A statistical methodology for analyzing co-occurrence data from a large sample

Determining important associations among items in a large database is challenging due to multiple simultaneous hypotheses and the ability to select weak associations that are statistically but not clinically significant. The simple application of the χ² test among all possible pairs of items results in mostly inappropriate associations surpassing the traditional (α = .05, χ² = 3.94) threshold. One can choose a stricter threshold to find stronger associations, but the choice may be arbitrary. We combined the volume test of Diaconis and Efron with a p-value plot to select a more rigorous and less arbitrary threshold. The volume test adjusts the p-value of the χ²-statistic. A plot of adjusted p-values (1-p versus N_p), where N_p is the number of test statistics with a p-value greater than p, should be linear if there are no true associations. The point where the plot deviates from a line can be used as a threshold. We used linear regression to select the threshold in a reproducible fashion. In one experiment, we found that the method selected a threshold similar to that previously obtained by manually reviewing associations.