KRV {MiRKAT}

Kernel RV Coefficient Test (KRV)

Description

Kernel RV coefficient test to evaluate the overall association between microbiome composition and high-dimensional or structured phenotype or genotype.

Usage

KRV(
  y = NULL,
  X = NULL,
  adjust.type = NULL,
  kernels.otu,
  kernel.y,
  omnibus = "kernel_om",
  returnKRV = FALSE,
  returnR2 = FALSE
)

Arguments

y

A numeric n by p matrix of p continuous phenotype variables and sample size n (default = NULL). If it is NULL, a phenotype kernel matrix must be entered for "kernel.y". Defaults to NULL.

X

A numeric n by q matrix, containing q additional covariates (default = NULL). If NULL, an intercept only model is used. If the first column of X is not uniformly 1, then an intercept column will be added.

adjust.type

Possible values are "none" (default if X is null), "phenotype" to adjust only the y variable (only possible if y is a numeric phenotype matrix rather than a pre-computed kernel), or "both" to adjust both the X and Y kernels.

kernels.otu

A numeric OTU n by n kernel matrix or a list of matrices, where n is the sample size. It can be constructed from microbiome data, such as by transforming from a distance metric.

kernel.y

Either a numerical n by n kernel matrix for phenotypes or a method to compute the kernel of phenotype. Methods are "Gaussian" or "linear". A Gaussian kernel (kernel.y="Gaussian") can capture the general relationship between microbiome and phenotypes; a linear kernel (kernel.y="linear") may be preferred if the underlying relationship is close to linear.

omnibus

A string equal to either "Cauchy" or "kernel_om" (or unambiguous abbreviations thereof), specifying whether to use the Cauchy combination test or an omnibus kernel to generate the omnibus p-value.

returnKRV

A logical indicating whether to return the KRV statistic. Defaults to FALSE.

returnR2

A logical indicating whether to return the R-squared coefficient. Defaults to FALSE.

Details

kernels.otu should be a list of numerical n by n kernel matrices, or a single n by n kernel matrix, where n is sample size.

When kernel.y is a method ("Gaussian" or "linear") to compute the kernel of phenotype, y should be a numerical phenotype matrix, and X (if not NULL) should be a numeric matrix of covariates. Both y and X should have n rows.

When kernel.y is a kernel matrix for the phenotype, there is no need to provide X and y, and they will be ignored if provided. In this case, kernel.y and kernel.otu should both be numeric matrices with the same number of rows and columns.

Missing data is not permitted. Please remove all individuals with missing kernel.otu, y (if not NULL), X (if not NULL), and kernel.y (if a matrix is entered) prior to analysis.

Value

If only one candidate kernel matrix is considered, returns a list containing the p-value for the candidate kernel matrix. If more than one candidate kernel matrix is considered, returns a list of two elements:

p_values

P-value for each candidate kernel matrix

omnibus_p

Omnibus p-value

KRV

A vector of kernel RV statistics (a measure of effect size), one for each candidate kernel matrix. Only returned if returnKRV = TRUE

R2

A vector of R-squared statistics, one for each candidate kernel matrix. Only returned if returnR2 = TRUE

Author(s)

Nehemiah Wilson, Haotian Zheng, Xiang Zhan, Ni Zhao

References

Zheng, Haotian, Zhan, X., Plantinga, A., Zhao, N., and Wu, M.C. A Fast Small-Sample Kernel Independence Test for Microbiome Community-Level Association Analysis. Biometrics. 2017 Mar 10. doi: 10.1111/biom.12684.

Liu, Hongjiao, Ling, W., Hua, X., Moon, J.Y., Williams-Nguyen, J., Zhan, X., Plantinga, A.M., Zhao, N., Zhang, A., Durazo-Arzivu, R.A., Knight, R., Qi, Q., Burk, R.D., Kaplan, R.C., and Wu, M.C. Kernel-based genetic association analysis for microbiome phenotypes identifies host genetic drivers of beta-diversity. 2021+

Examples

        
library(GUniFrac)
library(MASS)

data(throat.tree)
data(throat.otu.tab)
data(throat.meta)

## Simulate covariate data 
set.seed(123)
n = nrow(throat.otu.tab)
Sex <- throat.meta$Sex
Smoker <- throat.meta$SmokingStatus
anti <- throat.meta$AntibioticUsePast3Months_TimeFromAntibioticUsage
Male = (Sex == "Male")**2
Smoker = (Smoker == "Smoker") **2
Anti =  (anti != "None")^2
cova = cbind(1, Male, Smoker, Anti)

## Simulate microbiome data
otu.tab.rff <- Rarefy(throat.otu.tab)$otu.tab.rff
unifracs <- GUniFrac(otu.tab.rff, throat.tree, alpha=c(0, 0.5, 1))$unifracs
# Distance matrices
D.weighted = unifracs[,,"d_1"]
D.unweighted = unifracs[,,"d_UW"]
# Kernel matrices 
K.weighted = D2K(D.weighted)
K.unweighted = D2K(D.unweighted)

if (requireNamespace("vegan")) {
 library(vegan)
 D.BC = as.matrix(vegdist(otu.tab.rff, method="bray"))
 K.BC = D2K(D.BC)
} 

# Simulate phenotype data 
rho = 0.2
Va = matrix(rep(rho, (2*n)^2), 2*n, 2*n)+diag(1-rho, 2*n)
Phe = mvrnorm(n, rep(0, 2*n), Va)  
K.y = Phe %*% t(Phe)  # phenotype kernel 

# Simulate genotype data
G = matrix(rbinom(n*10, 2, 0.1), n, 10) 
K.g = G %*% t(G)  # genotype kernel


## Unadjusted analysis (microbiome and phenotype)
KRV(y = Phe, kernels.otu = K.weighted, kernel.y = "Gaussian")  # numeric y 
KRV(kernels.otu = K.weighted, kernel.y = K.y)  # kernel y 

## Adjusted analysis (phenotype only)
KRV(kernels.otu = K.weighted, y = Phe, kernel.y = "linear", X = cova, adjust.type = "phenotype")

if (requireNamespace("vegan")) {
  ## Adjusted analysis (adjust both kernels; microbiome and phenotype) 
  KRV(kernels.otu = K.BC, kernel.y = K.y, X = cova, adjust.type='both')

  ## Adjusted analysis (adjust both kernels; microbiome and genotype)
  KRV(kernels.otu = K.BC, kernel.y = K.g, X = cova, adjust.type='both')
}