A fast and scalable framework for large-scale and ultrahigh-dimensional sparse regression with application to the UK Biobank.

This difference may not be significant in small or moderate-sized problems, but can be critical in big data applications especially when the dataset cannot be fully loaded into the memory.

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We see although a general decreasing trend appears in the magnitude of the lasso coefficients with respect to increasing p -values (decreasing − log 10 ( p )), there are a number of spikes even in the large p -value region which is considered marginally insignificant.

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We select a subset of the K most marginally significant variants (after adjusting for the covariates), construct a new variable by linearly combining these variants using their univariate coefficients, and fit an ordinary least squares (OLS) on the new variable together with the adjustment variables.

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