Borrow strength across a whole network of pairwise comparisons

Two treatments never compared head to head still have a comparison implied by the trials each has against a common third: the consistency assumption turns a set of unconnected pairwise meta-analyses into one model with T - 1 free parameters. What is bought is a comparison that no trial made; what is risked is that the assumption is false, which is why the residual heterogeneity is reported alongside.

Usage

Manlmm(yi, vi, design)

Arguments

yi

Contrast estimates: the comparator against the baseline of the same row of design.

vi

Their sampling variances, strictly positive.

design

Baseline and comparator treatment labels, n by 2.

Value

List with theta, se_theta, ranks, tau2, QE, treatments, n, T.

Details

Formula: y_i = d_{t2(i)} - d_{t1(i)} + u_i + e_i with d of the reference treatment fixed at zero, Var(u) = tau^2 common across contrasts, weights 1/(v_i + tau^2) – Salanti et al. (2008) Section 3.

References

Salanti, G., Higgins, J. P. T., Ades, A. E. and Ioannidis, J. P. A. (2008). Statistical Methods in Medical Research 17(3):279-301. doi:10.1177/0962280207080643 .

Examples

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))
Manlmm(yi, vi, design)[c("theta", "se_theta")]
#> $theta
#> [1] 0.0000000 0.3056452 0.5032258
#> 
#> $se_theta
#> [1] 0.00000000 0.08230549 0.13912167
#>