Fig 6. Computing a p-value.

We use the multivariate Fisher’s noncentral hypergeometric distribution to obtain probabilities for outcomes and sum to obtain our probability mass function for the event P(K = k). We then sum over K ≥ k to obtain a p-value. fisher_nchgd_pmf is calculated using BiasedUrn [31]. Sorting and compressing the pathway vectors can greatly reduce the size of $S_k^{\prime }$. Across our test datasets, the median reduction of the number of calls per dataset to BiasedUrn by sorting and compressing the pathway vectors is 65 fold (the median of $({\sum }_{pathways}{\sum }_{j=k}^n\left|S_j\right|)/({\sum }_{pathways}{\sum }_{j=k}^n\left|S_j^{\prime }\right|)$).