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Correct a “combined table” for multiplicity **and** recompute *E*-values

Source: R/margot_correct_combined_table.R
margot_correct_combined_table.Rd

`margot_correct_combined_table()` takes the **combined_table** produced by the various *margot* models (or by your own code) and

  1. widens the confidence interval according to the chosen family–wise-error correction, **and**

  2. recalculates *E*-values (and their lower bounds) so they match the new interval.

By default it implements the single–step **Bonferroni** correction at \(\alpha = 0.05\) as advocated by VanderWeele & Mathur (2019).

Usage

margot_correct_combined_table(
  combined_table,
  adjust = c("bonferroni", "holm"),
  alpha = 0.05,
  scale = c("RD", "RR"),
  delta = 1,
  sd = 1
)

Arguments

combined_table

A data frame with *at least* the columns

  • `E[Y(1)]-E[Y(0)]` **or** `E[Y(1)]/E[Y(0)]`

  • `2.5

Extra columns (e.g. the original *E*-values) are carried through.

adjust

Multiplicity method: `"bonferroni"` (default) or `"holm"`. (Those are the two methods with strong FWER control; other `p.adjust()` flavours are deliberately **not** exposed.)

alpha

Family-wise error-rate to control. Default `0.05`.

scale

Scale to use when recomputing the *E*-value. `"RD"` (risk difference / ATE, **default**) or `"RR"` (risk ratio).

delta, sd

Arguments passed to [EValue::evalues.OLS()] when `scale = "RD"`. Ignored for `"RR"`.

Value

A data frame with the same rows (and order) as `combined_table`, but with

  • updated `2.5

  • freshly computed `E_Value` and `E_Val_bound`.

How the correction is applied

Let \(m\) be the number of rows (tests).

  • **Bonferroni** uses $$ z^* = \Phi^{-1}\!\bigl(1-\alpha/(2m)\bigr) $$ and rescales the original half-width.

  • **Holm** first step-down adjusts the (two-sided) *p*-value for each test, then back-calculates a *symmetric* CI whose coverage matches the adjusted *p*. Point estimates **never** change.

References

VanderWeele TJ, Mathur MB (2019). *Some desirable properties of the Bonferroni correction: Is the Bonferroni correction really so bad?* **Am J Epidemiol** 188(3): 617–618.