Null statistics for cascade calibration

Simulates the pooled aligned statistic under the global null for each unit shape present in the tree, so that dmsa_cascade() can convert observed statistics into calibrated p-values. Uses the supplied residual covariance structure by resampling the exposure within blocks.

Usage

dmsa_cascade_null(
  b,
  se,
  alignment,
  tree,
  exposure,
  M,
  block = NULL,
  B = 999L,
  method = c("expected", "fixed")
)

Arguments

b, se, alignment, tree

as in dmsa_cascade.

exposure

numeric exposure vector used to fit b.

M

matrix of probe values (rows = observations), used to refit under permutation.

block

optional grouping vector defining exchangeable units.

B

number of permutations.

method

pooling method.

Value

named list suitable for the nulls argument.

Examples

set.seed(1)
tree <- expand.grid(probe = 1:3, gene = 1:2, system = 1:4)
tree <- tree[, c("system", "gene")]      # outermost level first
P <- nrow(tree); n <- 60; x <- rnorm(n)
M <- matrix(rnorm(n * P), n, P)
al <- dmsa_align(data.frame(cpg = paste0("p", 1:P), d = 1, p_plus = 0.95),
                 genes = paste0("g", tree$gene), level = "gene")
fit <- lm(M ~ x); b <- coef(fit)["x", ]
se <- sqrt(colSums(residuals(fit)^2) / (n - 2) / sum((x - mean(x))^2))
# B = 49 keeps the example quick; a real calibration wants B >= 999
nulls <- dmsa_cascade_null(b, se, al, tree, exposure = x, M = M, B = 49)
vapply(nulls, length, integer(1))
#>        system          gene system_sparse 
#>           196           392           196