Empirical Copula in the Detection of Batch Effects
The activation of the complex biological systems is presented by different mathematical expressions, called models, under various assumptions. One of the common modeling types in this description is the steady-state approach. In this description, we assume that the stochastic behavior of the system may not be observed under the constant volume and the temperature, and the mean change in the states of the system’s components is bigger than the variation of the states. Since this sort of the system’s representation needs less information about the actual biological activation, and majority of the collected data is more suitable for this approach with respect to its stochastic alternates, it is the most common modeling type in the presentation of the biological networks. In this study, we particularly deal with the steady-state type of model and suggest a preprocessing step for the raw data that is based on the transformation via the empirical copula. Here, we use the empirical copula, also called the normal copula, for eliminating the batch effects in the measurements so that the new data can fit the multivariate normal distribution. Then, we implement both parametric and nonparametric models in order to describe the final transformed measurements. In the description of the systems, we choose the Gaussian graphical model as the parametric modeling approach and select the probabilistic Boolean as well as the lasso-based MARS model as its correspondence under the nonparametric representation. Finally, in the analyses, we evaluate the performance of all suggested models and the effect of the empirical copula based on various accuracy measures via Monte Carlo studies.
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