About statistical methods

The methods in ClusterSeer evaluate spatial, temporal, and spatio-temporal disease clusters. The fundamental question behind all these methods is whether clustering exists in the data. All the methods evaluate hypotheses; though these hypotheses are better considered exploratory, see Limits of cluster detection. The hypotheses differ between methods, but all the methods can be characterized using the following structure (from Waller and Jacquez 1995):

• The null spatial modeldefines the distribution of cases of the disease expected without clustering. This distribution may be spatial, temporal, or spatio-temporal depending on the data, question, and method.

• The null hypothesis is a prediction about spatial pattern based on the null spatial model.

• The test statisticsummarizes an aspect of the data of biological or epidemiological interest.

• The null distributionof the test statistic can be derived theoretically or empirically through Monte Carlo randomization.   Example theoretical null distributions include the Poisson null distribution. Either way, the null distribution reflects the null spatial model.

• The alternative hypothesisis a counter to the null hypothesis, a different prediction defined either in the terms of the null spatial model or in terms of additional parameters to define "clustering."

• The alternative spatial modelcan be very basic and all-inclusive "not the null spatial model," or it can be a more specific model defining a particular model of disease distribution.

Probability values (P-values) for the observed test statistics can be obtained by comparing them to the null distribution. This comparison gives a quantitative estimate of the probability of the observed value under the null hypothesis.