Table 1 Description of Hypothesis Testing Methods and Significance Cutoffs

Conditional Permutation Test

Select optimal span size for observed data by minimizing AIC statistic across range of spans. Compare difference in deviance statistic to conditional permutation distribution obtained by holding span size constant.

Fixed Span Permutation Test

Select span size a priori. Compare difference in deviance statistic to conditional permutation distribution obtained by holding span size constant.

Fixed Multiple Span Permutation Test

Select 3-5 span sizes a priori. For each span size, compare the difference in deviance statistic to corresponding conditional permutation distribution obtained by holding the span size constant. Reject the null hypothesis if at least one p-value falls below the significance cutoff.

Unconditional Permutation Test

Select optimal span size for observed data as in CPT. Compare difference in deviance statistic to unconditional permutation distribution obtained by selecting optimal span size for each permuted dataset.

Spatial Scan Statistic

Detects the most likely cluster through a likelihood ratio test comparing the likelihood of cases within to outside a circular zone of interest. P-values are obtained through Monte Carlo methods