To evaluate a new biomarker as an early index of infected pancreatic necrosis, you perform the measurement in a consecutive series of 200 critically ill patients with pancreatitis. You find that 100 of these patients had subsequently proven necrosis. Of these, 60 had a positive biomarker result. Of the remaining 100 patients without necrosis, 35 had a positive biomarker result.

Using the above data, show how you would calculate

a)  Sensitivity

b)  Specificity

c)  Positive predictive value

d)  Negative predictive value

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College Answer

a)  Sensitivity = (TP/ {TP + FN}) = 60/100

b)  Specificity = (TN/{TN + FP}) = 65/100

c)  Positive predictive value = (TP/{TP+FP})  = 60/95

d)  Negative predictive value = (TN({TN+FN}) = 65/105

Discussion

Its not easy to overdo this discussion, given that the premise of this question rests in basic arithmetic. Given that the question is essentially maths, it is difficult to produce a "model answer" which is somehow an improvement on the already correct college answer (the only possible correct answer)

However, many people (myself included) are biologically unsuited to memorising equations. For this reason, a short list of equations to memorise has been compiled. Perhaps that's an improvement.

Thus, for this biomarker, we have the following spread of data:

  • 60 true positives
  • 35 false positives
  • 65 true negatives
  • 40 false negatives

a) Sensitivity: True positives / (true positives + false negatives)

= 60 / (60 + 40) = 60%

b) Specificity: True negatives / (true negatives + false positives)

= 65 / (65 + 35) = 65%

c) Positive predictive value: True positives / total positives

= 60 / (60 + 35) = 63%

d) Negative predictive value: True negatives / total negatives

= 65 / (65 + 40) = 62%