Component matching-adjusted indirect comparison (cMAIC)

Anchored MAIC generalized to a (possibly disconnected) component network. Each IPD study is reweighted with maicplus::estimate_weights() so that its requested effect-modifier moments match a common target; the resulting target-matched within-study contrasts (with bootstrap standard errors that propagate the weighting uncertainty) then replace the corresponding unadjusted aggregate contrasts. Finally cnma_bridge() combines all contrasts through the additive component model. The bridge is gated because retained aggregate edges and nonlinear marginal effects can make that synthesis incoherent.

Usage

cmaic(
  network,
  target,
  effect_modifiers = NULL,
  target_sd = NULL,
  n_boot = 500,
  min_boot_success = 0.8,
  seed = NULL,
  common = FALSE,
  random = TRUE,
  reference = NULL,
  allow_experimental_bridge = FALSE,
  allow_ipd_only_studies = FALSE
)

Arguments

network: A cpaic_network() object that includes IPD.
target: Named numeric vector (or one-row data frame / list) giving target means of the effect modifiers.
effect_modifiers: Character vector of covariates to match on (defaults to all IPD covariates). Matching only on effect modifiers is the anchored-MAIC convention.
target_sd: Optional named numeric vector of target standard deviations; when supplied, second moments are matched as well.
n_boot: Number of bootstrap resamples for the adjusted-contrast standard errors. Default 500.
min_boot_success: Minimum fraction of bootstrap resamples that must succeed for a contrast. The enforced count is max(ceiling(min_boot_success * n_boot), min(20, n_boot)), so a run with fewer than 20 requested resamples requires every resample to succeed. Below this threshold the edge is rejected rather than given a fragile standard error from a selected subset. Default 0.8.
seed: Optional RNG seed for reproducible bootstrap. The caller's global RNG state is restored on exit, so calling cmaic() does not perturb a downstream random stream.
common, random: Passed to cnma_bridge().
reference: Optional anchor (comparator) arm to use in every IPD study in which it appears, instead of inferring it from the aggregate row order.
allow_experimental_bridge: Logical. The default FALSE stops when aggregate-only edges would be combined with target-matched IPD edges, or when a non-Gaussian cMAIC contrast would be forced through an additive component model. Set TRUE only for explicitly exploratory sensitivity work; the fit records the exact approximation reasons.
allow_ipd_only_studies: Logical. The default FALSE requires every IPD study to match exactly one aggregate two-arm edge. Set TRUE to append an IPD-derived edge that has no aggregate row. Such additions are recorded in the returned fit.

Value

An object of class cpaic_maic (also inheriting cpaic_bridge structure via $bridge), with the bridged fit, per-study effective sample sizes, and the target moments. Bootstrap diagnostic fields include $bootstrap_draws, $bootstrap_summary, $bootstrap_failures, $bootstrap_failure_table, $bootstrap_mcse_method, and $bootstrap_success_rule. A threshold failure raises a cpaic_bootstrap_error condition carrying the same diagnostic information.

What the two-stage bridge does and does not adjust

Only the edges carrying individual patient data are population-adjusted to the target moments. Every aggregate-only edge keeps its published study-specific contrast, and the additive bridge then combines all edges as if they estimated the same component effects. Under effect modification they do not: an aggregate edge estimates its contrast in its own trial population, while the reweighted IPD edge estimates it at the target. The two agree only when the aggregate populations resemble the target, or when the components on those edges are not effect-modified. Treat a cross-network contrast that leans on aggregate-only edges as adjusted for the IPD part alone. Prefer cmlnmr() for a joint model whose average conditional link-scale outputs are explicitly evaluated at common target effect-modifier means.

Non-collapsibility and the additive model

cMAIC returns a marginal effect in the reweighted IPD sample, and the additive component model assumes effects add. On a non-collapsible scale (the odds ratio, the hazard ratio) marginal effects do not add, even when every conditional effect does. In one simulated target population the marginal log-odds ratios satisfied marginal(A) + marginal(B) = 0.6615 while marginal(A+B) = 0.6411; the additive model is simply false on that scale. cMAIC therefore carries an irreducible approximation error that survives perfect matching and infinite sample size. Its size is problem-specific and cannot be assumed negligible.

Marginal component effects are not generally additive; they add exactly when the standardized treatment effects remain affine in the component design. Additivity is therefore a property of the conditional link scale that the marginal scale inherits only approximately, and the error does not vanish with sample size. Where it is material, cstc() or cmlnmr(), which target a conditional effect and inherit additivity exactly, are preferable. Note also that the two-stage route combines a conditional adjusted edge with aggregate edges reported on a marginal scale, so it should be regarded as approximate.

Examples

net <- cpaic_network(cpaic_bin_agd, ipd = cpaic_bin_ipd, sm = "OR",
                     family = "binomial", ipd_covariates = "x1",
                     inactive = "Placebo")
# \donttest{
fit <- cmaic(net, target = c(x1 = 0), effect_modifiers = "x1",
             n_boot = 100, seed = 1,
             allow_experimental_bridge = TRUE)
#> Warning: cmaic() cannot form a decision-grade component bridge:
#>   - retained aggregate-only edge(s) remain in their own study populations: S1: A vs Placebo; S2: B vs Placebo; S5: A+B+C vs A+B+D
#>   - cMAIC estimates marginal binomial contrasts, which are not generally additive in the component design on a nonlinear link scale
#> Use cmlnmr() for a joint model, restrict the analysis to a design in which every edge is adjusted and the estimand is additive, or set `allow_experimental_bridge = TRUE` only for explicitly exploratory sensitivity work.
relative_effects(fit)
#> Relative effects (OR, natural scale)
#>  treatment comparator estimate estimate_link se_link lower  upper   scale     z
#>          A    Placebo    1.649         0.500   0.401 0.752  3.615 natural 1.248
#>        A+B    Placebo    2.460         0.900   0.567 0.810  7.466 natural 1.589
#>      A+B+C    Placebo    4.941         1.597   0.672 1.323 18.448 natural 2.377
#>      A+B+D    Placebo    5.324         1.672   0.666 1.443 19.647 natural 2.510
#>          B    Placebo    1.492         0.400   0.401 0.680  3.271 natural 0.999
#>      p
#>  0.212
#>  0.112
#>  0.017
#>  0.012
#>  0.318
#>   `se_link` is on the log-ratio scale; the interval is back-transformed.
effective_sample_size(fit)
#>       S3       S4 
#> 207.4202 358.1461 
# }