Which population-adjusted contrasts are estimable at a target population?

Extends the row-space criterion of Wigle et al. (2026) from the component main effects to the population-adjusted estimand theta_t(x) = C_t' (beta + Gamma x). A relative effect is identified by the first-order information if and only if its augmented contrast vector (1, x) %x% (C_t - C_u) lies in the row space of the information design (see the file header for how that design is built from the IPD and aggregate evidence).

Usage

estimable_effects_at(object, newdata = NULL, reference = NULL, ...)

Arguments

object: A cpaic_mlnmr fit.
newdata: A one-row data frame giving the target population's effect-modifier values. Defaults to the covariate origin.
reference: Reference treatment. Defaults to the fit's reference.
...: Unused.

Value

A data frame with treatment, comparator, estimable, identified_by ("IPD", "aggregate", or "none") and basis ("exact", "first-order screen", or "not identified"); see the section below.

Details

Because the criterion depends on x, the estimable set can depend on the target population: a contrast estimable at the covariate origin need not be estimable in a target population where the component by effect-modifier interactions are not identified.

Strength of the guarantee

The basis column states how much the criterion actually proves for each contrast, which is not the same for every row.

"exact": The contrast is identified by individual-patient data under an injective link with no extra support-dependent nuisance, which means a binomial, poisson or gaussian IPD arm contrast. The IPD likelihood is then an ordinary regression in arm and covariates, so the within-study arm-by-covariate variation pins down m'beta and m'Gamma directly. Survival is excluded even for IPD, because its flexible baseline hazard and delayed entry add support-dependent nuisance parameters the covariate-support argument does not account for.
"first-order screen": The contrast is estimable by the linear row-space criterion, but that criterion is only a design-based screen here, not an exactness proof, so it can be optimistic. This covers two situations. Identification through aggregate arms under a nonlinear link: the aggregate likelihood is an integral over the covariate distribution, and a study pins the contrast down at a variance-weighted mean rather than at its raw covariate mean. With a log link, one aggregate study and a symmetric covariate P(x = -1) = P(x = +1) = 1/2, the arm means are exp(mu) and exp(mu + beta) cosh(gamma), so the data identify only beta + log cosh(gamma), not beta itself. And identification through aggregate arms under the identity link: this is exact only when the arms of each contributing study share a covariate distribution, so that the study intercept and the prognostic effects cancel from the contrast; cpaic does not enforce that balance, so it is reported as a screen rather than claimed exact. Verify these with prior_sensitivity().
"not identified": Not in the row space of the first-order information. Any number reported here would be the prior, not the data. These contrasts are returned as NA by relative_effects() and dropped by cpaic_ranks().

References

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