Fig 4. Power of indirect CTD p-value estimation compared to permutation-based p-value estimation.
For three separate network structures containing 50 nodes at variable levels of connectedness (network 1: 10% connected; network 2: 30% connected; network 3: 60% connected), p-values for node sets of size 5 were estimated by three estimation methods: “ground truth” enumeration, permutation-testing and upper bound estimation by CTD. Ground truth was calculated via brute force enumeration for all node set outcomes of size 5. (A) CTD p-value bounds were more conservative than permutation-based p-value estimates. However, for highly connected node sets which were given more significant p-value bounds by CTD, the difference between CTD’s upper p-value bounds and the ground truth p-value is smaller. (B) Power associated with CTD upper-bounds on p-values was estimated. For all experiments where the brute force p-value was less than or equal to a given significance level (e.g., 0.05), power is calculated based on the percentage of those experiments where the CTD upper bounds p-value estimate was also less than or equal to the given significance threshold (i.e., the true positive rate). Similar to the view of the data in (A), we see that CTD’s p-value bounds show higher power for highly connected node sets compared to sparsely connected node sets.