3
$\begingroup$

I read How to calculate specificity from accuracy and sensitivity, but I have two diagnostic performance measures more. Please correct me if I am wrong: if

  • Sensitivity=TP/(TP+FN)
  • Specificity=TN/(TN+FP)
  • Positive predictive value=TP/(TP+FP)
  • Negative predictive value=TN/(TN+FN)
  • Accuracy=(TP+TN)/(TP+TN+FP+FN)
  • Cohen's kappa=1-[(1-Po)/(1-Pe)]

Can I calculate the accuracy if I know the sensitivity, specificity, positive and negative predictive values? Can I calculate the Cohen's kappa too?

Unfortunately, that situation could happen if you read an abstract of a scientific work.

(I use R)

Improve this question
$\endgroup$
2
  • 1
    $\begingroup$ Interesting question. Looking at all possible combinations of TP, TN, FP, FN, each between 0 and 30, it appears like the answer is "yes", i.e., there are no two combinations with the same sensitivities, specificities, PPVs and NPVs but different accuracies. Of course, I still argue that you should not use accuracy to evaluate a classifier at all: Why is accuracy not the best measure for assessing classification models? and Is accuracy an improper scoring rule in a binary classification setting? $\endgroup$
    – Stephan Kolassa
    Oct 27, 2018 at 14:23
  • $\begingroup$ Thank you for your comment. I do understand accuracy limitations (that is why I asked about Cohen's kappa too), but in some fields it could be a commonly used value to communicate your results. Anyway, I tried to resolve a linear system with 4 equations, but I did not work as I intended (TP, TN, FP and FN were all equal to 0), probably I did something wrong $\endgroup$
    – statisticianwannabe
    Oct 27, 2018 at 20:32

1 Answer 1

Reset to default
2
$\begingroup$

You generally know TP, FN, FP, and TN, so based on this wiki:

Po = (TP + TN) / (TP + TN + FP + FN),

Pe = ((TP + FN) * (TP + FP) + (FP + TN) * (FN + TN)) / (TP + TN + FP + FN)^2

Kappa = (Po - Pe) / (1 - Pe)

Our friend Wolfram can then help to simplify this, leading to:

Kappa = 2 * (TP * TN - FN * FP) / (TP * FN + TP * FP + 2 * TP * TN + FN^2 + FN * TN + FP^2 + FP * TN)

So in R, the function would be:

cohens_kappa <- function(TP, FN, FP, TN) {
  return(2 * (TP * TN - FN * FP) / (TP * FN + TP * FP + 2 * TP * TN + FN^2 + FN * TN + FP^2 + FP * TN))
}
Improve this answer
$\endgroup$
1
  • $\begingroup$ Thank you for your answer. Unfortunately, I generally know TP, TN, FP and FN, but sometimes I do not if I am reading an abstract of a scientific work and I have only the sensitivity, specificity, positive and negative predictive values $\endgroup$
    – statisticianwannabe
    Nov 16, 2019 at 21:30

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.