Test statistic 8: Is metabolite m exchanged by cell i and other spatially proximal cells?

Visualizing the individual cell/spot contributions of the results obtained using the metabolite-based approach described in Test statistic 3 is also useful. For this, the equation below can be used for every metabolite (or ligand-receptor pathway), where the scores of the gene pairs (defined in Test statistic 7) that are associated with a given metabolite are summed up:

\[ H_{i}(m) = \sum_{a,b \in m}^{} H_{i} (ab) \]

To test for statistical significance, an empirical test has been implemented. Here, the equation above is computed in every shuffling iteration. This is done separately for genes a and b because, when a and b are different, the cell IDs corresponding to the counts matrices of both gene a and b are shuffled, giving rise to \(H_i(m)(a)\) and \(H_i(m)(b)\). However, if gene \(a=b\), then the same output is considered for both \(H_i(m)(a)\) and \(H_i(m)(b)\). Then, two sets of p-values are obtained through the \(p-value = \frac{x+1}{M+1}\) equation, and eventually, the most conservative p-values are selected. P-values are also adjusted using the Benjamini-Hochberg procedure.

Apart from using the empirical test, selecting the cells or spots based on the relative H scores is also a good option, where threshold values such as 1 standard deviation above the mean are especially recommended.