inner.KRV {MiRKAT}

Kernel RV Coefficient Test; Inner Function

Description

Function called when user calls function KRV. For each kernel matrix inputted into KRV, KRV runs inner.KRV on that kernel with the inputted kernel.y outcome matrix.

Usage

inner.KRV(
  y = NULL,
  X = NULL,
  adjust.type,
  kernel.otu,
  kernel.y,
  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.

kernel.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.

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

y and X (if not NULL) should all be numerical matrices or vectors with the same number of rows.

Ks should be a list of n by n matrices or a single matrix. If you have distance metric from metagenomic data, each kernel can be constructed through function D2K. Each kernel can also be constructed through other mathematical approaches.

Missing data is not permitted. Please remove all individuals with missing y, X, Ks prior to analysis

Parameter "method" only concerns how kernel specific p-values are generated. When Ks is a list of multiple kernels, omnibus p-value is computed through permutation from each individual p-value, which are calculated through method of choice.

Value

Returns a p-value for the candidate kernel matrix

pv

p-value for the candidate kernel matrix

KRV

KRV statistic for the candidate kernel matrix. Only returned if returnKRV = TRUE.

R2

R-squared for the candidate kernel matrix. Only returned if returnR2 = TRUE.

Author(s)

Haotian Zheng, Xiang Zhan, Ni Zhao

References

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.