Bridge fragility: how much cross-sub-network drift would change a conclusion

In a disconnected network the cross-gap contrast exists only because the component effects are assumed constant across sub-networks. That assumption cannot be tested from the data, because there is no cross-gap evidence. bridge_fragility() quantifies how sensitive a requested contrast is to a violation of it.

Usage

bridge_fragility(
  object,
  treatment,
  comparator = NULL,
  newdata = NULL,
  threshold = 0,
  plausible_drift = NULL,
  ...
)

Arguments

object: A cmlnmr() fit.
treatment, comparator: The contrast to assess. comparator defaults to the fit reference.
newdata: A one-row data frame giving target effect-modifier means (required when the model has effect modifiers). The assessed contrast is the average conditional link-scale effect at those means, not a marginal standardized effect.
threshold: Decision boundary on the link scale. Default 0 (no effect).
plausible_drift: Optional per-component drift bound (link scale) at which to report the posterior probability that the conclusion is robust.
...: Unused.

Value

An object of class cpaic_fragility: the contrast, the L1 drift loading, the posterior of the bridge fragility threshold, and (if plausible_drift is given) the probability the conclusion survives it.

Details

On the linear-predictor scale the contrast is $D = m'(\beta + \Gamma x)$ with $m = C_t - C_u$. A cross-sub-network drift $\Delta$ in the component effects shifts it to $D + m'\Delta$. Bounding each component's drift by $|\Delta_c| \le d$, the worst-case shift is $d \sum_c |m_c|$, so the smallest per-component drift that moves the contrast to a decision threshold $\tau$ (default 0, on the link scale) is the bridge fragility threshold $$\mathrm{BFT} = |D - \tau| / \textstyle\sum_c |m_c|,$$ reported per posterior draw. A small BFT means a clinically trivial amount of un-testable drift would overturn the conclusion. This is a conservative worst-case over the component main-effect drift; interaction drift $\Lambda$ is not included, so the true fragility is no larger than reported.

Examples

if (FALSE) {
bridge_fragility(fit, treatment = "A+B", newdata = data.frame(x1 = 0))
}