Two-Group t Tests of Every Row, With Permutation p-Values on a GPU

Tests every row of x (every gene of an expression matrix, say) for a difference in mean between two groups of columns, as t.test does one row at a time, and optionally gives each test a permutation p-value and a p-value adjusted for testing all the rows, by Westfall and Young's maxT. The permutations run on the GPU, every row under every relabelling of the samples at once.

Usage

gpuRowTtest(x, group, var.equal = FALSE, B = 0L,
    precision = getOption("gputools.precision", "single"))

Arguments

x: a numeric matrix, a row per variable (gene), a column per sample, with no missing values.
group: the samples' groups: a vector or factor with one entry per column of x and exactly two levels, at least two samples in each.
var.equal: FALSE for Welch's test, TRUE for Student's with the variances pooled, as in t.test.
B: the number of permutations, or 0 for none.
precision: "single" or "double": the floating point precision the GPU computes the permutations in; see gpuCor.

Details

The t statistics, degrees of freedom and parametric p-values are those of t.test(x[i, group == level1], x[i, group == level2], var.equal = var.equal), the first level's mean minus the second's. They are computed in double precision on the CPU: a t test of each row is too little work to be worth sending to the GPU.

With B > 0, the samples' labels are permuted B times (drawn with sample.int, so set.seed makes them reproducible) and every row's t statistic is computed under each permutation, on the GPU: two matrix products give every row's group sums and sums of squares under all the labellings. A row's permutation p-value is \((1 + b) / (1 + B)\) with \(b\) the permutations giving \(|t_b| \ge |t|\) (Phipson and Smyth 2010); its adjusted p-value counts the permutations whose largest \(|t_b|\) over all the rows reaches \(|t|\): single-step maxT, which controls the family-wise error rate (Westfall and Young 1993). Permuting the labels keeps the dependence between genes, which the adjustment exploits, and makes no assumption of normality.

A constant row, or one constant within both groups, has no test: its statistic is NaN and its p-values NA.

Value

A data frame, a row per row of x, named as x's rows:

mean1, mean2: the groups' means.
statistic: the t statistic.
df: its degrees of freedom.
p.value: the two-sided p-value from the t distribution.
p.perm: with B > 0, the permutation p-value.
p.adjusted: with B > 0, the maxT adjusted p-value.

References

Westfall, P. H. and Young, S. S. (1993) Resampling-Based Multiple Testing. Wiley.

Phipson, B. and Smyth, G. K. (2010) Permutation p-values should never be zero. Statistical Applications in Genetics and Molecular Biology 9, 39.

Examples

if (FALSE) { # gpuAvailable()
set.seed(1)
genes <- matrix(rnorm(2000 * 12), 2000, 12,
                dimnames = list(paste0("g", 1:2000), NULL))
group <- rep(c("treated", "control"), each = 6)
genes[1:5, group == "treated"] <- genes[1:5, group == "treated"] + 3
res <- gpuRowTtest(genes, group, B = 5000)
head(res[order(res$p.adjusted), ])
}