| Title: | 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 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>. |
| Authors: | Zachary McCaw [aut, cre]
|
| Maintainer: | Zachary McCaw <[email protected]> |
| License: | GPL-3 |
| Version: | 1.0.1.2 |
| Built: | 2024-11-03 06:26:19 UTC |
| Source: | CRAN |
Stops evaluation if inputs are improperly formatted.
BasicInputChecks(y, G, X)BasicInputChecks(y, G, X)
y |
Numeric phenotype vector. |
G |
Genotype matrix with observations as rows, SNPs as columns. |
X |
Covariate matrix. |
None.
Conducts tests of association between the loci in G and the
untransformed phenotype y, adjusting for the model matrix X.
BAT(y, G, X = NULL, test = "Score", simple = FALSE)BAT(y, G, X = NULL, test = "Score", simple = FALSE)
y |
Numeric phenotype vector. |
G |
Genotype matrix with observations as rows, SNPs as columns. |
X |
Model matrix of covariates and structure adjustments. Should include an intercept. Omit to perform marginal tests of association. |
test |
Either Score or Wald. |
simple |
Return the p-values only? |
If simple = TRUE, returns a vector of p-values, one for each column
of G. If simple = FALSE, returns a numeric matrix, including the
Wald or Score statistic, its standard error, the Z-score, and the p-value.
set.seed(100) # Design matrix X <- cbind(1, stats::rnorm(1e3)) # Genotypes G <- replicate(1e3, stats::rbinom(n = 1e3, size = 2, prob = 0.25)) storage.mode(G) <- "numeric" # Phenotype y <- as.numeric(X %*% c(1, 1)) + stats::rnorm(1e3) # Association test p <- BAT(y = y, G = G, X = X)set.seed(100) # Design matrix X <- cbind(1, stats::rnorm(1e3)) # Genotypes G <- replicate(1e3, stats::rbinom(n = 1e3, size = 2, prob = 0.25)) storage.mode(G) <- "numeric" # Phenotype y <- as.numeric(X %*% c(1, 1)) + stats::rnorm(1e3) # Association test p <- BAT(y = y, G = G, X = X)
Convert Cauchy Random Variable to P
CauchyToP(z)CauchyToP(z)
z |
Numeric Cauchy random variable. |
Numeric p-value.
Applies the rank-based inverse normal transformation (RankNorm)
to the phenotype y. Conducts tests of association between the loci in
G and transformed phenotype, adjusting for the model matrix X.
DINT( y, G, X = NULL, k = 0.375, test = "Score", ties.method = "average", simple = FALSE )DINT( y, G, X = NULL, k = 0.375, test = "Score", ties.method = "average", simple = FALSE )
y |
Numeric phenotype vector. |
G |
Genotype matrix with observations as rows, SNPs as columns. |
X |
Model matrix of covariates and structure adjustments. Should include an 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? |
If simple = TRUE, returns a vector of p-values, one for each column
of G. If simple = FALSE, returns a numeric matrix, including the
Wald or Score statistic, its standard error, the Z-score, and the p-value.
set.seed(100) # Design matrix X <- cbind(1, stats::rnorm(1e3)) # Genotypes G <- replicate(1e3, stats::rbinom(n = 1e3, size = 2, prob = 0.25)) storage.mode(G) <- "numeric" # Phenotype y <- exp(as.numeric(X %*% c(1, 1)) + stats::rnorm(1e3)) # Association test p <- DINT(y = y, G = G, X = X)set.seed(100) # Design matrix X <- cbind(1, stats::rnorm(1e3)) # Genotypes G <- replicate(1e3, stats::rbinom(n = 1e3, size = 2, prob = 0.25)) storage.mode(G) <- "numeric" # Phenotype y <- exp(as.numeric(X %*% c(1, 1)) + stats::rnorm(1e3)) # Association test p <- DINT(y = y, G = G, X = X)
Fits the standard OLS model.
FitOLS(y, X)FitOLS(y, X)
y |
Nx1 Numeric vector. |
X |
NxP Numeric matrix. |
List containing the following:
Beta |
Regression coefficient. |
V |
Outcome variance. |
Ibb |
Information matrix for beta. |
Resid |
Outcome residuals. |
Two-stage association testing procedure. In the first stage, phenotype
y and genotype G are each regressed on the model matrix
X to obtain residuals. The phenotypic residuals are transformed
using RankNorm. In the next stage, the INT-transformed
residuals are regressed on the genotypic residuals.
IINT(y, G, X = NULL, k = 0.375, ties.method = "average", simple = FALSE)IINT(y, G, X = NULL, k = 0.375, ties.method = "average", simple = FALSE)
y |
Numeric phenotype vector. |
G |
Genotype matrix with observations as rows, SNPs as columns. |
X |
Model matrix of covariates and structure adjustments. Should include an 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? |
If simple = TRUE, returns a vector of p-values, one for each column
of G. If simple = FALSE, returns a numeric matrix, including the
Wald or Score statistic, its standard error, the Z-score, and the p-value.
set.seed(100) # Design matrix X <- cbind(1, stats::rnorm(1e3)) # Genotypes G <- replicate(1e3, stats::rbinom(n = 1e3, size = 2, prob = 0.25)) storage.mode(G) <- "numeric" # Phenotype y <- exp(as.numeric(X %*% c(1,1)) + stats::rnorm(1e3)) # Association test p <- IINT(y = y, G = G, X = X)set.seed(100) # Design matrix X <- cbind(1, stats::rnorm(1e3)) # Genotypes G <- replicate(1e3, stats::rbinom(n = 1e3, size = 2, prob = 0.25)) storage.mode(G) <- "numeric" # Phenotype y <- exp(as.numeric(X %*% c(1,1)) + stats::rnorm(1e3)) # Association test p <- IINT(y = y, G = G, X = X)
Association test that synthesizes the DINT and
IINT tests. The first approach is most powerful for traits that
could have arisen from a rank-preserving transformation of a latent normal
trait. The second approach is most powerful for traits that are linear in
covariates, yet have skewed or kurtotic residual distributions. During the
omnibus test, the direct and indirect tests are separately applied, then the
p-values are combined via the Cauchy combination method.
OINT( y, G, X = NULL, k = 0.375, ties.method = "average", weights = c(1, 1), simple = FALSE )OINT( y, G, X = NULL, k = 0.375, ties.method = "average", weights = c(1, 1), simple = FALSE )
y |
Numeric phenotype vector. |
G |
Genotype matrix with observations as rows, SNPs as columns. |
X |
Model matrix of covariates and structure adjustments. Should include an 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? |
A numeric matrix of p-values, three for each column of G.
set.seed(100) # Design matrix X <- cbind(1, rnorm(1e3)) # Genotypes G <- replicate(1e3, rbinom(n = 1e3, size = 2, prob = 0.25)) storage.mode(G) <- "numeric" # Phenotype y <- exp(as.numeric(X %*% c(1, 1)) + rnorm(1e3)) # Omnibus p <- OINT(y = y, G = G, X = X, simple = TRUE)set.seed(100) # Design matrix X <- cbind(1, rnorm(1e3)) # Genotypes G <- replicate(1e3, rbinom(n = 1e3, size = 2, prob = 0.25)) storage.mode(G) <- "numeric" # Phenotype y <- exp(as.numeric(X %*% c(1, 1)) + rnorm(1e3)) # Omnibus p <- OINT(y = y, G = G, X = X, simple = TRUE)
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 Cauchy random 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>.
OmniP(p, w = NULL)OmniP(p, w = NULL)
p |
Numeric vector of p-values. |
w |
Numeric weight vector. |
OINT p-value.
Partition y and X according to the missingness pattern of g.
PartitionData(e, g, X)PartitionData(e, g, X)
e |
Numeric residual vector. |
g |
Genotype vector. |
X |
Model matrix of covariates. |
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
PtoCauchy(p)PtoCauchy(p)
p |
Numeric p-value. |
Numeric Cauchy random variable.
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, the observations are transformed onto the probability scale using the empirical cumulative distribution function (ECDF). In the second, the observations are transformed onto the real line, as Z-scores, using the probit function.
RankNorm(u, k = 0.375, ties.method = "average")RankNorm(u, k = 0.375, ties.method = "average")
u |
Numeric vector. |
k |
Offset. Defaults to (3/8), corresponding to the Blom transform. |
ties.method |
Method of breaking ties, passed to |
Numeric vector of rank normalized values.
# Draw from chi-1 distribution y <- stats::rchisq(n = 1e3, df = 1) # Rank normalize z <- RankNorm(y) # Plot density of transformed measurement plot(stats::density(z))# Draw from chi-1 distribution y <- stats::rchisq(n = 1e3, df = 1) # Rank normalize z <- RankNorm(y) # Plot density of transformed measurement plot(stats::density(z))