Build Status CRAN status # 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.

You can install konfound with:

install.packages("konfound")

You can install the development version 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 http://konfound-it.com.

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(est_eff = 2, 
          std_err = .4, 
          n_obs = 100, 
          n_covariates = 3)
#> Percent Bias Necessary to Invalidate the Inference:
#> To invalidate an inference, 60.3% 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.
#> 
#> Impact Threshold for a Confounding Variable:
#> 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 for statistical significance (alpha = 0.05).
#> 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()
#> Percent Bias Necessary to Invalidate the Inference:
#> To invalidate an inference, 66.664% of the estimate would have to be due to bias. This is based on a threshold of -1.293 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.
#> 
#> Impact Threshold for a Confounding Variable:
#> 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 for statistical significance (alpha = 0.05).
#> 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.
#> For more detailed output, consider setting `to_return` to table
#> To consider other predictors of interest, consider setting `test_all` to TRUE.

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     pct_bias_to_change_i…   itcv r_con
#>     <dbl> <int> <chr>      <chr>                         <dbl>  <dbl> <dbl>
#>  1  7.08    178 to_invali… reject_null                   68.8   0.378 0.614
#>  2  4.13    193 to_invali… reject_null                   50.6   0.168 0.41 
#>  3  1.89     47 to_sustain fail_to_reje…                  5.47 -0.012 0.11 
#>  4 -4.17    138 to_invali… reject_null                   50.3   0.202 0.449
#>  5 -1.19     97 to_sustain fail_to_reje…                 39.4  -0.065 0.255
#>  6  3.59     87 to_invali… reject_null                   41.9   0.19  0.436
#>  7  0.282   117 to_sustain fail_to_reje…                 85.5  -0.131 0.361
#>  8  2.55     75 to_invali… reject_null                   20.6   0.075 0.274
#>  9 -4.44    137 to_invali… reject_null                   53.0   0.225 0.475
#> 10 -2.05    195 to_invali… reject_null                    3.51  0.006 0.077
#> # … with 20 more rows

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/