Dataset Information

Assessing statistical significance in causal graphs.

ABSTRACT: Causal graphs are an increasingly popular tool for the analysis of biological datasets. In particular, signed causal graphs--directed graphs whose edges additionally have a sign denoting upregulation or downregulation--can be used to model regulatory networks within a cell. Such models allow prediction of downstream effects of regulation of biological entities; conversely, they also enable inference of causative agents behind observed expression changes. However, due to their complex nature, signed causal graph models present special challenges with respect to assessing statistical significance. In this paper we frame and solve two fundamental computational problems that arise in practice when computing appropriate null distributions for hypothesis testing.First, we show how to compute a p-value for agreement between observed and model-predicted classifications of gene transcripts as upregulated, downregulated, or neither. Specifically, how likely are the classifications to agree to the same extent under the null distribution of the observed classification being randomized? This problem, which we call "Ternary Dot Product Distribution" owing to its mathematical form, can be viewed as a generalization of Fisher's exact test to ternary variables. We present two computationally efficient algorithms for computing the Ternary Dot Product Distribution and investigate its combinatorial structure analytically and numerically to establish computational complexity bounds.Second, we develop an algorithm for efficiently performing random sampling of causal graphs. This enables p-value computation under a different, equally important null distribution obtained by randomizing the graph topology but keeping fixed its basic structure: connectedness and the positive and negative in- and out-degrees of each vertex. We provide an algorithm for sampling a graph from this distribution uniformly at random. We also highlight theoretical challenges unique to signed causal graphs; previous work on graph randomization has studied undirected graphs and directed but unsigned graphs.We present algorithmic solutions to two statistical significance questions necessary to apply the causal graph methodology, a powerful tool for biological network analysis. The algorithms we present are both fast and provably correct. Our work may be of independent interest in non-biological contexts as well, as it generalizes mathematical results that have been studied extensively in other fields.

SUBMITTER: Chindelevitch L

PROVIDER: S-EPMC3307026 | biostudies-literature | 2012 Feb

REPOSITORIES: biostudies-literature

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Assessing statistical significance in causal graphs.

Chindelevitch Leonid L Loh Po-Ru PR Enayetallah Ahmed A Berger Bonnie B Ziemek Daniel D

BMC bioinformatics 20120220

<h4>Background</h4>Causal graphs are an increasingly popular tool for the analysis of biological datasets. In particular, signed causal graphs--directed graphs whose edges additionally have a sign denoting upregulation or downregulation--can be used to model regulatory networks within a cell. Such models allow prediction of downstream effects of regulation of biological entities; conversely, they also enable inference of causative agents behind observed expression changes. However, due to their ...[more]

PMID: 22348444

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Project description:BACKGROUND:With the expanding use of next-gen sequencing (NGS) to diagnose the thousands of rare Mendelian genetic diseases, it is critical to be able to interpret individual DNA variation. To calculate the significance of finding a rare protein-altering variant in a given gene, one must know the frequency of seeing a variant in the general population that is at least as damaging as the variant in question. METHODS:We developed a general method to better interpret the likelihood that a rare variant is disease causing if observed in a given gene or genic region mapping to a described protein domain, using genome-wide information from a large control sample. Based on data from 2504 individuals in the 1000 Genomes Project dataset, we calculated the number of individuals who have a rare variant in a given gene for numerous filtering threshold scenarios, which may be used for calculating the significance of an observed rare variant being causal for disease. Additionally, we calculated mutational burden data on the number of individuals with rare variants in genic regions mapping to protein domains. RESULTS:We describe methods to use the mutational burden data for calculating the significance of observing rare variants in a given proportion of sequenced individuals. We present SORVA, an implementation of these methods as a web tool, and we demonstrate application to 20 relevant but diverse next-gen sequencing studies. Specifically, we calculate the statistical significance of findings involving multi-family studies with rare Mendelian disease and a large-scale study of a complex disorder, autism spectrum disorder. If we use the frequency counts to rank genes based on intolerance for variation, the ranking correlates well with pLI scores derived from the Exome Aggregation Consortium (ExAC) dataset (??=?0.515), with the benefit that the scores are directly interpretable. CONCLUSIONS:We have presented a strategy that is useful for vetting candidate genes from NGS studies and allows researchers to calculate the significance of seeing a variant in a given gene or protein domain. This approach is an important step towards developing a quantitative, statistics-based approach for presenting clinical findings.

Dataset Information

Assessing statistical significance in causal graphs.

Publications

Assessing statistical significance in causal graphs.

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