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. 2016 Dec 16;17(1):261.
doi: 10.1186/s13059-016-1114-x.

A Novel Independence Test for Somatic Alterations in Cancer Shows That Biology Drives Mutual Exclusivity but Chance Explains Most Co-Occurrence

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Free PMC article

A Novel Independence Test for Somatic Alterations in Cancer Shows That Biology Drives Mutual Exclusivity but Chance Explains Most Co-Occurrence

Sander Canisius et al. Genome Biol. .
Free PMC article

Abstract

In cancer, mutually exclusive or co-occurring somatic alterations across genes can suggest functional interactions. Existing tests for such patterns make the unrealistic assumption of identical gene alteration probabilities across tumors. We present Discrete Independence Statistic Controlling for Observations with Varying Event Rates (DISCOVER), a novel test that is more sensitive than other methods and controls its false positive rate. A pan-cancer analysis using DISCOVER finds no evidence for widespread co-occurrence, and most co-occurrences previously detected do not exceed expectation by chance. Many mutual exclusivities are identified involving well-known genes related to cell cycle and growth factor signaling, as well as lesser known regulators of Hedgehog signaling.

Keywords: Co-occurrence; Computational biology; Mutual exclusivity.

Figures

Fig. 1
Fig. 1
Overview of the DISCOVER method. a The input to the method is a binary alteration matrix with genes in the rows and tumors in the columns. The following panels illustrate how the two genes highlighted in red and green are tested for co-occurrence. b To identify co-occurrences or mutual exclusivities, a null distribution is estimated that describes the overlap in alterations of two genes expected by chance. Co-occurrence and mutual exclusivity correspond to the tails of this distribution. c In the binomial model, a single alteration probability is estimated per gene that applies to all tumors. The expected number of alterations per gene matches the observed number. The expected number of alterations per tumor does not match the observed number. The product of two genes’ alteration probabilities gives the probability of overlap by chance, which multiplied by the number of tumors gives the expected number of tumors with alterations in both genes, in this case 0.8. d In the Poisson-binomial model, gene alteration probabilities are estimated for each tumor individually. The expected number of alterations both per gene and per tumor match the observed numbers. The product of two gene alteration probabilities is also computed per tumor. The expected number of tumors with alterations in both genes according to this model is 1.5
Fig. 2
Fig. 2
Histograms of P values obtained on simulated data using either the binomial test (ad) or the DISCOVER test (eh). The P values apply to gene pairs with three different types of relation: gene pairs with independent alterations (a, c, e, g), gene pairs with co-occurring alterations (b, f), and gene pairs with mutually exclusive alterations (d, h)
Fig. 3
Fig. 3
Extension of the DISCOVER test for mutual exclusivity within groups of genes. a Three alternative statistics for measuring the degree of mutual exclusivity within a group of genes. Coverage refers to the number of tumors that have an alteration in at least one of the genes. Exclusivity refers to the number of tumors that have an alteration in exactly one gene. Impurity refers to the number of tumors that have an alteration in more than one gene. b P-value reliability curves comparing DISCOVER with other mutual exclusivity tests. The false positive rate should not exceed the significance level α. In such a case, the calibration curve will be below the diagonal. For all tests but muex, this is the case. The curves for CoMEt, MEGSA, mutex, and TiMEx are mostly overlapping; their false positive rate stays at 0 until the significance level is almost 1. c Sensitivity curves comparing DISCOVER with other mutual exclusivity tests. More sensitive tests will attain higher true positive rates at lower significance levels. Two discontinuities that occur at a significance level of approximately 1×10−16 are marked with dotted lines. First, muex compresses all lower P values to 0; hence, all lower significance levels have the same true positive rate. Second, this significance level coincides with the change from the slower CoMEt exact test to the binomial approximation (see Methods); the two tests seem to behave quite differently
Fig. 4
Fig. 4
Overview of detected pairwise mutual exclusivities. a Comparison of the number of significant mutual exclusivities found for a gene and the number of tumors in which it has been altered. b Mutual exclusivities that overlap with high-confidence interactions in the STRING functional interaction network depicted in their biological context. Red lines represent a mutual exclusivity between the connected genes. Dotted lines depict a functional interaction
Fig. 5
Fig. 5
Examples of gene sets with mutually exclusive alterations. The P values were computed using DISCOVER’s group-based test. Panels a and b show predefined gene sets extracted from MSigDB. Panels c and d show gene sets identified using our de novo group detection approach

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