Quantify the Robustness of Causal Inferences.
konfound
In social science (and educational) research, we often wish to understand how robust inferences about effects are to unobserved (or controlled for) covariates, possible problems with measurement, and other sources of bias. The goal of konfound is to carry out sensitivity analysis to help analysts to quantify how robust inferences are to potential sources of bias. This R package provides tools to carry out sensitivity analysis as described in Frank, Maroulis, Duong, and Kelcey (2013) based on Rubin’s (1974) causal model as well as in Frank (2000) based on the impact threshold for a confounding variable.
Installation
You can install the CRAN version of konfound with:
install.packages("konfound")
You can install the development version from GitHub with:
install.packages("devtools")
devtools::install_github("konfound-project/konfound")
Use of konfound
pkonfound() for published studies
pkonfound(), for published studies, calculates (1) how much bias there must be in an estimate to invalidate/sustain an inference; (2) the impact of an omitted variable necessary to invalidate/sustain an inference for a regression coefficient:
library(konfound)
#> Sensitivity analysis as described in Frank,
#> Maroulis, Duong, and Kelcey (2013) and in
#> Frank (2000).
#> For more information visit http://konfound-it.com.
pkonfound(est_eff = 2,
std_err = .4,
n_obs = 100,
n_covariates = 3)
#> Robustness of Inference to Replacement (RIR):
#> To invalidate an inference, 60.29 % of the estimate would have to be due to bias.
#> This is based on a threshold of 0.794 for statistical significance (alpha = 0.05).
#>
#> To invalidate an inference, 60 observations would have to be replaced with cases
#> for which the effect is 0 (RIR = 60).
#>
#> See Frank et al. (2013) for a description of the method.
#>
#> Citation: Frank, K.A., Maroulis, S., Duong, M., and Kelcey, B. (2013).
#> What would it take to change an inference?
#> Using Rubin's causal model to interpret the
#> robustness of causal inferences.
#> Education, Evaluation and
#> Policy Analysis, 35 437-460.
#> For other forms of output, run
#> ?pkonfound and inspect the to_return argument
#> For models fit in R, consider use of konfound().
konfound() for models fit in R
konfound() calculates the same for models fit in R. For example, here are the coefficients for a linear model fit with lm() using the built-in dataset mtcars:
m1 <- lm(mpg ~ wt + hp, data = mtcars)
m1
#>
#> Call:
#> lm(formula = mpg ~ wt + hp, data = mtcars)
#>
#> Coefficients:
#> (Intercept) wt hp
#> 37.22727 -3.87783 -0.03177
summary(m1)
#>
#> Call:
#> lm(formula = mpg ~ wt + hp, data = mtcars)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -3.941 -1.600 -0.182 1.050 5.854
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 37.22727 1.59879 23.285 < 2e-16 ***
#> wt -3.87783 0.63273 -6.129 1.12e-06 ***
#> hp -0.03177 0.00903 -3.519 0.00145 **
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 2.593 on 29 degrees of freedom
#> Multiple R-squared: 0.8268, Adjusted R-squared: 0.8148
#> F-statistic: 69.21 on 2 and 29 DF, p-value: 9.109e-12
Sensitivity analysis for the effect for wt on mpg can be carried out as follows, specifying the fitted model object:
konfound(m1, wt)
#> Robustness of Inference to Replacement (RIR):
#> To invalidate an inference, 66.521 % of the estimate would have to be due to bias.
#> This is based on a threshold of -1.298 for statistical significance (alpha = 0.05).
#>
#> To invalidate an inference, 21 observations would have to be replaced with cases
#> for which the effect is 0 (RIR = 21).
#>
#> See Frank et al. (2013) for a description of the method.
#>
#> Citation: Frank, K.A., Maroulis, S., Duong, M., and Kelcey, B. (2013).
#> What would it take to change an inference?
#> Using Rubin's causal model to interpret the
#> robustness of causal inferences.
#> Education, Evaluation and
#> Policy Analysis, 35 437-460.
#> NULL
mkonfound for meta-analyses including sensitivity analysis
We can use an existing (and built-in) dataset, such as mkonfound_ex.
mkonfound_ex
#> # A tibble: 30 × 2
#> t df
#> <dbl> <dbl>
#> 1 7.08 178
#> 2 4.13 193
#> 3 1.89 47
#> 4 -4.17 138
#> 5 -1.19 97
#> 6 3.59 87
#> 7 0.282 117
#> 8 2.55 75
#> 9 -4.44 137
#> 10 -2.05 195
#> # ℹ 20 more rows
mkonfound(mkonfound_ex, t, df)
#> # A tibble: 30 × 7
#> t df action inference pct_bias_to_change_i…¹ itcv r_con
#> <dbl> <dbl> <chr> <chr> <dbl> <dbl> <dbl>
#> 1 7.08 178 to_invalidate reject_null 68.8 0.378 0.614
#> 2 4.13 193 to_invalidate reject_null 50.6 0.168 0.41
#> 3 1.89 47 to_sustain fail_to_rejec… 5.47 -0.012 0.11
#> 4 -4.17 138 to_invalidate reject_null 50.3 0.202 0.449
#> 5 -1.19 97 to_sustain fail_to_rejec… 39.4 -0.065 0.255
#> 6 3.59 87 to_invalidate reject_null 41.9 0.19 0.436
#> 7 0.282 117 to_sustain fail_to_rejec… 85.5 -0.131 0.361
#> 8 2.55 75 to_invalidate reject_null 20.6 0.075 0.274
#> 9 -4.44 137 to_invalidate reject_null 53.0 0.225 0.475
#> 10 -2.05 195 to_invalidate reject_null 3.51 0.006 0.077
#> # ℹ 20 more rows
#> # ℹ abbreviated name: ¹pct_bias_to_change_inference
Other information
How to learn more about sensitivity analysis
To learn more about sensitivity analysis, please visit:
- The Introduction to konfound vignette, with detailed information about each of the functions (
pkonfound(),konfound(), andmkounfound()) - The Konfound-It! interactive web application, with links to PowerPoints and key publications
Issues, feature requests, and contributing
We prefer for issues to be filed via GitHub (link to the issues page for konfoundhere) though we also welcome questions or feedback requests via email (see the DESCRIPTION file).
Contributing guidelines are here.
Code of Conduct
Please note that the konfound project is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms.