Table 1. Comparison of methods for multiple regression of case-control GWAS data.

All methods use the point-normal prior (Eq (4)) for the effect sizes of the SNPs. The posterior probability is obtained by integrating out these effect sizes, either via MCMC sampling or analytically (column 2). Column 3 compares the approximations to the logistic or probit likelihood model. Column 4 shows which hyperparameters of the prior distribution are estimated from the data, and the method of hyperparameter estimation is shown in column 5. Column 6 shows whether the method analyzes multiple loci together (“Yes”) or independently (“No”). Column 7 lists which tools can perform meta-analysis. MCMC: Markov Chain Monte Carlo sampling, EM: expectation-maximization, CG: conjugate gradient method.

Method	Integration method	Approximation	Hyperparameters (HP) learnt from data	Method for HP estimation	Multiple loci	Meta-analysis
BIMBAM [4]	MCMC	Laplace	None	–	No	No
piMASS [5]	MCMC	Probit	πi, σ	MCMC	No	No
GEMMA [3, 14]	MCMC	Probit	πi, σ	MCMC	No	No
CAVIAR [8]	Analytic	Linear	None	–	No	Yes
CAVIARBF [9]	Analytic	Linear	None	–	No	Yes
FINEMAP [10]	Analytic	Linear	None	–	No	Yes
PAINTOR [6, 7]	Analytic	Linear	πi	EM	Yes	Yes
B-LORE	Analytic	quasi-Laplace	πi, σ	CG	Yes	Yes