| Title: | Rank Normal Transformation Omnibus Test |
| Version: | 1.0.1.2 |
| Date: | 2023-09-10 |
| Description: | Inverse normal transformation (INT) based genetic association testing. These tests are recommend for continuous traits with non-normally distributed residuals. INT-based tests robustly control the type I error in settings where standard linear regression does not, as when the residual distribution exhibits excess skew or kurtosis. Moreover, INT-based tests outperform standard linear regression in terms of power. These tests may be classified into two types. In direct INT (D-INT), the phenotype is itself transformed. In indirect INT (I-INT), phenotypic residuals are transformed. The omnibus test (O-INT) adaptively combines D-INT and I-INT into a single robust and statistically powerful approach. See McCaw ZR, Lane JM, Saxena R, Redline S, Lin X. "Operating characteristics of the rank-based inverse normal transformation for quantitative trait analysis in genome-wide association studies" <doi:10.1111/biom.13214>. |
| Depends: | R (≥ 3.2.2) |
| Imports: | plyr, Rcpp, stats |
| LinkingTo: | Rcpp, RcppArmadillo |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.1.2 |
| Suggests: | testthat (≥ 3.0.0), withr, R.rsp |
| VignetteBuilder: | R.rsp |
| Config/testthat/edition: | 3 |
| NeedsCompilation: | yes |
| Packaged: | 2023-09-11 00:26:43 UTC; zmccaw |
| Author: | Zachary McCaw [aut, cre] |
| Maintainer: | Zachary McCaw <zmccaw@alumni.harvard.edu> |
| Repository: | CRAN |
| Date/Publication: | 2023-09-11 03:50:02 UTC |
RNOmni: Rank Normal Transformation Omnibus Test
Description
Inverse normal transformation (INT) based genetic association testing. These tests are recommend for continuous traits with non-normally distributed residuals. INT-based tests robustly control the type I error in settings where standard linear regression does not, as when the residual distribution exhibits excess skew or kurtosis. Moreover, INT-based tests dominate standard linear regression in terms of power. These tests may be classified into two types. In direct INT (D-INT), the phenotype is itself transformed. In indirect INT (I-INT), phenotypic residuals are transformed. The omnibus test (O-INT) adaptively combines D-INT and I-INT into a single robust and statistically powerful approach. See McCaw ZR, Lane JM, Saxena R, Redline S, Lin X. "Operating characteristics of the rank-based inverse normal transformation for quantitative trait analysis in genome-wide association studies" <doi:10.1111/biom.13214>.
Author(s)
Maintainer: Zachary McCawzmccaw@alumni.harvard.edu (ORCID)
Basic Association Test
Description
Conducts tests of association between the loci inG and theuntransformed phenotypey, adjusting for the model matrixX.
Usage
BAT(y, G, X = NULL, test = "Score", simple = FALSE)Arguments
y | Numeric phenotype vector. |
G | Genotype matrix with observations as rows, SNPs as columns. |
X | Model matrix of covariates and structure adjustments. Should includean intercept. Omit to perform marginal tests of association. |
test | Either Score or Wald. |
simple | Return the p-values only? |
Value
Ifsimple = TRUE, returns a vector of p-values, one for each columnofG. Ifsimple = FALSE, returns a numeric matrix, including theWald or Score statistic, its standard error, the Z-score, and the p-value.
See Also
Examples
set.seed(100)# Design matrixX <- cbind(1, stats::rnorm(1e3))# GenotypesG <- replicate(1e3, stats::rbinom(n = 1e3, size = 2, prob = 0.25))storage.mode(G) <- "numeric"# Phenotypey <- as.numeric(X %*% c(1, 1)) + stats::rnorm(1e3)# Association testp <- BAT(y = y, G = G, X = X)Basic Input Checks
Description
Stops evaluation if inputs are improperly formatted.
Usage
BasicInputChecks(y, G, X)Arguments
y | Numeric phenotype vector. |
G | Genotype matrix with observations as rows, SNPs as columns. |
X | Covariate matrix. |
Value
None.
Convert Cauchy Random Variable to P
Description
Convert Cauchy Random Variable to P
Usage
CauchyToP(z)Arguments
z | Numeric Cauchy random variable. |
Value
Numeric p-value.
Direct-INT
Description
Applies the rank-based inverse normal transformation (RankNorm)to the phenotypey. Conducts tests of association between the loci inG and transformed phenotype, adjusting for the model matrixX.
Usage
DINT( y, G, X = NULL, k = 0.375, test = "Score", ties.method = "average", simple = FALSE)Arguments
y | Numeric phenotype vector. |
G | Genotype matrix with observations as rows, SNPs as columns. |
X | Model matrix of covariates and structure adjustments. Should includean intercept. Omit to perform marginal tests of association. |
k | Offset applied during rank-normalization. See |
test | Either Score or Wald. |
ties.method | Method of breaking ties, passed to |
simple | Return the p-values only? |
Value
Ifsimple = TRUE, returns a vector of p-values, one for each columnofG. Ifsimple = FALSE, returns a numeric matrix, including theWald or Score statistic, its standard error, the Z-score, and the p-value.
See Also
Examples
set.seed(100)# Design matrixX <- cbind(1, stats::rnorm(1e3))# GenotypesG <- replicate(1e3, stats::rbinom(n = 1e3, size = 2, prob = 0.25))storage.mode(G) <- "numeric"# Phenotypey <- exp(as.numeric(X %*% c(1, 1)) + stats::rnorm(1e3))# Association testp <- DINT(y = y, G = G, X = X)Ordinary Least Squares
Description
Fits the standard OLS model.
Usage
FitOLS(y, X)Arguments
y | Nx1 Numeric vector. |
X | NxP Numeric matrix. |
Value
List containing the following:
Beta | Regression coefficient. |
V | Outcome variance. |
Ibb | Information matrix for beta. |
Resid | Outcome residuals. |
Indirect-INT
Description
Two-stage association testing procedure. In the first stage, phenotypey and genotypeG are each regressed on the model matrixX to obtain residuals. The phenotypic residuals are transformedusingRankNorm. In the next stage, the INT-transformedresiduals are regressed on the genotypic residuals.
Usage
IINT(y, G, X = NULL, k = 0.375, ties.method = "average", simple = FALSE)Arguments
y | Numeric phenotype vector. |
G | Genotype matrix with observations as rows, SNPs as columns. |
X | Model matrix of covariates and structure adjustments. Should includean intercept. Omit to perform marginal tests of association. |
k | Offset applied during rank-normalization. See |
ties.method | Method of breaking ties, passed to |
simple | Return the p-values only? |
Value
Ifsimple = TRUE, returns a vector of p-values, one for each columnofG. Ifsimple = FALSE, returns a numeric matrix, including theWald or Score statistic, its standard error, the Z-score, and the p-value.
See Also
Examples
set.seed(100)# Design matrixX <- cbind(1, stats::rnorm(1e3))# GenotypesG <- replicate(1e3, stats::rbinom(n = 1e3, size = 2, prob = 0.25))storage.mode(G) <- "numeric"# Phenotypey <- exp(as.numeric(X %*% c(1,1)) + stats::rnorm(1e3))# Association testp <- IINT(y = y, G = G, X = X)Omnibus-INT
Description
Association test that synthesizes theDINT andIINT tests. The first approach is most powerful for traits thatcould have arisen from a rank-preserving transformation of a latent normaltrait. The second approach is most powerful for traits that are linear incovariates, yet have skewed or kurtotic residual distributions. During theomnibus test, the direct and indirect tests are separately applied, then thep-values are combined via the Cauchy combination method.
Usage
OINT( y, G, X = NULL, k = 0.375, ties.method = "average", weights = c(1, 1), simple = FALSE)Arguments
y | Numeric phenotype vector. |
G | Genotype matrix with observations as rows, SNPs as columns. |
X | Model matrix of covariates and structure adjustments. Should includean intercept. Omit to perform marginal tests of association. |
k | Offset applied during rank-normalization. See |
ties.method | Method of breaking ties, passed to |
weights | Respective weights to allocate the DINT and IINT tests. |
simple | Return the OINT p-values only? |
Value
A numeric matrix of p-values, three for each column ofG.
See Also
Examples
set.seed(100)# Design matrixX <- cbind(1, rnorm(1e3))# GenotypesG <- replicate(1e3, rbinom(n = 1e3, size = 2, prob = 0.25))storage.mode(G) <- "numeric"# Phenotypey <- exp(as.numeric(X %*% c(1, 1)) + rnorm(1e3))# Omnibusp <- OINT(y = y, G = G, X = X, simple = TRUE)Omnibus P-value.
Description
Obtains an omnibus p-value from a vector of potentially dependent p-values using the method of Cauchy combination. The p-values are converted to Cauchyrandom deviates then averaged. The distribution of the average of these deviates is well-approximated by a Cauchy distribution in the tails. See<https://doi.org/10.1080/01621459.2018.1554485>.
Usage
OmniP(p, w = NULL)Arguments
p | Numeric vector of p-values. |
w | Numeric weight vector. |
Value
OINT p-value.
Partition Data
Description
Partition y and X according to the missingness pattern of g.
Usage
PartitionData(e, g, X)Arguments
e | Numeric residual vector. |
g | Genotype vector. |
X | Model matrix of covariates. |
Value
List containing:
"g_obs", observed genotype vector.
"X_obs", covariates for subjects with observed genotypes.
"X_mis", covariates for subjects with missing genotypes.
"e_obs", residuals for subjects with observed genotypes.
Convert P-value to Cauchy Random
Description
Convert P-value to Cauchy Random
Usage
PtoCauchy(p)Arguments
p | Numeric p-value. |
Value
Numeric Cauchy random variable.
Rank-Normalize
Description
Applies the rank-based inverse normal transform (INT) to a numeric vector.The INT can be broken down into a two-step procedure. In the first, theobservations are transformed onto the probability scale using the empiricalcumulative distribution function (ECDF). In the second, the observations aretransformed onto the real line, as Z-scores, using the probit function.
Usage
RankNorm(u, k = 0.375, ties.method = "average")Arguments
u | Numeric vector. |
k | Offset. Defaults to (3/8), corresponding to the Blom transform. |
ties.method | Method of breaking ties, passed to |
Value
Numeric vector of rank normalized values.
See Also
Examples
# Draw from chi-1 distributiony <- stats::rchisq(n = 1e3, df = 1)# Rank normalizez <- RankNorm(y)# Plot density of transformed measurementplot(stats::density(z))