Sensitivity analysis for unmeasured M-Y confounding

Randomizing the treatment does not remove mediator-outcome confounding. pmed_sensitivity() tracks one assumption, A4 (no exposure-induced mediator-outcome confounding). It biases the cross-world mean in the indirect component and leaves the total effect, which is identified from observable means, unaffected. The function adds a stated numerator bias b and reports the resulting share (indirect + b)/total over a grid.

Scope. The additive-offset model is exact for the mean-based shares: the gauge (ward_residual()) and incremental (incr_pmed()) estimands. It is not the right object for the Sobol variance share, and it is not applied to the core pmed() probability. Do not read its grid as a corrected estimate.

From components

If you have an indirect and a total effect from any source:

library(probmed)
pmed_sensitivity(indirect = 0.30, total = 0.50, threshold = 0, evalue = TRUE)

The printed result gives the tipping bias that drives the indirect effect to zero and the bias that drives the share to threshold. With evalue = TRUE it adds a coarse E-value, which needs the suggested package EValue; se (the standard error of indirect) is used only for the E-value’s interval bound.

From a fitted object

fit <- ward_residual(data.frame(A, M, Y, C))
pmed_sensitivity(fit, threshold = 0)

The default grid spans plus and minus the absolute indirect effect in 11 points; pass bias_grid to change it. The share can leave [0, 1] on the grid. That signals an implausibly large bias, not a valid share.

Incremental version

incr_sensitivity() gives the same tipping analysis per shift value delta for incr_pmed(). See Incremental P_med.

Reading the result

  1. Pick a threshold that matters substantively (zero is the usual one).
  2. Compare the tipping bias to the size of covariate effects you can name. A tipping bias larger than any measured confounder is evidence of robustness; a smaller one is not.
  3. Report the E-value, if used, as a coarse summary, not as a test.

This analysis addresses M-Y confounding only. It does not address treatment-mediator confounding, measurement error, or the boundary behavior described in Modern estimands.