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Rosenbaum Sensitivity Analysis

Source: R/matching_sensitivity.R
sensitivity_analysis.Rd

Assesses how sensitive a matched comparison is to hidden bias using Rosenbaum bounds on the Wilcoxon signed-rank statistic.

Usage

sensitivity_analysis(
  result,
  left,
  right,
  outcome_var,
  gamma = seq(1, 3, by = 0.25),
  alternative = c("greater", "less", "two.sided"),
  left_id = "id",
  right_id = "id"
)

Arguments

result

A matching_result object from match_couples() or greedy_couples()

left

Original left (treated) dataset

right

Original right (control) dataset

outcome_var

Name of the outcome column in left and right

gamma

Numeric vector of sensitivity parameters (default: seq(1, 3, by = 0.25)). Gamma = 1 means no hidden bias.

alternative

Direction of the test: "greater" (default), "less", or "two.sided"

left_id

Name of ID column in left (default: "id")

right_id

Name of ID column in right (default: "id")

Value

An S3 object of class sensitivity_analysis containing:

results

Tibble with columns: gamma, t_stat, p_upper, p_lower

n_pairs

Number of matched pairs analyzed

critical_gamma

Smallest gamma at which p_upper > 0.05

alternative

Direction of test

Details

Rosenbaum (2002, Chapter 4) bounds quantify how much hidden bias (an unobserved confounder) would be needed to explain away the observed treatment effect. The sensitivity parameter Gamma represents the maximum ratio of treatment odds between two matched units:

  • Gamma = 1: No hidden bias (standard Wilcoxon test)

  • Gamma = 2: One unit could be twice as likely to receive treatment due to an unobserved factor

The function computes upper and lower bounds on the p-value of the Wilcoxon signed-rank test under each level of hidden bias. A finding is "insensitive to bias" if p_upper remains below 0.05 even at large Gamma.

References

Rosenbaum, P.R. (2002). Observational Studies, 2nd edition. Springer.

Examples

set.seed(42)
left <- data.frame(id = 1:20, x = rnorm(20), outcome = rnorm(20, 1, 1))
right <- data.frame(id = 21:40, x = rnorm(20), outcome = rnorm(20, 0, 1))
result <- match_couples(left, right, vars = "x")
sens <- sensitivity_analysis(result, left, right, outcome_var = "outcome")
print(sens)