Abstract
BackgroundThere are several studies in the literature depicting measurement error in gene expression data and also, several others about regulatory network models. However, only a little fraction describes a combination of measurement error in mathematical regulatory networks and shows how to identify these networks under different rates of noise.ResultsThis article investigates the effects of measurement error on the estimation of the parameters in regulatory networks. Simulation studies indicate that, in both time series (dependent) and non-time series (independent) data, the measurement error strongly affects the estimated parameters of the regulatory network models, biasing them as predicted by the theory. Moreover, when testing the parameters of the regulatory network models, p-values computed by ignoring the measurement error are not reliable, since the rate of false positives are not controlled under the null hypothesis. In order to overcome these problems, we present an improved version of the Ordinary Least Square estimator in independent (regression models) and dependent (autoregressive models) data when the variables are subject to noises. Moreover, measurement error estimation procedures for microarrays are also described. Simulation results also show that both corrected methods perform better than the standard ones (i.e., ignoring measurement error). The proposed methodologies are illustrated using microarray data from lung cancer patients and mouse liver time series data.ConclusionsMeasurement error dangerously affects the identification of regulatory network models, thus, they must be reduced or taken into account in order to avoid erroneous conclusions. This could be one of the reasons for high biological false positive rates identified in actual regulatory network models.
Highlights
There are several studies in the literature depicting measurement error in gene expression data and several others about regulatory network models
Despite these results in gene expression analysis and a large amount of research performed in modeling regulatory networks (Bayesian networks [10,11], Boolean networks [12,13], Relevance networks [14], Graphical Gaussian models [15], Differential equations [16], etc), only a fraction of the statistical studies use procedures designed for modeling networks taking into account measurement error
We have shown evidence that presence of the measurement errors has a high impact in regulatory network models
Summary
There are several studies in the literature depicting measurement error in gene expression data and several others about regulatory network models. In the last few years, a considerable number of reports on the problem of quantifying and separating “true” gene expression signal from noise [5,6,7] has been published with the main aim to find differentially expressed genes [8,9] Despite these results in gene expression analysis and a large amount of research performed in modeling regulatory networks (Bayesian networks [10,11], Boolean networks [12,13], Relevance networks [14], Graphical Gaussian models [15], Differential equations [16], etc), only a fraction of the statistical studies use procedures designed for modeling networks taking into account measurement error
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