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Prior robust empirical Bayes inference for large-scale data by conditioning on rank with application to microarray data.

ABSTRACT: Empirical Bayes methods have been extensively used for microarray data analysis by modeling the large number of unknown parameters as random effects. Empirical Bayes allows borrowing information across genes and can automatically adjust for multiple testing and selection bias. However, the standard empirical Bayes model can perform poorly if the assumed working prior deviates from the true prior. This paper proposes a new rank-conditioned inference in which the shrinkage and confidence intervals are based on the distribution of the error conditioned on rank of the data. Our approach is in contrast to a Bayesian posterior, which conditions on the data themselves. The new method is almost as efficient as standard Bayesian methods when the working prior is close to the true prior, and it is much more robust when the working prior is not close. In addition, it allows a more accurate (but also more complex) non-parametric estimate of the prior to be easily incorporated, resulting in improved inference. The new method's prior robustness is demonstrated via simulation experiments. Application to a breast cancer gene expression microarray dataset is presented. Our R package rank.Shrinkage provides a ready-to-use implementation of the proposed methodology.

SUBMITTER: Liao JG

PROVIDER: S-EPMC3862209 | biostudies-literature | 2014 Jan

REPOSITORIES: biostudies-literature

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Prior robust empirical Bayes inference for large-scale data by conditioning on rank with application to microarray data.

Liao J G JG McMurry Timothy T Berg Arthur A

Biostatistics (Oxford, England) 20130808 1

Empirical Bayes methods have been extensively used for microarray data analysis by modeling the large number of unknown parameters as random effects. Empirical Bayes allows borrowing information across genes and can automatically adjust for multiple testing and selection bias. However, the standard empirical Bayes model can perform poorly if the assumed working prior deviates from the true prior. This paper proposes a new rank-conditioned inference in which the shrinkage and confidence intervals ...[more]

PMID: 23934072

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Project description:BackgroundMicroarray data enables the high-throughput survey of mRNA expression profiles at the genomic level; however, he data presents a challenging statistical problem because of the large number of transcripts with small sample sizes that are obtained. To reduce the dimensionality, various Bayesian or empirical Bayes hierarchical models have been developed. However, because of the complexity of the microarray data, no model can explain the data fully. It is generally difficult to scrutinize the irregular patterns of expression that are not expected by the usual statistical gene by gene models.ResultsAs an extension of empirical Bayes (EB) procedures, we have developed the β-empirical Bayes (β-EB) approach based on a β-likelihood measure which can be regarded as an 'evidence-based' weighted (quasi-) likelihood inference. The weight of a transcript t is described as a power function of its likelihood, fβ(yt|θ). Genes with low likelihoods have unexpected expression patterns and low weights. By assigning low weights to outliers, the inference becomes robust. The value of β, which controls the balance between the robustness and efficiency, is selected by maximizing the predictive β₀-likelihood by cross-validation. The proposed β-EB approach identified six significant (p<10⁻⁵) contaminated transcripts as differentially expressed (DE) in normal/tumor tissues from the head and neck of cancer patients. These six genes were all confirmed to be related to cancer; they were not identified as DE genes by the classical EB approach. When applied to the eQTL analysis of Arabidopsis thaliana, the proposed β-EB approach identified some potential master regulators that were missed by the EB approach.ConclusionsThe simulation data and real gene expression data showed that the proposed β-EB method was robust against outliers. The distribution of the weights was used to scrutinize the irregular patterns of expression and diagnose the model statistically. When β-weights outside the range of the predicted distribution were observed, a detailed inspection of the data was carried out. The β-weights described here can be applied to other likelihood-based statistical models for diagnosis, and may serve as a useful tool for transcriptome and proteome studies.

Project description:Air pollution is a matter of concern among the public, especially for those living in urban and industrial areas. Markov chain modeling is often used to model the underlying dynamics of air pollution, which involves describing the transition probability of going from one air pollution state to another. Thus, estimating the transition probability matrix for the data of the air pollution index (API) is an essential process in the modeling. However, one may observe many zero probabilities in the transition probability matrix, especially when faced with a small sample, interpreting the results with respect to the climate condition less realistic. This study proposes a robust empirical Bayes method, which incorporates a method of smoothing the zero frequencies in the count matrix, contributing to an improved estimation of the transition probability matrix. The robustness of the empirical Bayesian estimation is investigated based on Bayes risk. The transition probability matrices estimated based on the robust empirical Bayes method for the hourly API data collected from seven monitoring stations in Malaysia for the period 2012 to 2014 are used for determining the air pollution characteristics such as the mean residence time, the steady-state probability and the mean recurrence time. Furthermore, the proposed method has been evaluated by Monte Carlo simulations. Results suggest that it is quite effective in producing non-zero transition probability estimates, and superior to the maximum likelihood method in terms of minimizing the mean squared error for individual and entire transition probabilities. Therefore, the robust empirical Bayes method proves to be an improved approach to the estimation of the Markov chain. When applied to API data, it could provide important information on air pollution dynamics that may help guiding the development of proper strategies for managing the impact of air quality.Supplementary informationThe online version contains supplementary material available at 10.1007/s40201-020-00607-4.

Dataset Information

Prior robust empirical Bayes inference for large-scale data by conditioning on rank with application to microarray data.

Publications

Prior robust empirical Bayes inference for large-scale data by conditioning on rank with application to microarray data.

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