Toward Establishing Internal Validity for Correlated Gene Expression Measures in Imaging Genomics of Functional Networks: Why Distance Corrections and External Face Validity Alone Fall Short. Reply to "Distance Is Not Everything in Imaging Genomics of Functional Networks: Reply to a Commentary on Correlated Gene Expression Supports Synchronous Activity in Brain Networks".

The primary claim of the Richiardi et al. (2015) Science article is that a measure of correlated gene expression, significant strength fraction (SSF), is related to resting state fMRI (rsfMRI) networks. However, there is still debate about this claim and whether spatial proximity, in the form of contiguous clusters, accounts entirely, or only partially, for SSF (Pantazatos and Li, 2017; Richiardi et al., 2017). Here, 13 distributed networks were simulated by combining 34 contiguous clusters randomly placed throughout cortex, with resulting edge distance distributions similar to rsfMRI networks. Cluster size was modulated (6-15 mm radius) to test its influence on SSF false positive rate (SSF-FPR) among the simulated "noise" networks. The contribution of rsfMRI networks on SSF-FPR was examined by comparing simulated networks whose clusters were sampled from: (1) all 1,777 cortical tissue samples, (2) all samples, but with non-rsfMRI cluster centers, and (3) only 1,276 non-rsfMRI samples. Results show that SSF-FPR is influenced only by cluster size ( > 0.9, < 0.001), not by rsfMRI samples. Simulations using 14 mm radius clusters most resembled rsfMRI networks. When thresholding at < 10, the SSF-FPR was 0.47. Genes that maximize SF have high spatial autocorrelation. In conclusion, SSF is unrelated to rsfMRI networks. The main conclusion of Richiardi et al. (2015) is based on a finding that is ∼50% likely to be a false positive, not <0.01% as originally reported in the article (Richiardi et al., 2015). We discuss why distance corrections alone and external face validity are insufficient to establish a trustworthy relationship between correlated gene expression measures and rsfMRI networks, and propose more rigorous approaches to preclude common pitfalls in related studies.