • first column is k, the number of nearest neighbors;
    • second column is Tk, the test statistic;
    • third column is E[Tk], the expected value of Tk under H0;
    • forth column is the variance of Tk under the null;
    • fifth column is the z-score;
    • sixth column is the probability under H0, of observing Tk as large or larger than the one given in column 2; and

    the p-values from each row are combined using both the Bonferroni and Simes corrections

    In GeoMed, Monte Carlo randomizations using a kNN-like distance measure can be run, to compare how extreme the observed statistic is against the randomized values.

    In Stat!, Upper and lower bounds on Tk are calculated when distance ties are encountered (Jacquez, 1994).

    Example Analysis Reference: Cuzick, J. and Edwards, R. 1990. Spatial clustering for inhomogeneous populations. Journal of the Royal Statistical Society Series B, 52:73-104.
    Jacquez, G. M. 1994. Cuzick and Edwards' test when exact locations are unknown. American Journal of Epidemiology, 140:58-64.
    Website maintained by Andy Long. Comments appreciated.
    longa@nku.edu