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Asymptotic variance component test statistic and p-value

Source: R/vc_test_asym.R
vc_test_asym.Rd

This function computes an approximation of the variance component test based on the asymptotic distribution of a mixture of \(\chi^{2}\)s using the saddlepoint method from pchisqsum, as per Chen & Lumley 20219 CSDA.

Usage

vc_test_asym(
  y,
  x,
  indiv = rep(1, nrow(x)),
  phi,
  w,
  Sigma_xi = diag(ncol(phi)),
  genewise_pvals = FALSE,
  homogen_traj = FALSE,
  na.rm = FALSE
)

Arguments

y

a numeric matrix of dim g x n containing the raw or normalized RNA-seq counts for g genes from n samples.

x

a numeric design matrix of dim n x p containing the p covariates to be adjusted for

indiv

a vector of length n containing the information for attributing each sample to one of the studied individuals. Coerced to be a factor.

phi

a numeric design matrix of size n x K containing the K longitudinal variables to be tested (typically a vector of time points or functions of time)

w

numeric matrix of dim G x n containing the weights for G genes from the n samples, corresponding to the inverse of the diagonal of the estimated covariance matrix of y.

Sigma_xi

a matrix of size K x K containing the covariance matrix of the K random effects corresponding to phi.

genewise_pvals

a logical flag indicating whether gene-wise p-values should be returned. Default is FALSE in which case gene set p-value is computed and returned instead.

homogen_traj

a logical flag indicating whether trajectories should be considered homogeneous. Default is FALSE in which case trajectories are not only tested for trend, but also for heterogeneity.

na.rm

logical: should missing values (including NA and NaN) be omitted from the calculations? Default is FALSE.

Value

A list with the following elements when the set p-value is computed:

  • set_score_obs: the approximation of the observed set score

  • set_pval: the associated set p-value

or a list with the following elements when gene-wise p-values are computed:

  • gene_scores_obs: vector of approximating the observed gene-wise scores

  • gene_pvals: vector of associated gene-wise p-values

References

Chen T & Lumley T (2019), Numerical evaluation of methods approximating the distribution of a large quadratic form in normal variables, Computational Statistics & Data Analysis, 139:75-81.

See also

pchisqsum

Examples

set.seed(123)

##generate some fake data
########################
n <- 100
r <- 12
t <- matrix(rep(1:(r/4)), 4, ncol=1, nrow=r)
sigma <- 0.4
b0 <- 1

#under the null:
b1 <- 0
#under the alternative:
#b1 <- 0.5
y.tilde <- b0 + b1*t + rnorm(r, sd = sigma)
y <- t(matrix(rnorm(n*r, sd = sqrt(sigma*abs(y.tilde))), ncol=n, nrow=r) +
      matrix(rep(y.tilde, n), ncol=n, nrow=r))
x <- matrix(1, ncol=1, nrow=r)

#run test
asymTestRes <- vc_test_asym(y, x, phi=cbind(t, t^2),
                           w=matrix(1, ncol=ncol(y), nrow=nrow(y)),
                           Sigma_xi=diag(2), indiv=1:r, genewise_pvals=TRUE)
plot(density(asymTestRes$gene_pvals))

quantile(asymTestRes$gene_pvals)
#>           0%          25%          50%          75%         100% 
#> 0.0009203156 0.1781485954 0.3160782864 0.6375846661 0.9785602303