GWASinlps.RdGWASinlps performs variable selection with data from Genome-wide association studies (GWAS), or other high-dimensional data with continuous, binary or survival outcomes, combining in an iterative framework, the computational efficiency of the structured screen-and-select variable selection strategy based on some association learning and the parsimonious uncertainty quantification provided by the use of non-local priors (see the References).
GWASinlps(
y,
event,
x,
family = c("normal","binomial","survival"),
method = c("rigorous","quick"),
cor_xy = NULL,
mmle_xy = NULL,
mu_xy = NULL,
prior = c("mom", "imom", "emom", "zellner", "horseshoe"),
tau,
priorDelta = modelbbprior(1,1),
k0,
m,
rxx,
nskip = 3,
niter = 2000,
verbose = FALSE,
seed = NULL,
tau.hs.method = "halfCauchy",
sigma.hs.method = "Jeffreys"
)The vector of continuous response (phenotype) for linear models (LM), or binary response (phenotype) for generalized linear models (GLM), or survival times for accelerated failure time models (AFTM). Binary response values must be 0 or 1.
Only for AFTM. The vector of status indicator for the survival data.
The design matrix with subjects in rows and independent variables (e.g., SNPs) in columns. Missing values are not accepted currently.
"normal" for continuous data, "binomial" for binary data (logit link is used), "survival" for survival data.
Applies only when family="binomial". The rigorous method uses logistic regression based analysis which is theoretically appropriate but can be slow. The quick method uses a curious combination of linear model and logistic regression based analyses and is considerably faster. See Details.
Used only when family="normal". Vector of (Pearson) correlation coefficients of y with the individual columns of x.
Used only when family="binomial". Vector of maximum marginal likelihood estimates of the regression parameters corresponding to the x variables (e.g., SNPs). These are obtained from GLM fits of y with the individual columns of x including an intercept.
Used only when family="survival". Vector of marginal utility estimates of the variables (SNPs) in x. These may be obtained by fitting AFT model to y with individual columns of x using the survreg function of the package survival.
"mom" for pMOM prior, "imom" for piMOM prior, "emom" for peMOM prior, "zellner" for Zellner's g-prior, "horseshoe" for horseshoe prior. For GLM, "zellner" considers group Zellner prior and "emom" and "horseshoe" are not available. For AFTM, "horseshoe" is not available.
The value of the scale parameter tau of the non-local prior.
Prior for model space. Defaults to modelbbprior(1,1), which is beta-binomial(1,1) prior.
GWASinlps tuning parameter denoting the number of leading SNPs/variables (see Details).
GWASinlps tuning parameter, denoting the maximum number of SNPs/variables to be selected.
GWASinlps tuning parameter denoting the correlation threshold to determine leading sets (see References).
GWASinlps tuning parameter denoting the maximum allowed count of skipping an iteration that does not select any variable (SNP) (see References).
Number of MCMC iterations for non-local prior based Bayesian variable selection. Defaults to 2000.
If TRUE, prints result from the iterations progressively. FALSE by default.
For reproducibility. If provided, the random seed is set to this value at the beginning of the function.
Necessary only when prior="horseshoe". See horseshoe function reference.
Necessary only when prior="horseshoe". See horseshoe function reference.
The GWASinlps method selects variables (SNPs) iteratively.
For continuous response (phenotype), the procedure starts with an initial set of independent variables (SNPs), a design matrix (SNP genotype matrix) x and a response (phenotype) vector y.
- An iteration proceeds by determining the k0 leading SNPs/variables having the highest association with y. The measure of association is the absolute value of the Pearson's correlation coefficient cor_xy. These k0 leading SNPs/variables, in turn, determine k0 leading sets, where each leading set consists of all SNPs/variables with absolute correlation coefficient more than or equal to rxx with the correspondng leading SNP/variable.
- Within each leading set, non-local prior based Bayesian variable selection for linear models is performed (using package mombf). The variables (SNPs) appearing in the highest posterior probability model (HPPM) are considered selected in the current iteration. Note that a single variable (SNP) can be selected from multiple leading sets. The selected variables (SNPs) are regressed out from y using lm fit. The variables (SNPs) that are included in one or more of the leading sets but do not appear in any HPPM are dropped from further analysis.
- With updated y and variable (SNP) set, next iteration proceeds similarly. And so on like this. The procedure continues until the stopping point, which is determined by the GWASinlps tuning parameters m, rxx, and nskip, is reached. For more details, see References.
For binary response (phenotype), the procedure starts with an initial set of variables (SNPs), a design matrix (SNP genotype matrix) x and a binary response (phenotype) vector y. If method="rigorous",
- The first iteration proceeds by determining the k0 leading SNPs/variables having the highest association with y. The measure of association is the absolute value of the maximum marginal likelihood estimate mmle_xy. These k0 leading SNPs/variables, in turn, determine k0 leading sets, where each leading set consists of all SNPs/variables with absolute correlation coefficient more than or equal to rxx with the correspondng leading SNP.
- Within each leading set, non-local prior based Bayesian variable selection for logistic regression model is performed (using package mombf). The variables (SNPs) appearing in the HPPM are considered selected in the first iteration. Note that a single variable (SNP) can be selected from multiple leading sets. The variables (SNPs) which are included in one or more leading sets but do not appear in any HPPM are dropped from further analysis. After this, the selected variables (SNPs) are accounted for by including them in glm fits of y with each of the remaining variables (SNPs). The glm coefficients of the remaining variables, thus obtained, reflect their contribution in presence of the selected variables (SNPs) of the first iteration.
- Considering the absolute values of these glm coefficients as the measure of association, we proceed with the second iteration with updated variable (SNP) set. And so on in this manner. The procedure continues until the stopping point, which is determined by the GWASinlps tuning parameters m, rxx, and nskip, is reached.
If method="quick", the procedure is similar to above except at the following points. In this method, non-local prior based Bayesian variable selection using logistic regression model is performed until one or more variables (SNP) are selected in an iteration. Until a variable is selected, there is no need to account for anything, so the initial maximum marginal likelihood estimates continue to be used. After the first selections (if any) are made, a glm fit of y on the selected variables is performed and the deviance residuals are computed. In the subsequent iterations, considering these (continuous) deviance residuals as response, non-local prior based Bayesian variable selection for linear models is performed till the stopping point is reached.
For survival data, the procedure starts with an initial set of variables (SNPs), a design matrix (SNP genotype matrix) x and a binary response (phenotype) vector y.
- The first iteration proceeds by determining the k0 leading SNPs/variables having the highest association with y. The measure of association is the absolute value of the marginal utility mu_xy. These k0 leading SNPs/variables, in turn, determine k0 leading sets, where each leading set consists of all SNPs with absolute correlation coefficient more than or equal to rxx with the correspondng leading SNP.
- Within each leading set, non-local prior based Bayesian variable selection for accelerated failure time model is performed (using package mombf). The variables (SNPs) appearing in the HPPM are considered selected in the first iteration. Note that a single variable (SNP) can be selected from multiple leading sets. The variables (SNPs) which are included in one or more leading sets but do not appear in any HPPM are dropped from further analysis. After this, to account for the selected variables (SNPs), conditional utilities of each of the remaining variables (SNPs) are computed in the presence of the selected variables (SNPs) in the model. These conditional utilities reflect the contribution of the remaining variables (SNPs) in presence of the selected variables (SNPs) of the first iteration.
- Considering the absolute values of these conditional utilities as the measure of association, we proceed with the second iteration with updated variable (SNP) set. And so on in this manner. The procedure continues until the stopping point, which is determined by the GWASinlps tuning parameters m, rxx, and nskip, is reached.
A list containing
Vector with names of the GWASinlps selected variables (SNPs) in the order they were selected.
List with selected variables (SNPs) from each iteration.
Sanyal et al. (2019), "GWASinlps: Non-local prior based iterative SNP selection tool for genome-wide association studies". Bioinformatics, 35(1), 1-11.
Sanyal, N. (2022). "Iterative variable selection for high-dimensional data with binary outcomes". arXiv preprint arXiv:2211.03190.
n = 200
p = 1000
m = 10
# Generate design matrix (genotype matrix)
set.seed(1)
f = runif( p, .1, .2 ) # simulate minor allele frequency
x = matrix( nrow = n, ncol = p )
colnames(x) = 1:p
for(j in 1:p)
x[,j] = rbinom( n, 2, f[j] )
# Generate true effect sizes
causal_snps = sample( 1:p, m )
beta = rep( 0, p )
set.seed(1)
beta[causal_snps] = rnorm(m, mean = 0, sd = 2 )
# Generate continuous (phenotype) data
y = x %*% beta + rnorm(n, 0, 1)
# Fix scale parameter tau
tau = 0.2
# GWASinlps analysis
inlps = GWASinlps(y=y, x=x, family="normal", prior="mom", tau=tau, k0=1,
m=50, rxx=0.2)
#> =================================
#> Number of selected variables: 17
#> Time taken: 0 min
#> =================================
cat( "GWASinlps selected", length(inlps$selected), "SNPs with",
length(intersect(inlps$selected, causal_snps)), "true positive(s) and",
length(setdiff(causal_snps, inlps$selected)), "false negative(s) out
of a pool of", p, "SNPs with data from", n, "persons." )
#> GWASinlps selected 17 SNPs with 10 true positive(s) and 0 false negative(s) out
#> of a pool of 1000 SNPs with data from 200 persons.
# Compare with LASSO
library(glmnet)
#> Loading required package: Matrix
#> Loaded glmnet 4.1-4
fit.cvlasso = cv.glmnet( x, y, alpha = 1 )
l.min = fit.cvlasso $lambda.min # lambda that gives minimum cvm
l.1se = fit.cvlasso $lambda.1se # largest lambda such that error is
# within 1 se of the minimum
lasso_min = which( as.vector( coef( fit.cvlasso, s = l.min ) )[-1] != 0 )
cat( "LASSO with lambda.min selected", length(lasso_min), "SNPs with",
length(intersect(lasso_min, causal_snps)), "true positives and",
length(setdiff(causal_snps, inlps$selected)), "false negative(s)." )
#> LASSO with lambda.min selected 63 SNPs with 10 true positives and 0 false negative(s).
lasso_1se = which( as.vector( coef( fit.cvlasso, s = l.1se ) )[-1] != 0 )
cat( "LASSO with lambda.1se selected", length(lasso_1se), "SNPs with",
length(intersect(lasso_1se, causal_snps)), "true positives and",
length(setdiff(causal_snps, inlps$selected)), "false negative(s)." )
#> LASSO with lambda.1se selected 24 SNPs with 9 true positives and 0 false negative(s).