Supplement to “ Subnetwork State Functions Define Dysregulated Subnetworks in Cancer ” ∗ Salim

In this supplementary document, we prove two theorems that support the algorithms described in [1] and we present experimental results from systematic study of the performance of Crane when the value of the tuneable parameters are varied. First, in Theorem 1, we provide bound on the score of a state function that can be obtained by extending that state function, in terms of simple statistics of the smaller state function. We use this result to develop efficient search algorithms that grow subnetworks in a bottom-up fashion, effectively pruning the search space using the bound provided by this theorem. Then we provide two lemmas that are used in the proof of this theorem. Subsequently, in Theorem 2, we provide a tight bound on the information that any subnetwork state function can provide on the phenotype (J(fS , C)), for given number of phenotype and control samples. This result is useful for obtaining a uniform criterion to score subnetwork state functions. Specifically, by normalizing J(.) by the bound provided by this theorem, we obtain a scoring criterion that ranges from 0 to 1 regardless of the number of phenotype and control samples in the dataset. Finally, we provide the pseudo-code for the subnetwork search algorithm implemented by Crane. In this document, we use the following conventions for notational convenience: