REGENIE from Regeneron

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Jonathan Marchini's group at Regeneron have a new preprint: Computationally efficient whole genome regression for quantitative and binary traits (2020).

Here we present a novel machine learning method called REGENIE for fitting a whole genome regression model that is orders of magnitude faster than alternatives, while maintaining statistical efficiency. The method naturally accommodates parallel analysis of multiple phenotypes, and only requires local segments of the genotype matrix to be loaded in memory ... The method is applicable to both quantitative and binary phenotypes

Another method to consider alongside BOLT-LMM, fastGWA, and SAIGE.

The project website claims their C++ implementation will be MIT-licensed and available at rgcgithub/regenie, but that repo does not yet exist.

They also claim there's an implementation in Glow, but I don't see it.

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Jonathan Marchini posted a Twitter thread about REGENIE this morning.

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Okay rgcgithub/regenie now has the C++ code and Introducing GloWGR: An industrial-scale, ultra-fast and sensitive method for genetic association studies details the Glow implementation. Notably:

Glow provides an implementation of the WGR method for quantitative traits, and a binary trait variant is in progress.

The code for the Glow implementation is in two places:

• https://github.com/projectglow/glow/tree/master/core/src/main/scala/io/projectglow/transformers/blockvariantsandsamples
• https://github.com/projectglow/glow/tree/master/python/glow/wgr

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(Posted by @eric-czech)

A few other notes on the paper:

• BOLT-LMM, fastGWA and SAIGE all operate one trait at a time while REGENIE (like BGENIE) operates on multiple traits in one regression
• There are at least 3 approximations approximations that go into the method:
  • Variants are "compressed" block-wise using ridge regression predictions so that the second stage association testing (also using ridge regressors) are based on an approximation to the original genotype matrix
  • A new approximation to solving firth regressions for binary traits
  • Rather than model sample covariance explicitly, it seems as though they simply leave handling the sample correlation off to L2 regularization in ridge regressions
    • There is a mention of needing a spectral decomposition of a GRM in each block, but this definitely isn't equivalent to usual GRM treatment, i.e. using the decomposition to transform variables globally, and I'm not sure what implications it has
• Despite all the new approximations, correlations in p-values w/ SAIGE are very high
  • Correlations with BOLT and fastGWA are lower, though this is expected since an advance in SAIGE was better management of test statistic inflation for rare variants and unbalanced traits
    • The authors mention that they even see an improvement on this inflation vs SAIGE for "ultra-rare variants" because of their Firth approximation
• One advance in BOLT was the assumption of non-infinitesimal genetic architecture. This is widely believed to be the correct assumption to base modeling on and equates (in BOLT) to not putting a gaussian prior on all SNP effects but rather making the effects a mixture of effects with 0s and effects with gaussian priors (the mixture param is learned). REGENIE seems to assume the infinitesimal model, though it's hard to say for certain what impact this has given that the second modeling stage might correct for some of the biases that result from assuming all SNPs have a causal effect -- the authors don't talk about it much.
• Missing phenotypes are mean imputed in the first stage but then only complete cases are considered in the second stage
• On UKB data, somewhere on the order of ~450k SNPs are used to fit the null model and then ~10M SNPs out of the full 90M imputed set are tested for association
• The c++ benchmarks show 7x+ improvements in time taken vs SAIGE, BOLT, and fastGWA (especially in null model fits), but I don't see any Glow benchmarks. It should distribute well though since it was designed for the bulk of the work to be done on individual blocks.
  • Note: It isn't 100% clear to me yet if there are caveats to this, but by "block" they do seem to mean chunking along both axes, i.e. not tall-skinny/short-fat. I'm not sure if that's true in both stages but it shouldn't matter as much in stage 2 after the variant dimension is reduced.

In general, the method looks pretty straightforward to implement with a block-wise API like dask, for continuous phenotypes at least. The tight correlation with SAIGE results is also great since that appears to be the SOA at the moment for binary traits.

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(Posted by @eric-czech)

The PR tracking support for logistic regression in Glow: projectglow/glow#245.

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REGENIE v2 Twitter thread from Jonathan Marchini. The highlight appears to be burden testing.