Evaluation of a novel serum biomarker for the rapid diagnosis of sepsis is performed in a sample of 100 patients with fever. The biomarker is compared with positive culture results as the gold standard and yields the following information:

Sepsis present

{culture positive)

Sepsis absent

{culture negative)

Biomarker  positive

30

10

Biomarker negative

30

30

n

60

40

With reference to these results, define the following and give the values for the performance of the test:

a) Sensitivity. (20% marks)

b) Specificity. (20% marks)

c) Positive predictive value. (20% marks)

d) Negative predictive value. (20% marks)

e) Accuracy . (20% marks)

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College answer

 

Sepsis present  (culture positive)

Sepsis absent (culture negative)

 

Biomarker positive

30 (a)

10 (b)

(a + b)

Biomarker negative

30 (c)

30 (d)

(c + d)

n

60 (a + c)

40 (b + d)

(a+b+c+d)

a)    Ability of test to identify true positives 
Or the probability the test will be positive in individuals who do have the disease 
    Sensitivity          a/(a+c)          30/60      50% 
 
b)    Ability of test to identify true negatives 
Or the probability the test will be negative in individuals who do not have the disease. 
   Specificity          d/(b+d)          30/40      75% 
 
c)    Likelihood of positive test meaning patient has sepsis 
    PPV           a/(a+b)          30/40      75% 
      
 
d)    Likelihood of negative test meaning patient does not have sepsis 
    NPV           d/(c+d)          30/60      50% 
 
e)    The ability to differentiate patient and healthy cases correctly. 
    Accuracy          (a+d)/(a+b+c+d)          60/100     60% 

Additional Examiners' Comments: 
The question clearly stated that a definition was required. Many candidates either could not define the terms or just missed this part of the question and therefore missed out on marks. This question has come up a number of times in past exams and these are basic statistical concepts that some candidates clearly do not understand. 

Discussion

This question closely resembles all other previous questions about the measures of diagnostic test accuracy:

  • Question 19.2 from the first paper of 2010 (Calculate sensitivity, specificity, PPV and NPV)
  • Question 29.2 from the first paper of 2008 (Calculate sensitivity, specificity, PPV and NPV)
  • Question 15 from the first paper of 2007 (Calculate sensitivity, specificity, PPV,  NPV and PLR)
  • Question 13 from the first paper of 2005 (Define sensitivity, specificity, PPV and NPV)
  • Question 14 from the second paper of 2002 (Define sensitivity, specificity, PPV and NPV)

After being absent from the papers for over five years, one might have been forgiven for thinking that such calculator-intense statistics questions were demoted to the level of primary exam material (as most recent statistics questions in the Fellowship Exam have been more about interpretation of meta-analysis data and other such ultra-clever "fellow level" uses of EBM).  The main difference in 2016 was the addition of accuracy as one of the examined parameters. This has never been examined previously, and is not a frequently mentioned measure (even though colloquially we might use the term near-constantly). An excellent 2008 article was used to define it for the purposes of this model answer.

Clearly, at least one candidate remembered all the definitions, and got 10 marks. 

a)

  • Sensitivity = true positives / (true positives + false negatives)
  • This is the proportion of disease which was correctly identified.
  • In this case, Sn = 30 / (30 + 30) = 50%

b)

  • Specificity = true negatives / (true negatives + false positives)
  • This is the proportion of healthy patients in who disease was correctly excluded
  • In this case, Sp = 30 / (30 + 10) = 75%

c)

  • Positive Predictive Value = true positives / total positives (true and false)
  • This is the proportion of the positive tests results which are actually positive
  • In this case, PPV = 30 / (30 + 10) = 75%

d)

  • Negative Predictive Value = true negatives / total negatives (true and false)
  • This is the proportion of negative test results which are actually negative
  • In this case, NPV = 30 / (30 + 30) = 50%

e)

  • Accuracy = (true positives + true negatives) / (total)
  • This is the proportion of correctly classified subjects among all subjects
  • In this case, accuracy = (30+30) / 100 = 50%

References

Šimundić, Ana-Maria. "Measures of diagnostic accuracy: basic definitions." Med Biol Sci 22.4 (2008): 61-5.