False Discovery Rate Control

The foundational algorithm for controlling FDR in multiple hypothesis testing. It operates on a list of p-values sorted in ascending order, comparing each to a linearly adjusted threshold.

• Step 1: Rank all p-values from smallest to largest: p(1), p(2), ..., p(m)
• Step 2: Find the largest rank k where p(k) ≤ (k/m) * α
• Step 3: Reject all null hypotheses with rank 1 through k

This guarantees that the expected FDR is at most α under independence or positive regression dependency. For variant calling, this means if you set α=0.05, you expect no more than 5% of your called variants to be false positives.

Understanding the distinction between FDR and the more conservative Family-Wise Error Rate (FWER) is critical for genomic applications.

• FWER: Controls the probability of making any Type I error. Suitable when a single false positive is catastrophic.
• FDR: Controls the expected proportion of false positives. Tolerates a few errors to gain substantial power.

In a genome with 3 billion bases, using a strict Bonferroni correction (FWER) often eliminates true signals. FDR control allows researchers to discover real variants while quantifying the acceptable noise level, making it the standard for genome-wide association studies and differential expression analysis.

The q-value, introduced by John Storey, is the minimum FDR at which a specific test can be called significant. It provides a per-feature significance measure analogous to the p-value but adjusted for multiplicity.

• A p-value of 0.01 means there is a 1% chance of observing data this extreme if the null is true.
• A q-value of 0.01 means that among all features with a q-value ≤ 0.01, the expected FDR is 1%.

For variant callers, reporting a q-value for each candidate locus gives downstream analysts a direct, interpretable confidence metric. A variant with a q-value of 0.001 has a 0.1% expected false discovery rate within that set.

Standard FDR methods assume p-values are uniformly distributed under the null hypothesis. In high-throughput sequencing, systematic biases from GC-content, mappability, and batch effects often violate this assumption.

Empirical null estimation corrects for this by modeling the observed distribution of test statistics directly:

• Efron's method fits a central distribution to the bulk of observed z-scores or p-values, ignoring the tails where true signals reside.
• This separates the empirical null from the theoretical null, preventing inflated false positive rates.

Variant callers like GATK's VQSR implicitly use this principle by learning the error distribution from known true-negative sites.

Applying a single FDR threshold across all variant types masks critical performance differences. Stratified FDR partitions discoveries into biologically meaningful categories before applying control.

• SNPs vs. Indels: Indels have inherently higher error rates; a combined FDR would be dominated by SNP calls.
• Exonic vs. Intergenic: Coding regions may warrant a stricter threshold due to functional impact.
• Depth Strata: Low-coverage regions require separate calibration.

By controlling FDR independently within each stratum, pipelines produce uniformly reliable calls across all variant classes. This prevents the systematic loss of true indels while maintaining global error control.

Modern neural variant callers like DeepVariant output raw scores that are not inherently calibrated probabilities. Temperature scaling is a post-hoc method that rescales logits to align confidence with empirical accuracy.

• A single scalar parameter T divides all logits before the softmax layer.
• T > 1 softens probabilities, correcting overconfidence.
• Optimized on a held-out calibration set to minimize expected calibration error.

When combined with FDR control, a well-calibrated model ensures that a q-value threshold of 0.05 truly corresponds to a 5% false discovery rate, not an arbitrary score cutoff. This is essential for clinical pipelines requiring auditable confidence metrics.

A step-up method that controls the False Discovery Rate (FDR) by sequentially comparing sorted p-values to linearly scaled thresholds. It is less conservative than family-wise error rate control, making it ideal for high-dimensional genomic testing where thousands of variants are evaluated simultaneously. The procedure ranks p-values from smallest to largest and rejects hypotheses where the p-value falls below a critical value determined by the rank and desired FDR level.

A measure of significance in terms of the minimum FDR at which a test may be called significant. Unlike a standard p-value, the q-value assigns an error rate to each individual feature, enabling direct control over the expected proportion of false positives among all discoveries. Storey's method is widely used to estimate q-values by modeling the distribution of p-values and estimating the proportion of true null hypotheses.

The probability of making one or more Type I errors across a family of hypothesis tests. Control methods like the Bonferroni correction divide the significance threshold by the number of tests, ensuring strict protection against any false positive. While mathematically rigorous, FWER control is often too stringent for genomic studies involving millions of independent loci, leading to a substantial loss of statistical power.

A machine learning approach that uses a Gaussian Mixture Model to assign a well-calibrated probability of error to each variant call. It leverages known truth sets and multiple annotation features to distinguish true variants from sequencing artifacts. The resulting VQSLOD score allows users to apply a single, unified FDR threshold across the entire call set, replacing hard filters on individual metrics.

An empirical Bayes approach that estimates the posterior probability that a specific null hypothesis is true given its test statistic. Unlike the standard FDR, which controls an average rate over a rejection region, the local FDR provides a direct probabilistic assessment for each individual feature. It is particularly powerful for density-based classification of true and null signals in large-scale genomic data.

An extension of FDR methodology that partitions hypotheses into distinct biological strata or annotation categories before applying error control. This prevents the masking of signals in sparse categories by abundant signals in dense ones. In variant calling, strata may be defined by genomic context (e.g., exons vs. introns), minor allele frequency bins, or functional annotation scores, ensuring balanced discovery across the genome.