Estimating the effective sample size (ESS) of a prior distribution is an age-old yet pivotal challenge, with great implications for clinical trials and various biomedical applications. Although numerous endeavors have been dedicated to this pursuit, most of them neglect the likelihood context in which the prior is embedded, thereby considering all priors as “beneficial”. In the limited studies of addressing harmful priors, specifying a baseline prior remains an indispensable step. By means of the elegant bridge between the p-value and the posterior probability of the null hypothesis, we propose a new ESS estimation method based on p-value in the framework of hypothesis testing, expanding the scope of existing ESS estimation methods in three key aspects: (i) We address the specific likelihood context of the prior, enabling the possibility of negative ESS values in case of prior–likelihood disconcordance; (ii) By leveraging the well-established bridge between the frequentist and Bayesian configurations under noninformative priors, there is no need to specify a baseline prior which incurs another criticism of subjectivity; (iii) By incorporating ESS into the hypothesis testing framework, our hypothesis test-based ESS estimation method transcends the conventional one-ESS-one-prior paradigm and accommodates one-ESS-multiple-priors paradigm, where the sole ESS may reflect the collaborative impact of multiple priors in diverse contexts. Through comprehensive simulation analyses, we demonstrate the superior performance of the hypothesis test-based ESS estimation method in comparison with existing approaches. Furthermore, by applying this approach to an expression quantitative trait loci (eQTL) data analysis, we show the effectiveness of informative priors in uncovering gene eQTL loci.

MOTIVATION: Transcriptome-wide association study (TWAS) aims to identify trait-associated genes regulated by significant variants to explore the underlying biological mechanisms at a tissue-specific level. Despite the advancement of current TWAS methods to cover diverse traits, traditional approaches still face two main challenges: (i) the lack of methods that can guarantee finite-sample false discovery rate (FDR) control in identifying trait-associated genes; and (ii) the requirement for individual-level data, which is often inaccessible. RESULTS: To address this challenge, we propose a powerful knockoff inference method termed TWAS-GKF to identify candidate trait-associated genes with a guaranteed finite-sample FDR control. TWAS-GKF introduces the main idea of Ghostknockoff inference to generate knockoff variables using only summary statistics instead of individual-level data. In extensive studies, we demonstrate that TWAS-GKF successfully controls the finite-sample FDR under a pre-specified FDR level across all settings. We further apply TWAS-GKF to identify genes in brain cerebellum tissue from the Genotype-Tissue Expression (GTEx) v8 project associated with schizophrenia (SCZ) from the Psychiatric Genomics Consortium (PGC), and genes in liver tissue related to low-density lipoprotein cholesterol (LDL-C) from the UK Biobank, respectively. The results reveal that the majority of the identified genes are validated by Open Targets Validation Platform. AVAILABILITY AND IMPLEMENTATION: The R package TWAS.GKF is publicly available at https://github.com/AnqiWang2021/TWAS.GKF.

Biological networks are important for the analysis of human diseases, which summarize the regulatory interactions and other relationships between different molecules. Understanding and constructing networks for molecules, such as DNA, RNA and proteins, can help elucidate the mechanisms of complex biological systems. The Gaussian Graphical Models (GGMs) are popular tools for the estimation of biological networks. Nonetheless, reconstructing GGMs from high-dimensional datasets is still challenging. The current methods cannot handle the sparsity and high-dimensionality issues arising from datasets very well. Here, we developed a new GGM, called the GR2D2 (Graphical $R^2$-induced Dirichlet Decomposition) model, based on the R2D2 priors for linear models. Besides, we provided a data-augmented block Gibbs sampler algorithm. The R code is available at https://github.com/RavenGan/GR2D2. The GR2D2 estimator shows superior performance in estimating the precision matrices compared with the existing techniques in various simulation settings. When the true precision matrix is sparse and of high dimension, the GR2D2 provides the estimates with smallest information divergence from the underlying truth. We also compare the GR2D2 estimator with the graphical horseshoe estimator in five cancer RNA-seq gene expression datasets grouped by three cancer types. Our results show that GR2D2 successfully identifies common cancer pathways and cancer-specific pathways for each dataset.

MOTIVATION: Variable selection is a common statistical approach to identifying genes associated with clinical outcomes of scientific interest. There are thousands of genes in genomic studies, while only a limited number of individual samples are available. Therefore, it is important to develop a method to identify genes associated with outcomes of interest that can control finite-sample false discovery rate (FDR) in high-dimensional data settings. RESULTS: This article proposes a novel method named Grace-AKO for graph-constrained estimation (Grace), which incorporates aggregation of multiple knockoffs (AKO) with the network-constrained penalty. Grace-AKO can control FDR in finite-sample settings and improve model stability simultaneously. Simulation studies show that Grace-AKO has better performance in finite-sample FDR control than the original Grace model. We apply Grace-AKO to the prostate cancer data in The Cancer Genome Atlas program by incorporating prostate-specific antigen (PSA) pathways in the Kyoto Encyclopedia of Genes and Genomes as the prior information. Grace-AKO finally identifies 47 candidate genes associated with PSA level, and more than 75% of the detected genes can be validated.