Clumping and Thresholding (C+T)

The 'C' in C+T. This step partitions the genome into independent loci by selecting the most significant variant within a sliding window and removing all nearby variants that exceed a specified LD correlation threshold (typically r² > 0.1 or 0.2).

• Window size: Commonly 250-500 kilobases
• Purpose: Ensures retained variants are statistically independent
• Tooling: Implemented via PLINK --clump
• Reference panel: Requires a matched-ancestry LD reference (e.g., 1000 Genomes) to compute correlations accurately

Clumping prevents double-counting of a single causal signal tagged by multiple correlated SNPs, which would artificially inflate the score's variance.

The 'T' in C+T. After clumping, only variants with a GWAS association p-value below a predefined significance cutoff are retained for the score. This threshold acts as a complexity parameter controlling the bias-variance tradeoff.

• Common thresholds: 5×10⁻⁸ (genome-wide significant), 0.01, 0.05, 0.1, 0.5, or 1.0 (all variants)
• Optimization: The optimal threshold is typically identified by testing multiple values in an independent validation dataset and selecting the one maximizing variance explained (R²)
• Polygenicity assumption: More liberal thresholds (e.g., p < 0.5) assume a highly polygenic architecture where many sub-significant variants contribute meaningful signal

The threshold directly determines the number of variants included, ranging from dozens (strict) to hundreds of thousands (lenient).

Once variants are selected via clumping and thresholding, the polygenic risk score is computed as a weighted sum of risk alleles:

PRSᵢ = Σⱼ βⱼ × Gᵢⱼ

Where:

• βⱼ: The log-odds ratio or beta coefficient for variant j from the base GWAS summary statistics
• Gᵢⱼ: The number of effect alleles carried by individual i at variant j (0, 1, or 2)
• j: Indexes over all variants surviving the C+T filters

This additive model assumes each variant contributes independently and linearly to the overall genetic liability. No interaction terms or non-linear effects are modeled.

The C+T method requires a hold-out validation dataset to tune the p-value threshold hyperparameter. Without this step, the score's predictive performance cannot be optimized.

• Process: Iterate through a grid of p-value thresholds (e.g., 5×10⁻⁸, 1×10⁻⁵, 0.001, 0.01, 0.05, 0.1, 0.5, 1.0), compute the PRS for each, and evaluate AUC-ROC or R² in the validation set
• Overfitting risk: If the same dataset is used for threshold selection and final evaluation, predictive performance will be optimistically biased
• Best practice: Use a three-way split—discovery GWAS, validation for tuning, and an independent test set for unbiased reporting

The optimal threshold reflects the trait's underlying genetic architecture: highly polygenic traits benefit from liberal thresholds, while oligogenic traits favor stringent cutoffs.

C+T makes several simplifying assumptions that constrain its performance relative to more sophisticated Bayesian methods like LDpred2 or PRS-CS:

• Hard thresholding: Variants just above the p-value cutoff are completely excluded, discarding potentially useful signal. Bayesian methods apply continuous shrinkage instead
• Single causal variant per locus: Clumping retains only the top SNP per LD block, ignoring the possibility of multiple independent causal variants within a region
• No effect size shrinkage: GWAS effect sizes are used as-is without correction for Winner's Curse overestimation
• Ancestry specificity: Performance degrades substantially when the LD reference panel does not match the target population's ancestry
• No modeling of genetic architecture: The method does not incorporate prior knowledge about the distribution of true effect sizes

The non-random association of alleles at different loci, which is the fundamental biological phenomenon that clumping corrects for. LD arises because genetic variants physically close on a chromosome are often inherited together. In PRS construction, failing to account for LD leads to double-counting the same genetic signal, inflating the score's variance. Clumping selects a single index variant to represent an entire LD block, ensuring statistical independence among the variants included in the final score.

The thresholding component of C+T, which filters variants based on their GWAS association significance. Common thresholds include:

• 5 × 10⁻⁸: The genome-wide significance standard
• 1 × 10⁻⁵: A relaxed suggestive threshold
• 0.01 to 0.5: Highly inclusive thresholds for traits with polygenic architecture The optimal threshold is typically determined empirically by testing multiple values in a validation dataset and selecting the one that maximizes prediction accuracy, a process known as p-value optimization.

A Bayesian alternative to C+T that models the full genetic architecture without explicit pruning or hard thresholding. Instead of selecting independent variants, LDpred2 uses a point-normal mixture prior on effect sizes and a Gibbs sampler to infer posterior mean effects for all variants simultaneously. This approach accounts for LD directly in the model rather than removing correlated variants, often yielding higher predictive accuracy than C+T, especially for highly polygenic traits where many small-effect variants contribute to risk.

A statistical bias that inflates effect size estimates for variants selected based on significance thresholds. When variants are chosen because they exceed a p-value cutoff in the discovery GWAS, their estimated effects are systematically overestimated due to random sampling error. This bias is particularly severe for C+T methods that use stringent thresholds. Correction methods such as empirical Bayes shrinkage or bootstrap bias correction adjust effect sizes downward, improving PRS predictive accuracy in independent target samples.

Systematic allele frequency differences between ancestry groups that can confound both GWAS discovery and PRS prediction. C+T scores trained in one population often show poor cross-ancestry portability because LD patterns and variant effect sizes differ across ancestries. Principal component analysis (PCA) is routinely applied to correct for stratification during GWAS, but residual confounding can still bias the variant selection and thresholding steps. Cross-ancestry PRS methods address this by incorporating multi-population summary statistics and ancestry-specific LD references.