Probabilities of spurious connections in gene networks: Application to expression time series

Motivation: The reconstruction of gene networks from gene expression microarrays is gaining popularity as methods improve and as more data become available. The reliability of such networks could be judged by the probability that a connection between genes is spurious, resulting from chance fluctuations rather than from a true biological relationship. Results: Unlike the false discovery rate and positive false discovery rate, the decisive false discovery rate (dFDR) is exactly equal to a conditional probability without assuming independence or the randomness of hypothesis truth values. This property is useful not only in the common application to the detection of differential gene expression, but also in determining the probability of a spurious connection in a reconstructed gene network. Estimators of the dFDR can estimate each of three probabilities: 1. The probability that two genes that appear to be associated with each other lack such association. 2. The probability that a time ordering observed for two associated genes is misleading. 3. The probability that a time ordering observed for two genes is misleading, either because they are not associated or because they are associated without a lag in time. The first probability applies to both static and dynamic gene networks, and the other two only apply to dynamic gene networks. Availability: Cross-platform software for network reconstruction, probability estimation, and plotting is free from http://www.davidbickel.com as R functions and a Java application.Comment: Like q-bio.GN/0404032, this was rejected in March 2004 because it was submitted to the math archive. The only modification is a corrected reference to q-bio.GN/0404032, which was not modified at al

Empirical Bayes estimation of posterior probabilities of enrichment

To interpret differentially expressed genes or other discovered features, researchers conduct hypothesis tests to determine which biological categories such as those of the Gene Ontology (GO) are enriched in the sense of having differential representation among the discovered features. We study application of better estimators of the local false discovery rate (LFDR), a probability that the biological category has equivalent representation among the preselected features. We identified three promising estimators of the LFDR for detecting differential representation: a semiparametric estimator (SPE), a normalized maximum likelihood estimator (NMLE), and a maximum likelihood estimator (MLE). We found that the MLE performs at least as well as the SPE for on the order of 100 of GO categories even when the ideal number of components in its underlying mixture model is unknown. However, the MLE is unreliable when the number of GO categories is small compared to the number of PMM components. Thus, if the number of categories is on the order of 10, the SPE is a more reliable LFDR estimator. The NMLE depends not only on the data but also on a specified value of the prior probability of differential representation. It is therefore an appropriate LFDR estimator only when the number of GO categories is too small for application of the other methods. For enrichment detection, we recommend estimating the LFDR by the MLE given at least a medium number (~100) of GO categories, by the SPE given a small number of GO categories (~10), and by the NMLE given a very small number (~1) of GO categories.Comment: exhaustive revision of Zhenyu Yang and David R. Bickel, "Minimum Description Length Measures of Evidence for Enrichment" (December 2010). COBRA Preprint Series. Article 76. http://biostats.bepress.com/cobra/ps/art7