MiRKAT (version 1.2.3)

MiRKATS: Microiome Regression-based Kernel Association Test for Survival

Description

Community level test for association between microbiome composition and survival outcomes (right-censored time-to-event data) using kernel matrices to compare similarity between microbiome profiles with similarity in survival times.

Usage

MiRKATS(
  obstime,
  delta,
  X = NULL,
  Ks,
  beta = NULL,
  perm = FALSE,
  omnibus = "permutation",
  nperm = 999,
  returnKRV = FALSE,
  returnR2 = FALSE
)

Value

Return value depends on the number of kernel matrices inputted. If more than one kernel matrix is given, MiRKATS returns two items; a vector of the labeled individual p-values for each kernel matrix, as well as an omnibus p-value from the Optimal-MiRKATS omnibus test. If only one kernel matrix is given, then only its p-value will be given, as no omnibus test will be needed.

p_values

individual p-values for each inputted kernel matrix

omnibus_p

overall 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

Arguments

obstime

A numeric vector of follow-up (survival/censoring) times.

delta

Event indicator: a vector of 0/1, where 1 indicates that the event was observed for a subject (so "obstime" is survival time), and 0 indicates that the subject was censored.

X

A vector or matrix of numeric covariates, if applicable (default = NULL).

Ks

A list of or a single numeric n by n kernel matrices or matrix (where n is the sample size).

beta

A vector of coefficients associated with covariates. If beta is NULL and covariates are present, coxph is used to calculate coefficients (default = NULL).

perm

Logical, indicating whether permutation should be used instead of analytic p-value calculation (default=FALSE). Not recommended for sample sizes of 100 or more.

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

Integer, number of permutations used to calculate p-value if perm==TRUE (default=1000) and to calculate omnibus p-value if omnibus=="permutation".

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.

Author

Nehemiah Wilson, Anna Plantinga

Details

obstime, delta, and X should all have n rows, and the kernel or distance matrix should be a single n by n matrix. If a distance matrix is entered (distance=TRUE), a kernel matrix will be constructed from the distance matrix.

Update in v1.1.0: MiRKATS also utilizes the OMiRKATS omnibus test if more than one kernel matrix is provided by the user. The OMiRKATS omnibus test calculates an overall p-value for the test via permutation.

Missing data is not permitted. Please remove individuals with missing data on y, X or in the kernel or distance matrix prior to using the function.

The Efron approximation is used for tied survival times.

References

Plantinga, A., Zhan, X., Zhao, N., Chen, J., Jenq, R., and Wu, M.C. MiRKAT-S: a distance-based test of association between microbiome composition and survival times. Microbiome, 2017:5-17. doi: 10.1186/s40168-017-0239-9

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

Efron, B. (1977) "The efficiency of Cox's likelihood function for censored data." Journal of the American statistical Association 72(359):557-565.

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

Examples

###################################
# Generate data
library(GUniFrac)


# Throat microbiome data
data(throat.tree)
data(throat.otu.tab)

unifracs = GUniFrac(throat.otu.tab, throat.tree, alpha = c(1))$unifracs
if (requireNamespace("vegan")) {
 library(vegan)
 BC= as.matrix(vegdist(throat.otu.tab, method="bray"))
 Ds = list(w = unifracs[,,"d_1"], uw = unifracs[,,"d_UW"], BC = BC)
} else {
 Ds = list(w = unifracs[,,"d_1"], uw = unifracs[,,"d_UW"])
}

Ks = lapply(Ds, FUN = function(d) D2K(d))

# Covariates and outcomes
covar <- matrix(rnorm(120), nrow=60)
S <- rexp(60, 3)   # survival time 
C <- rexp(60, 1)   # censoring time 
D <- (S<=C)        # event indicator
U <- pmin(S, C)    # observed follow-up time

MiRKATS(obstime = U, delta = D, X = covar, Ks = Ks, beta = NULL)