Assess connectivity and component-bridge identifiability of a network

Reports whether the treatment network is connected and, for a disconnected network, which relative effects the additive component structure makes estimable.

Usage

cpaic_connectivity(network, tol = 1e-08)

Arguments

network: A cpaic_network() object.
tol: Numerical tolerance for the rank and null-space computations.

Value

An object of class cpaic_connectivity: a list with connected (logical), n_subnetworks, subnetworks (list of treatment-label vectors), bridging_components (components shared across sub-networks), rank and n_components, identifiable (logical: rank == n_components), null_space, estimable_components, estimable (a data frame of estimable relative effects versus the reference), and the B/C/X matrices.

Details

Two distinct questions are answered, and they are not the same (Wigle et al. 2026):

Are all component effects identified? Yes if and only if the component design matrix X = B C has full column rank (rank(X) equal to n_components). Reported as identifiable.
Is a particular relative effect estimable? Yes if and only if its contrast vector lies in the row space of X. Full column rank is sufficient but not necessary, so a rank-deficient network can still identify useful cross-sub-network contrasts. Reported per treatment in estimable (see estimable_effects()).

References

Wigle A, Beliveau A, Nikolakopoulou A, Lin L (2026). Creating Treatment and Component Hierarchies in Component Network Meta-Analysis.

Examples

net <- cpaic_network(cpaic_bin_agd, sm = "OR", inactive = "Placebo")
cpaic_connectivity(net)
#> cpaic connectivity
#>   Connected network: FALSE
#>   Sub-networks:      2
#>     [1] 3 treatments
#>     [2] 3 treatments
#>   Bridging components: A, B
#>   Component design:  rank(X) = 4 / 4 components -> all component effects identified
#>   Estimable effects: 5 / 5 vs Placebo