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

Presently, konfound is available only on GitHub. You can install konfound from GitHub with:

install.packages("devtools")
devtools::install_github("jrosen48/konfound")
#> Loading konfound
#> Sensitivity analysis as described in Frank, Maroulis, Duong, and Kelcey (2013) and in Frank (2000).
#> For more information visit https://jmichaelrosenberg.shinyapps.io/shinykonfound/.

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)
pkonfound(2, .4, 100, 3)
#> Replacement of Cases Approach:
#> To invalidate the inference, 60.3% of the estimate would have to be due to bias based on a threshold of 0.794 and statistical significance.
#> To invalidate the inference, 60 observations would have to be replaced with cases for which the effect is 0.
#> 
#> Correlation-based Approach:
#> An omitted variable would have to be correlated at 0.568 with the outcome and at 0.568 with the predictor of interest (conditioning on observed covariates) to invalidate an inference based on a threshold of 0.201 and statistical significance.
#> Correspondingly the impact of an omitted variable (as defined in Frank 2000) must be 0.568 X 0.568 = 0.323 to invalidate an inference.
#> For other forms of output, change `to_return` to table, raw_output, thres_plot, or corr_plot.
#> 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)
#> Note that this output is calculated based on the correlation-based approach used in mkonfound()
#> Replacement of Cases Approach:
#> To invalidate the inference, 66.664% of the estimate would have to be due to bias based on a threshold of -1.293 and statistical significance.
#> To invalidate the inference, 21 observations would have to be replaced with cases for which the effect is 0.
#> 
#> Correlation-based Approach:
#> An omitted variable would have to be correlated at 0.787 with the outcome and at 0.787 with the predictor of interest (conditioning on observed covariates) to invalidate an inference based on a threshold of -0.36 and statistical significance.
#> Correspondingly the impact of an omitted variable (as defined in Frank 2000) must be 0.787 X 0.787 = 0.619 to invalidate an inference.
#> NULL

mkonfound for meta-analyses including sensitivity analysis

We can use an existing dataset, such as the CSV file here.

d <- read.csv("https://msu.edu/~kenfrank/example%20dataset%20for%20mkonfound.csv")
head(d)
#>           t  df
#> 1  7.076763 178
#> 2  4.127893 193
#> 3  1.893137  47
#> 4 -4.166395 138
#> 5 -1.187599  97
#> 6  3.585478  87
mkonfound(d, t, df)
#> # A tibble: 30 x 7
#>            t    df        action           inference
#>        <dbl> <int>         <chr>               <chr>
#>  1  7.076763   178 to_invalidate         reject_null
#>  2  4.127893   193 to_invalidate         reject_null
#>  3  1.893137    47    to_sustain fail_to_reject_null
#>  4 -4.166395   138 to_invalidate         reject_null
#>  5 -1.187599    97    to_sustain fail_to_reject_null
#>  6  3.585478    87 to_invalidate         reject_null
#>  7  0.281938   117    to_sustain fail_to_reject_null
#>  8  2.549647    75 to_invalidate         reject_null
#>  9 -4.436048   137 to_invalidate         reject_null
#> 10 -2.045373   195 to_invalidate         reject_null
#> # ... with 20 more rows, and 3 more variables:
#> #   pct_bias_to_change_inference <dbl>, itcv <dbl>, r_con <dbl>

Other information

How to learn more about sensitivity analysis

To learn more about sensitivity analysis, please visit:

Feedback, issues, and feature requests

We prefer for issues to be filed via GitHub (link to the issues page for konfound here) though we also welcome questions or feedback via email.

Code of Conduct

Please note that this project is released with a Contributor Code of Conduct available at http://contributor-covenant.org/version/1/0/0/