Genome-wide association analysis by lasso penalized logistic regression

Regularization Paths for Generalized Linear Models via Coordinate Descent

We develop fast algorithms for estimation of generalized linear models with convex penalties. The models include linear regression, two-class logistic regression, and multinomial regression problems while the penalties include ℓ(1) (the lasso), ℓ(2) (ridge regression) and mixtures of the two (the elastic net). The algorithms use cyclical coordinate descent, computed along a regularization path. The methods can handle large problems and can also deal efficiently with sparse features. In comparative timings we find that the new algorithms are considerably faster than competing methods.

Regularization Paths for Generalized Linear Models via Coordinate Descent

We develop fast algorithms for estimation of generalized linear models with convex penalties. The models include linear regression, two-class logistic regression, and multinomial regression problems while the penalties include ℓ(1) (the lasso), ℓ(2) (ridge regression) and mixtures of the two (the elastic net). The algorithms use cyclical coordinate descent, computed along a regularization path. The methods can handle large problems and can also deal efficiently with sparse features. In comparative timings we find that the new algorithms are considerably faster than competing methods.

Regularization Paths for Generalized Linear Models via Coordinate Descent

We develop fast algorithms for estimation of generalized linear models with convex penalties. The models include linear regression, two-class logistic regression, and multinomial regression problems while the penalties include ℓ(1) (the lasso), ℓ(2) (ridge regression) and mixtures of the two (the elastic net). The algorithms use cyclical coordinate descent, computed along a regularization path. The methods can handle large problems and can also deal efficiently with sparse features. In comparative timings we find that the new algorithms are considerably faster than competing methods.

Prioritizing GWAS results: A review of statistical methods and recommendations for their application

Genome-wide association studies (GWAS) have rapidly become a standard method for disease gene discovery. A substantial number of recent GWAS indicate that for most disorders, only a few common variants are implicated and the associated SNPs explain only a small fraction of the genetic risk. This review is written from the viewpoint that findings from the GWAS provide preliminary genetic information that is available for additional analysis by statistical procedures that accumulate evidence, and that these secondary analyses are very likely to provide valuable information that will help prioritize the strongest constellations of results. We review and discuss three analytic methods to combine preliminary GWAS statistics to identify genes, alleles, and pathways for deeper investigations. Meta-analysis seeks to pool information from multiple GWAS to increase the chances of finding true positives among the false positives and provides a way to combine associations across GWAS, even when the original data are unavailable. Testing for epistasis within a single GWAS study can identify the stronger results that are revealed when genes interact. Pathway analysis of GWAS results is used to prioritize genes and pathways within a biological context. Following a GWAS, association results can be assigned to pathways and tested in aggregate with computational tools and pathway databases. Reviews of published methods with recommendations for their application are provided within the framework for each approach.

Identification of non-Hodgkin's lymphoma prognosis signatures using the CTGDR method

MOTIVATION

Although NHL (non-Hodgkin's lymphoma) is the fifth leading cause of cancer incidence and mortality in the USA, it remains poorly understood and is largely incurable. Biomedical studies have shown that genomic variations, measured with SNPs (single nucleotide polymorphisms) in genes, may have independent predictive power for disease-free survival in NHL patients beyond clinical measurements.

RESULTS

We apply the CTGDR (clustering threshold gradient directed regularization) method to genetic association studies using SNPs, analyze data from an association study of NHL and identify prognosis signatures to diffuse large B cell lymphoma (DLBCL) and follicular lymphoma (FL), the two most common subtypes of NHL. With the CTGDR method, we are able to account for the joint effects of multiple genes/SNPs, whereas most existing studies are single-marker based. In addition, we are able to account for the 'gene and SNP-within-gene' hierarchical structure and identify not only predictive genes but also predictive SNPs within identified genes. In contrast, existing studies are limited to either gene or SNP identification, but not both. We propose using resampling methods to evaluate the predictive power and reproducibility of identified genes and SNPs. Simulation study and data analysis suggest satisfactory performance of the CTGDR method.