FDR Control Setup Guide: A Comprehensive Overview of Modern Methods

False Discovery Rate (FDR) control is a crucial aspect of statistical hypothesis testing, particularly in high-throughput experiments across genomics, bioinformatics, and beyond. When dealing with thousands or even millions of simultaneous tests, such as in gene expression analysis or genome-wide association studies (GWAS), the risk of false positives increases dramatically. FDR control methods aim to manage this risk by controlling the expected proportion of false discoveries among all rejected hypotheses. This guide provides a comprehensive overview of modern FDR control setup, drawing insights from a detailed benchmark study of various methodologies.

This article is adapted from a rigorous study evaluating the performance of different FDR control methods, including both classical and contemporary approaches that leverage informative covariates. The original research benchmarked methods across diverse scenarios, from in silico experiments and simulations to real-world case studies in genomics and microbiome research. Our aim here is to translate these findings into a practical guide for researchers seeking to implement robust FDR control in their analyses.

Understanding the Landscape of FDR Control Methods

Traditional methods like the Benjamini-Hochberg (BH) procedure offer simplicity and broad applicability, adjusting p-values to control the FDR. However, recent advancements have introduced covariate-adjusted FDR methods that can significantly boost statistical power by incorporating auxiliary information. These covariates, often readily available in high-dimensional datasets, can inform the likelihood of a hypothesis being truly null or alternative.

Here’s a look at the methods benchmarked in the original study, which form the basis of this Fdr Control Setup Guide:

• Benjamini-Hochberg (BH): A foundational method, BH provides a straightforward approach to FDR control without relying on covariates. It’s widely used due to its ease of implementation and general applicability. In R, the p.adjust function with method="BH" in the stats package performs BH adjustment.
• Storey’s q-value: This method estimates the proportion of true null hypotheses and uses this information to calculate q-values, which are analogous to adjusted p-values but with a focus on FDR control. The qvalue function in the qvalue Bioconductor package is used for this purpose.
• Independent Hypothesis Weighting (IHW): IHW enhances the BH procedure by weighting hypotheses based on an independent covariate. By assigning lower weights to hypotheses with a higher probability of being null, IHW increases power while maintaining FDR control. The ihw and adj_pvalues functions in the IHW Bioconductor package facilitate IHW implementation.

Alt text: Conceptual diagram illustrating Independent Hypothesis Weighting (IHW) for FDR control, showing how covariates inform hypothesis weights to improve power.

• Blum-Storey (BL): This method combines BH with an estimate of the proportion of true null hypotheses (π0) derived from the informative covariate, aiming for improved power. In practice, BL adjusted p-values are obtained by multiplying BH adjusted p-values with π0 estimates from the lm_pi0 function in the swfdr Bioconductor package.
• Local False Discovery Rate (lfdr): Lfdr provides estimates of the probability that a specific rejected hypothesis is false. The implementation used in the benchmark study involves binning the covariate into discrete groups and applying the fdrtool function from the fdrtool CRAN package within each bin, following recommendations to ensure sufficient tests per bin.
• FDRreg: This Bayesian method uses regression to model the FDR as a function of an informative covariate, offering flexibility in incorporating complex covariate relationships. The FDRreg function from the FDRreg R package (available on GitHub) is used, with options for empirical or theoretical null implementations.
• Adaptive Shrinkage (ASH): ASH is an empirical Bayes method that shrinks effect size estimates, leading to improved FDR control and power, particularly when dealing with noisy data. The ash and get_qvalue functions from the ashr CRAN package are used, requiring effect sizes and standard errors as input.
• AdaPT: AdaPT is an adaptive multiple testing procedure that uses machine learning to model both the null proportion and the effect size distribution as functions of covariates. The adapt_glm function from the adaptMT CRAN package implements AdaPT, allowing for flexible model specification using spline basis matrices.

Setting Up FDR Control: A Step-by-Step Guide

Choosing and implementing the right FDR control method involves several key considerations. Here’s a setup guide to navigate this process effectively:

1. Understand Your Data and Research Question: Before selecting an FDR control method, clearly define your research question and the nature of your data. Are you working with gene expression data, GWAS results, microbiome data, or something else? What kind of test statistics or p-values are you using? The characteristics of your data will influence the suitability of different FDR methods.

2. Identify Potential Informative Covariates: Covariate-adjusted FDR methods rely on auxiliary information to improve power. Think about variables in your dataset that might be related to the probability of a hypothesis being truly null or alternative. For example, in gene expression analysis, mean gene expression is often a useful covariate, as genes with higher expression levels may be more likely to be differentially expressed. In GWAS, minor allele frequency or sample size can serve as informative covariates. For ChIP-seq data, region width or coverage might be relevant.

3. Verify Covariate Independence Under the Null Hypothesis: A critical assumption for covariate-adjusted FDR methods is that the chosen covariate is independent of the p-value or test statistic under the null hypothesis. In simpler terms, if a test is truly negative (null hypothesis is true), knowing the covariate value should not change the validity of the p-value. Violation of this assumption can lead to inflated false discovery rates. Visual diagnostics, as suggested by Ignatiadis et al. [15], can help assess both informativeness and independence.

4. Select an Appropriate FDR Control Method: Based on your data, research question, and available covariates, choose an FDR control method.

   • For general use and simplicity: BH and q-value are robust choices, especially when no strong informative covariates are available or when computational efficiency is paramount.
   • To leverage informative covariates for increased power: Consider IHW, BL, lfdr, FDRreg, AdaPT, or ASH. IHW is often a good starting point due to its ease of use and general applicability. For more complex covariate relationships or Bayesian approaches, FDRreg, ASH, or AdaPT might be suitable. Lfdr can be useful when covariates can be naturally binned into discrete groups.
   • Consider method assumptions: Be mindful of the assumptions of each method. For instance, FDRreg and ASH assume normally distributed test statistics, which may not always be met in all applications (as highlighted by their exclusion from χ2-distributed test statistic simulations in the benchmark study).

5. Implement the Chosen Method: Utilize the readily available R packages to implement your selected method. The “Implementation of benchmarked methods” section of the original article provides specific R code snippets for each method, using packages like stats, qvalue, IHW, swfdr, fdrtool, FDRreg, ashr, and adaptMT. These code examples serve as a practical starting point for your FDR control setup.

6. Evaluate and Interpret Results: After applying FDR control, examine the number of rejections and the adjusted p-values or q-values. Consider different alpha levels (e.g., 0.01, 0.05, 0.10) to assess the sensitivity of your findings. For covariate-adjusted methods, visualize how the covariate influences the number of discoveries or the adjusted p-values to ensure the covariate is indeed informative.

Benchmarking Insights: Performance and Practicality

The benchmark study provides valuable insights into the performance and practical aspects of these FDR control methods. Key findings relevant to FDR control setup include:

• FDR Control: Most methods, including BH, q-value, IHW, BL, lfdr, and AdaPT, effectively controlled the FDR at the nominal level in most scenarios. However, some methods like ASH and FDRreg require careful attention to their underlying assumptions.
• Power: Covariate-adjusted methods generally offered increased power compared to BH and q-value, particularly when informative covariates were available. IHW consistently demonstrated good power gains across various settings.
• Consistency: IHW, BL, and lfdr showed good consistency in performance across different simulation settings and case studies, indicating their robustness.
• Applicability and Usability: BH, q-value, and IHW stand out for their broad applicability and ease of use. Methods like FDRreg, ASH, and AdaPT, while potentially powerful, may require more specialized knowledge and data preprocessing. Usability is also a factor, with well-documented R packages available for most methods, but some requiring more effort for installation or implementation.

Alt text: Bar chart summarizing the ratings of different FDR control methods across key metrics: FDR control, Power, Consistency, Applicability, and Usability.

Conclusion: Choosing the Right Approach for Your FDR Control Setup

This guide, informed by a comprehensive benchmark study, offers a practical framework for setting up FDR control in your research. While traditional methods like BH and q-value remain valuable for their simplicity and robustness, modern covariate-adjusted methods like IHW, BL, and lfdr provide powerful tools to enhance discovery when informative covariates are available.

When setting up FDR control, carefully consider your data, research question, and the assumptions of each method. Start by exploring potential informative covariates and verifying their independence under the null hypothesis. For many applications, IHW presents a compelling balance of power, robustness, and usability. For more complex scenarios or when specific assumptions are met, FDRreg, ASH, or AdaPT may offer advantages.

Ultimately, the best FDR control setup depends on the specific context of your research. By understanding the strengths and limitations of different methods and following a systematic setup process, you can ensure robust and powerful statistical inference in your high-throughput data analyses.

References

The original article and its supplementary materials contain a comprehensive list of references, which are embedded in the original markdown text and available at the provided GitHub repository. For detailed citations and access to additional files, please refer to the original publication.