Empirical Bayes ranking and selection methods via semiparametric hierarchical mixture models in microarray studies

Efficient testing and effect size estimation for set-based genetic association inference via semiparametric multilevel mixture modeling

In genetic association studies, rare variants with extremely low allele frequencies play a crucial role in complex traits. Therefore, set-based testing methods that jointly assess the effects of groups of single nucleotide polymorphisms (SNPs) were developed to increase the powers of the association tests. However, these powers are still insufficient, and precise estimations of the effect sizes of individual SNPs are largely impossible. In this article, we provide an efficient set-based statistical inference framework that addresses both of these important issues simultaneously using an empirical Bayes method with semiparametric multilevel mixture modeling. We propose to utilize the hierarchical model that incorporates variations in set-specific effects and to apply the optimal discovery procedure (ODP) that achieves the largest overall power in multiple significance testing. In addition, we provide an optimal "set-based" estimator of the empirical distribution of effect sizes. The efficiency of the proposed methods is demonstrated through application to a genome-wide association study of coronary artery disease and through simulation studies. The results demonstrated numerous rare variants with large effect sizes for coronary artery disease, and the number of significant sets detected by the ODP was much greater than those identified by existing methods.

Efficient screening of predictive biomarkers for individual treatment selection

The development of molecular diagnostic tools to achieve individualized medicine requires identifying predictive biomarkers associated with subgroups of individuals who might receive beneficial or harmful effects from different available treatments. However, due to the large number of candidate biomarkers in the large-scale genetic and molecular studies, and complex relationships among clinical outcome, biomarkers, and treatments, the ordinary statistical tests for the interactions between treatments and covariates have difficulties from their limited statistical powers. In this paper, we propose an efficient method for detecting predictive biomarkers. We employ weighted loss functions of Chen et al. to directly estimate individual treatment scores and propose synthetic posterior inference for effect sizes of biomarkers. We develop an empirical Bayes approach, namely, we estimate unknown hyperparameters in the prior distribution based on data. We then provide efficient screening methods for the candidate biomarkers via optimal discovery procedure with adequate control of false discovery rate. The proposed method is demonstrated in simulation studies and an application to a breast cancer clinical study in which the proposed method was shown to detect the much larger numbers of significant biomarkers than existing standard methods.

An empirical Bayesian ranking method, with applications to high throughput biology

MOTIVATION

In bioinformatics, genome-wide experiments look for important biological differences between two groups at a large number of locations in the genome. Often, the final analysis focuses on a P-value-based ranking of locations which might then be investigated further in follow-up experiments. However, this strategy may result in small effect sizes, with low P-values, being ranked more favorably than larger more scientifically important effects. Bayesian ranking techniques may offer a solution to this problem provided a good prior distribution for the collective distribution of effect sizes is available.

RESULTS

We develop an Empirical Bayes ranking algorithm, using the marginal distribution of the data over all locations to estimate an appropriate prior. In simulations and analysis using real datasets, we demonstrate favorable performance compared to ordering P-values and a number of other competing ranking methods. The algorithm is computationally efficient and can be used to rank the entirety of genomic locations or to rank a subset of locations, pre-selected via traditional FWER/FDR methods in a 2-stage analysis.

AVAILABILITY AND IMPLEMENTATION

An R-package, EBrank, implementing the ranking algorithm is available on CRAN.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

An empirical Bayes optimal discovery procedure based on semiparametric hierarchical mixture models

Multiple testing has been widely adopted for genome-wide studies such as microarray experiments. For effective gene selection in these genome-wide studies, the optimal discovery procedure (ODP), which maximizes the number of expected true positives for each fixed number of expected false positives, was developed as a multiple testing extension of the most powerful test for a single hypothesis by Storey (Journal of the Royal Statistical Society, Series B, vol. 69, no. 3, pp. 347–368, 2007). In this paper, we develop an empirical Bayes method for implementing the ODP based on a semiparametric hierarchical mixture model using the “smoothing-by-roughening" approach. Under the semiparametric hierarchical mixture model, (i) the prior distribution can be modeled flexibly, (ii) the ODP test statistic and the posterior distribution are analytically tractable, and (iii) computations are easy to implement. In addition, we provide a significance rule based on the false discovery rate (FDR) in the empirical Bayes framework. Applications to two clinical studies are presented.

Genomic biomarkers for personalized medicine: development and validation in clinical studies

The establishment of high-throughput technologies has brought substantial advances to our understanding of the biology of many diseases at the molecular level and increasing expectations on the development of innovative molecularly targeted treatments and molecular biomarkers or diagnostic tests in the context of clinical studies. In this review article, we position the two critical statistical analyses of high-dimensional genomic data, gene screening and prediction, in the framework of development and validation of genomic biomarkers or signatures, through taking into consideration the possible different strategies for developing genomic signatures. A wide variety of biomarker-based clinical trial designs to assess clinical utility of a biomarker or a new treatment with a companion biomarker are also discussed.