Ask whether the direct evidence on one comparison agrees with the rest

A network estimate is a weighted blend of what the head-to-head trials say and what the rest of the network implies. If those two disagree the blend is meaningless, and no global fit statistic will show it, because the blend absorbs the disagreement. Splitting the node computes them separately and tests the difference, which is the only way to localise inconsistency to an edge.

Usage

Manh2h(yi, vi, design, edge)

Arguments

yi

Contrast estimates.

vi

Their sampling variances, strictly positive.

design

Baseline and comparator treatment labels, n by 2.

edge

The comparison to split, as (baseline, comparator).

Value

List with direct, v_direct, indirect, v_indirect, diff, z, p, k_direct, k_indirect.

Details

Formula: direct is the inverse-variance pool of the studies making that comparison; indirect is the consistency-model estimate of the same contrast from all the other studies; the test is z = (direct - indirect)/sqrt(v_dir + v_ind) – Dias et al. (2010) Section 3.

References

Dias, S., Welton, N. J., Caldwell, D. M. and Ades, A. E. (2010). Statistics in Medicine 29(7-8):932-944. doi:10.1002/sim.3767 .

Examples

# three trials of 1 vs 2, one of 1 vs 3, one of 2 vs 3 (integer treatment labels)
yi <- c(0.30, 0.25, 0.35, 0.50, 0.20)
vi <- c(0.02, 0.03, 0.02, 0.04, 0.03)
design <- rbind(c(1, 2), c(1, 2), c(1, 2), c(1, 3), c(2, 3))
Manh2h(yi, vi, design, edge = c(1, 3))[c("direct", "indirect", "p")]
#> $direct
#> [1] 0.5
#> 
#> $indirect
#> [1] 0.50625
#> 
#> $p
#> [1] 0.9820885
#>