Konfound Sensitivity Analysis

A skill for conducting sensitivity analysis to unmeasured confounding using the konfound package. Quantifies how strong an omitted variable would need to be to invalidate causal inferences.

Quick Start

Stata

stata

* After regression
svy: regress outcome controls treatment
konfound treatment, indx("IT")
konfound treatment, indx("RIR")

R

library(konfound)
konfound(model, "treatment")

Key Concepts

Metric	Name	Interpretation
ITCV	Impact Threshold for Confounding Variable	Minimum correlation product (r_OY × r_OX) needed to nullify effect
RIR	Robustness of Inference to Replacement	% of cases that would need to be replaced to change conclusion

Key Patterns

1. Basic Sensitivity Analysis (Stata)

stata

* Run your main model
svy: regress outcome controls treatment

* Impact Threshold (ITCV)
konfound treatment, indx("IT")

* Robustness of Inference to Replacement
konfound treatment, indx("RIR")

2. Store and Export Results (Stata)

stata

* Create frames to store results
capture frame drop summary
frame create summary str20 outcome str20 exposure str6 metric ///
    double impact_threshold double rir_cases double rsq

* After running model
svy: regress pace controls treatment
estimates store main_model

* Get ITCV
estimates restore main_model
konfound treatment, indx("IT")
local itcv = r(itcv)
local uncond_itcv = r(unconitcv)
local rsq = r(Rsq)
local r_ycv = r(r_ycv)
local r_xcv = r(r_xcv)

* Get RIR
estimates restore main_model
konfound treatment, indx("RIR")
local rir = r(rir)

* Store in frame
frame summary {
    set obs 1
    replace outcome = "pace" in 1
    replace exposure = "treatment" in 1
    replace metric = "IT" in 1
    replace impact_threshold = `itcv' in 1
    replace rsq = `rsq' in 1
}

3. Compare with Observed Covariate Impacts (Stata)

stata

* Define covariates for comparison
local covariates batch_int_2-batch_int_7 leukocytes age race_2 race_3 female educ_2 educ_3

* Identify estimation sample
tempvar sample
svy: regress outcome `covariates' treatment
gen byte `sample' = e(sample)

* Compute correlations between covariates and treatment/outcome
quietly corr `covariates' treatment if `sample' == 1
matrix mat_corrx = r(C)

quietly corr `covariates' outcome if `sample' == 1
matrix mat_corry = r(C)

* Calculate impact for each covariate
local n_cov : word count `covariates'
local col = `n_cov' + 1

forvalues i = 1/`n_cov' {
    local cov : word `i' of `covariates'
    scalar corr_vx = mat_corrx[`i', `col']
    scalar corr_vy = mat_corry[`i', `col']
    local impact = scalar(corr_vx) * scalar(corr_vy)
    display "`cov': r_x = " %6.3f scalar(corr_vx) " r_y = " %6.3f scalar(corr_vy) " impact = " %6.4f `impact'
}

4. Partial Correlations (Stata)

stata

* Partial correlations (controlling for other covariates)
quietly pcorr treatment `covariates' if `sample' == 1
matrix mat_partx = r(p_corr)

quietly pcorr outcome `covariates' if `sample' == 1
matrix mat_party = r(p_corr)

* Calculate partial impact
forvalues i = 1/`n_cov' {
    local cov : word `i' of `covariates'
    scalar corr_vx = mat_partx[`i', 1]
    scalar corr_vy = mat_party[`i', 1]
    local impact = scalar(corr_vx) * scalar(corr_vy)
    display "`cov' (partial): impact = " %6.4f `impact'
}

5. R Implementation

library(konfound)
library(data.table)

# Fit model
model <- lm(outcome ~ treatment + age + race + gender + education, data = dt)

# Sensitivity analysis
sens <- konfound(model, "treatment")

# Get specific metrics
sens$itcv      # Impact threshold
sens$rir       # Robustness of inference to replacement

# Visualize
plot(sens)

6. For Survey-Weighted Models (R)

library(survey)
library(konfound)

# Create survey design
svy_design <- svydesign(id = ~1, weights = ~weight, data = dt)

# Fit weighted model
model <- svyglm(outcome ~ treatment + controls, design = svy_design)

# Extract coefficients for manual konfound calculation
coef_trt <- coef(model)["treatment"]
se_trt <- sqrt(vcov(model)["treatment", "treatment"])
n <- nrow(model$data)

# Manual ITCV calculation
t_stat <- coef_trt / se_trt
t_crit <- qt(0.975, n - length(coef(model)))
itcv <- (t_stat^2 - t_crit^2) / (t_stat^2 + n - 1)

Complete Example (Stata)

stata

*------------------------------------------------------------
* Konfound Sensitivity Analysis
*------------------------------------------------------------
version 17
clear all
set more off

use "analysis_data.dta", clear
svyset fips [pweight = wt_final2]

* Create dummy variables for factor variables
tab race3, gen(race3_)
tab educ3, gen(educ3_)
tab marital3, gen(marital3_)
tab batch_int, gen(batch_int_)
gen female = (gender_birth == 2) if !missing(gender_birth)

* Define covariates (dummies, not factors)
local control_var batch_int_2-batch_int_7 leukocytes_ic age ///
                  race3_2 race3_3 female educ3_2 educ3_3 marital3_2 marital3_3

* Create results frames
capture frame drop summary
frame create summary str20 outcome str20 exposure str6 metric ///
    double impact_threshold double unconditional_impact double rir_cases ///
    double rsq double corr_y_ov double corr_x_ov

*--- Outcome: PACE ---
tempvar sample_pace
svy: regress pace `control_var' c.n_size_hassler if !missing(n_size_hassler)
gen byte `sample_pace' = e(sample)
estimates store pace_reg

* ITCV
estimates restore pace_reg
konfound n_size_hassler, indx("IT")
local pace_it = r(itcv)
local pace_uncon = r(unconitcv)
local pace_rsq = r(Rsq)
local pace_rycv = r(r_ycv)
local pace_rxcv = r(r_xcv)

frame summary {
    local newobs = _N + 1
    quietly set obs `newobs'
    replace outcome = "pace" in `newobs'
    replace exposure = "n_size_hassler" in `newobs'
    replace metric = "IT" in `newobs'
    replace impact_threshold = `pace_it' in `newobs'
    replace unconditional_impact = `pace_uncon' in `newobs'
    replace rsq = `pace_rsq' in `newobs'
    replace corr_y_ov = `pace_rycv' in `newobs'
    replace corr_x_ov = `pace_rxcv' in `newobs'
}

* RIR
estimates restore pace_reg
konfound n_size_hassler, indx("RIR")
local pace_rir = r(rir)

frame summary {
    local newobs = _N + 1
    quietly set obs `newobs'
    replace outcome = "pace" in `newobs'
    replace exposure = "n_size_hassler" in `newobs'
    replace metric = "RIR" in `newobs'
    replace rir_cases = `pace_rir' in `newobs'
}

*--- Export ---
frame summary: export delimited using "konfound_results.csv", replace

file open fh using "konfound.ok", write replace
file close fh

Interpretation Guide

ITCV (Impact Threshold)

•ITCV = 0.10: Omitted variable must have r=0.32 with both X and Y
•ITCV = 0.25: Omitted variable must have r=0.50 with both X and Y
•Compare ITCV to observed covariate impacts to assess plausibility

RIR (Robustness of Inference to Replacement)

•RIR = 50%: Half the cases would need to be replaced with null-effect cases
•RIR = 90%: Very robust; 90% replacement needed to nullify
•Higher RIR = more robust findings

Required Packages

Stata:

stata

ssc install konfound, replace

install.packages("konfound")

Tips

•Always report both ITCV and RIR for complete picture
•Compare ITCV to observed covariate impacts for context
•Document the threshold interpretation in your paper
•Consider both raw and partial correlation impacts
•Pre-specify sensitivity thresholds if possible