Identifying significant edges in graphical models of molecular networks

Abstract

Objective

Modelling the associations from high-throughput experimental molecular data has provided unprecedented insights into biological pathways and signalling mechanisms. Graphical models and networks have especially proven to be useful abstractions in this regard. Ad hoc thresholds are often used in conjunction with structure learning algorithms to determine significant associations. The present study overcomes this limitation by proposing a statistically motivated approach for identifying significant associations in a network.

Methods and materials

A new method that identifies significant associations in graphical models by estimating the threshold minimising the L ₁ norm between the cumulative distribution function (CDF) of the observed edge confidences and those of its asymptotic counterpart is proposed. The effectiveness of the proposed method is demonstrated on popular synthetic data sets as well as publicly available experimental molecular data corresponding to gene and protein expression profiles.

Results

The improved performance of the proposed approach is demonstrated across the synthetic data sets using sensitivity, specificity and accuracy as performance metrics. The results are also demonstrated across varying sample sizes and three different structure learning algorithms with widely varying assumptions. In all cases, the proposed approach has specificity and accuracy close to 1, while sensitivity increases linearly in the logarithm of the sample size. The estimated threshold systematically outperforms common ad hoc ones in terms of sensitivity while maintaining comparable levels of specificity and accuracy. Networks from experimental data sets are reconstructed accurately with respect to the results from the original papers.

Conclusion

Current studies use structure learning algorithms in conjunction with ad hoc thresholds for identifying significant associations in graphical abstractions of biological pathways and signalling mechanisms. Such an ad hoc choice can have pronounced effect on attributing biological significance to the associations in the resulting network and possible downstream analysis. The statistically motivated approach presented in this study has been shown to outperform ad hoc thresholds and is expected to alleviate spurious conclusions of significant associations in such graphical abstractions.