To evaluate a new biomarker as an early index of bacteraemia, you perform the measurement in a consecutive series of 200 critically ill septic patients. You find that 100 of these patients had subsequently proven bacteraemia. Of these, 70 had a positive biomarker result. Of the remaining 100 patients without bacteraemia, 40 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

e) Positive Likelihood ratio

Bacteremia present |
Bacteremia absent |
||||

Biomarker+ |
70 |
40 |
|||

Biomarker- |
30 |
60 |
|||

100 |
100 |

## College Answer

a) Sensitivity= (TP/ {TP + FN}) = 70/100

b) Specificity= (TN/{TN + FP}) = 60/100

c) PPV = (TP/{TP+FP}) = 70/110

d) NPV = (TN({TN+FN}) = = 60/90

e) Positive likelihood ratio= Sensitivity /1-specificity = 70/40

## Discussion

This question is very similar to Question 19.1 from the first paper of 2010, and almost entirely identical to Question 29.2 from the first paper of 2008.

However, it also presents one with a 2×2 table breakdown of results, and there is the added question (e), which asks the candidate to calculate a positive likelihood ratio.

That formula, and relevant others, is presented in the helpful list of equations one must memorise for the fellowship.

Thus, going through the motions...

true positives = 70

false positives = 40

true negatives = 60

false negatives = 30

**a) Sensitivity** = True positives / ( true positives + false negatives)

= 70 / (70 + 30) = 70%

**b) Specificity** = True negatives / (true negatives + false positives)

= 60 / (60 + 40) = 60%

**c) Positive predictive value** = True positives / (true positives + false positives)

= 70 / (70 + 40) = 63.6%

**d) Negative predictive value** = True negatives / (true negatives + false negatives)

= 60 / (60+30) = 66.6%

**e) Positive Likelihood ratio **= sensitivity / (1-specificity)

= 0.7 / (1 - 0.6) = 1.75