regenie

The qf library provides C code designed to compute the p-value from a linear combination of $\chi^2(1)$ (chi-squared with 1 degree of freedom) distributions. It achieves this by inverting the characteristic function.

Note: This implementation was modified from Robert Davies' original code to remove dependencies on the setjmp library, ensuring compatibility with C++ environments.

In Step 1, REGENIE reduces the dimensionality of the genetic data to create efficient predictors.

Level 0: Ridge Regression

REGENIE reads markers in blocks of size $B$ (controlled by --bsize). For each block, it calculates a set of ridge regression predictors using a range of $J$ shrinkage parameters (controlled by --l0, default is 5). This captures the effects of markers within the block while accounting for Linkage Disequilibrium (LD).

Level 1: Cross-validation

To account for the correlation between the Level 0 predictors and the phenotype, REGENIE performs a second level of ridge regression on the full set of predictors.

• Quantitative Traits: Uses ridge regression and selects the best shrinkage parameter ($\phi$) via K-fold cross-validation to prevent overfitting.
• Binary Traits: Uses a logistic ridge regression model to combine predictors.

REGENIE implements a two-step method for genome-wide association testing designed to handle large sample sizes (e.g., UK Biobank) and diverse genetic data (microarray, imputation, exome sequencing).

1. Step 1: Whole genome model: A subset of genetic markers (typically several hundred thousand common markers) is used to fit a whole genome regression model. This captures a significant portion of the phenotype variance attributable to genetic effects.
2. Step 2: Association testing: A larger set of markers (e.g., imputed markers) is tested for association with the phenotype. This testing is performed conditional upon the predictions from Step 1 using a Leave One Chromosome Out (LOCO) scheme to avoid proximal contamination (where a marker's effect is accidentally captured by the Step 1 model because it is physically near the marker being tested).

regenie supports Leave-One-Variant-Out (LOVO) and Leave-One-Domain-Out (LODO) schemes to analyze the impact of specific variants or domains on the mask.

• LOVO (--mask-lovo): Builds masks by leaving out one variant at a time from the full set. The argument is a comma-separated list: [set/gene name],[mask name],[AAF cutoff]. If using 4-column annotations, use [gene name],[domain name],[mask name],[AAF cutoff].
• LODO (--mask-lodo): Builds a LODO mask for each domain by excluding all variants in that domain. The argument is [gene name],[mask name],[AAF cutoff].

Note: LOVO/LODO schemes cannot be used with --write-mask (PLINK bed output).

To use the L-BFGS solver, you must define a functor (a class or struct) that represents the multivariate function to be minimized. The functor must implement an operator() with the following signature:

double operator()(const VectorXd& x, VectorXd& grad)

• x: The current point (input).
• grad: The gradient vector, which must be overwritten with the gradient evaluated at x (output).
• The return value must be the objective function value at x.

class Rosenbrock
{
private:
    int n;
public:
    Rosenbrock(int n_) : n(n_) {}
    double operator()(const Eigen::VectorXd& x, Eigen::VectorXd& grad)
    {
        double fx = 0.0;
        // ... calculate fx and populate grad ...
        return fx;
    }
};

The remeta helper classes are designed to store sparse compressed covariance or Linkage Disequilibrium (LD) matrices originating from SKAT for use in meta-analysis.

Note on Compilation: These classes depend on HTSlib. If HTSlib is not available on your system, these classes will not be compiled unless the WITH_HTSLIB macro is explicitly set during the build process.

When building masks, the calculation of A1FREQ depends on the rule used:

• max and comphet rules: The burden masks take values in [0, 2]. A1FREQ is calculated as the mean genotype divided by 2 (mean(G)/2), consistent with single variants.
• sum rule: A1FREQ is calculated as the average of the effect allele frequencies across all sites included in the mask.

When performing large-scale analyses (like UK Biobank), regenie can analyze multiple traits at once for higher computational efficiency.

Guidelines:

• Imputation: regenie uses an imputation scheme to handle missing data. This is effective for quantitative traits with up to ~20% missingness and binary traits with up to ~5% missingness.
• Grouping: Group traits that have similar missingness patterns and keep missingness reasonably low (<15%) to ensure accuracy.