MiRKAT_continuous {MiRKAT}

Microbiome Regression-based Analysis Test for a continuous outcome variable

Description

Inner function for MiRKAT; computes MiRKAT for continuous outcomes. Called by MiRKAT if out_type="C"

Usage

MiRKAT_continuous(
  y,
  X = NULL,
  Ks,
  method,
  omnibus,
  nperm = 999,
  returnKRV = FALSE,
  returnR2 = FALSE
)

Arguments

y

A numeric vector of the continuous outcome variable

X

A numeric matrix or data frame containing additional covariates (default = NULL). If NULL, an intercept only model is used.

Ks

A list of n by n kernel matrices (or a single n by n kernel matrix), where n is the sample size. It can be constructed from microbiome data through distance metric or other approaches, such as linear kernels or Gaussian kernels.

method

A method to compute the kernel specific p-value (Default= "davies"). "davies" represents an exact method that computes the p-value by inverting the characteristic function of the mixture chisq. We adopt an exact variance component tests because most of the studies concerning microbiome compositions have modest sample size. "moment" represents an approximation method that matches the first two moments. "permutation" represents a permutation approach for p-value calculation.

omnibus

A string equal to either "Cauchy" or "permutation" (or nonambiguous abbreviations thereof), specifying whether to use the Cauchy combination test or residual permutation to generate the omnibus p-value.

nperm

the number of permutations if method = "permutation" or when multiple kernels are considered. If method = "davies" or "moment", nperm is ignored. Defaults to 999.

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

This function is called by the exported function "MiRKAT" when the argument of MiRKAT, out_type, is set equal to "C".

Each argument of MiRKAT_continuous is given the value of the corresponding argument given by the user to MiRKAT.

Function not exported

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: the individual p-values for each candidate kernel matrix, and the omnibus p-value

p_values

p-value for each candidate kernel matrix

omnibus_p

omnibus p-value considering multiple candidate kernel matrices

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)

Ni Zhao

References

Zhao, N., Chen, J.,Carroll, I. M., Ringel-Kulka, T., Epstein, M.P., Zhou, H., Zhou, J. J., Ringel, Y., Li, H. and Wu, M.C. (2015)). Microbiome Regression-based Kernel Association Test (MiRKAT). American Journal of Human Genetics, 96(5):797-807

Chen, J., Chen, W., Zhao, N., Wu, M~C.and Schaid, D~J. (2016) Small Sample Kernel Association Tests for Human Genetic and Microbiome Association Studies. 40: 5-19. doi: 10.1002/gepi.21934

Davies R.B. (1980) Algorithm AS 155: The Distribution of a Linear Combination of chi-2 Random Variables, Journal of the Royal Statistical Society. Series C , 29, 323-333.

Satterthwaite, F. (1946). An approximate distribution of estimates of variance components. Biom. Bull. 2, 110-114.

Lee S, Emond MJ, Bamshad MJ, Barnes KC, Rieder MJ, Nickerson DA; NHLBI GO Exome Sequencing Project-ESP Lung Project Team, Christiani DC, Wurfel MM, Lin X. (2012) Optimal unified approach for rare variant association testing with application to small sample case-control whole-exome sequencing studies. American Journal of Human Genetics, 91, 224-237.

Zhou, J. J. and Zhou, H.(2015) Powerful Exact Variance Component Tests for the Small Sample Next Generation Sequencing Studies (eVCTest), in submission.