Confounding and Interaction

Confounding asks whether adjustment changes the exposure effect. Interaction asks whether the exposure effect differs across another variable.

These checks are screening aids for viewing and organising results. Use DAGs, subject-matter knowledge, and study design to decide which variables are confounders or effect modifiers. Automated change-in-estimate and interaction checks should not be used as the sole basis for model adjustment.

Which Function Should I Use?

Question	Use	Why
Could these candidate variables be confounders or effect modifiers?	`identify_confounder()`	Screens crude, adjusted, Mantel-Haenszel, and interaction signals together.
Does this planned interaction term improve the model?	`interaction_models()`	Compares models with and without `exposure:effect_modifier` using LRT or Wald tests.
Do I need a Mantel-Haenszel estimate?	`identify_confounder(method = "mh")` or `identify_confounder(method = "both")`	MH is a stratified pooled estimate for eligible binary/categorical settings, not a formal interaction-term test.

A practical workflow is:

Use DAGs, prior literature, and study design to list important variables.
Use identify_confounder() to organise screening evidence for candidate confounders or effect modifiers.
Use interaction_models() when you have a planned interaction hypothesis.
If interaction is important, consider stratified reporting with stratified_uni_reg() or stratified_multi_reg().

library(gtregression)
library(dplyr)

data("data_birthwt", package = "gtregression")

birthwt_data <- data_birthwt |>
  mutate(
    race = factor(race, levels = c(1, 2, 3),
                  labels = c("White", "Black", "Other")),
    smoke = factor(smoke, levels = c(0, 1), labels = c("No", "Yes")),
    ht = factor(ht, levels = c(0, 1), labels = c("No", "Yes")),
    low = factor(low, levels = c(0, 1), labels = c("Normal BW", "Low BW"))
  )

Identify Confounders

Use method = "change" for the model-based change-in-estimate method. Use method = "mh" or method = "both" when Mantel-Haenszel is appropriate. The output is intentionally tidy rather than publication-first.

confounder_check <- identify_confounder(
  data = birthwt_data,
  outcome = "low",
  exposure = "smoke",
  potential_confounder = c("race", "ht"),
  approach = "logit",
  method = "both"
)

confounder_check$summary

## # A tibble: 2 × 13
##   exposure candidate crude_est adjusted_est mh_est percent_change
##   <chr>    <chr>         <dbl>        <dbl>  <dbl>          <dbl>
## 1 smoke    race           2.02         3.05   3.09          51.0 
## 2 smoke    ht             2.02         2.04   2.03           0.78
## # ℹ 7 more variables: percent_change_model <dbl>, percent_change_mh <dbl>,
## #   is_confounder <lgl>, interaction_p <dbl>, is_effect_modifier <lgl>,
## #   decision <chr>, recommendation <chr>

Test Interaction

interaction_models() compares models with and without the interaction term. It is deliberately model-based and uses LRT or Wald, not Mantel-Haenszel. Use it when the interaction term is planned or supported by clinical, causal, or subject-matter reasoning.

interaction_check <- interaction_models(
  data = birthwt_data,
  outcome = "low",
  exposure = "smoke",
  effect_modifier = "race",
  covariates = c("age", "lwt"),
  approach = "logit",
  test = "LRT",
  format = "gt"
)

interaction_check$table

Outcome	Exposure	Effect modifier	Approach	Test	p-value	Alpha	Interaction?	Decision	Interpretation
Interaction screening
low	smoke	race	logit	Likelihood Ratio Test	0.319	0.050	No	No interaction	No statistical evidence of interaction between smoke and race at alpha = 0.05.
Screening aid only; interaction decisions should be interpreted with subject-matter knowledge, study design, and stratum-specific estimates.

What To Inspect

identify_confounder(): $summary, $table, and $details.
interaction_models(): $summary, $table, $p_value, $decision, and fitted model objects.
Use subject-matter knowledge with these outputs. The functions support interpretation; they do not replace the study design.

- Confounding and Interaction