Quantify the Robustness of Causal Inferences

Statistical methods that quantify the conditions necessary to alter inferences, also known as sensitivity analysis, are becoming increasingly important to a variety of quantitative sciences. A series of recent works, including Frank (2000) and Frank et al. (2013) extend previous sensitivity analyses by considering the characteristics of omitted variables or unobserved cases that would change an inference if such variables or cases were observed. These analyses generate statements such as "an omitted variable would have to be correlated at xx with the predictor of interest (e.g., treatment) and outcome to invalidate an inference of a treatment effect". Or "one would have to replace pp percent of the observed data with null hypothesis cases to invalidate the inference". We implement these recent developments of sensitivity analysis and provide modules to calculate these two robustness indices and generate such statements in R. In particular, the functions konfound(), pkonfound() and mkonfound() allow users to calculate the robustness of inferences for a user's own model, a single published study and multiple studies respectively.


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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 konfound with:

install.packages("konfound")

You can install the development version from GitHub with:

install.packages("devtools")
devtools::install_github("jrosen48/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)
#> 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/

News

konfound 0.1.2

  • Thanks to J. Murphy for pointing out a bug in how mkonfound works for lme4 output, a bug in the code of konfound-lm related to when the message is displayed when all coefficients are tested, and suggesting to add the name of the variable to the data frame returned when all variables are tested

konfound 0.1.1

  • Update license to include our names

konfound 0.1.0

  • Added a NEWS.md file to track changes to the package.

Reference manual

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install.packages("konfound")

0.1.2 by Joshua M Rosenberg, 2 months ago


https://github.com/jrosen48/konfound


Report a bug at https://github.com/jrosen48/konfound/issues


Browse source code at https://github.com/cran/konfound


Authors: Joshua M Rosenberg [aut, cre] , Ran Xu [ctb] , Kenneth A Frank [ctb]


Documentation:   PDF Manual  


MIT + file LICENSE license


Imports broom, dplyr, ggplot2, margins, pbkrtest, purrr, rlang, tidyr

Suggests devtools, forcats, knitr, lme4, rmarkdown, roxygen2, testthat, mice


See at CRAN