Sensitivity & Specificity, Positive & negative predictive values

Exam Cram

• A highly sensitive test catches all of those with the disease (and some without), e.g. d-dimer

• A highly specific test is negative for all of those without the disease (and some with the disease), e.g. anti CCP

• Sensitivity = true positive / total with disease

• Specificity = true negative / total without disease

• Positive predictive value = true positive / total positive

• Negative predictive value = true negative / total negative

• Positive and negative predictive values change between populations with different ratios of disease but sensitivity and specificity don't

The tables visualise this far clearer than I can ever explain!

Sensitivity and Specificity

For me the easiest way to explain this is using a fish analogy and a table. 

Imagine you're fishing for cod. You can use a big net with small holes that will catch everything- all of the cod and lots of other things- trout, haddock, lobsters etc. This net is a highly sensitive net- it is catching everything, including all of the cod. Therefore it is a useful 'screening net'- you are happy the fish missed are unlikely to be cod. 

You can then use a second net. This net has big holes with specific cod shaped gaps. This net is excellent at not catching the animals that aren't cod as only the cod get caught in its cod shaped nets. This net is highly specific for cod (but may not catch every cod)! You are confident the fish caught with this net is cod and hence this test is better for diagnosis!

For myself, the table, figure 1, visualises the terms clearer than any explanation:

Definitions: 

1. Sensitivity refers to the proportion of the population with the disease with an appropriately positive test (true positive)

2. Specificity refers to the proportion of the population without the disease with an appropriately negative test (true negative)

3. Sensitivity & specificity remain constant against a changing prevalence

Note the prevalence of cod is 20%. If these tests were applied to a different population with a cod prevalence of 1%, sensitivity and specificity would remain constant. 

Positive and negative predictive values

Definitions: 

• Positive predictive value (PPV) refers to the group who test positive

• Negative predictive value (NPV) refers to the group who test negative

• PPV = the percentage of those with the disease who tested positive (TP/ TP +FP)

• NPV = the percentage of those without the disease who tested negative (TN / TN + FN)

Prevalence

Sensitivity and specificity are constant for an investigation, however positive and negative predictive values will CHANGE depending upon the baseline prevalence. 

Look at the total number of cod and trout in the example given, figure 1. There are 50 cod and 200 trout therefore the cod make up 20% (50/250) of the population, imagine that is the Atlantic Ocena. If we were to apply the same test to another group, for example the Pacific Ocean, the ratio of cod to trout might be 1%. This changes the PPV and NPV !  

Figure 2 below. 

The sensitivity/ specificity are constant but the PPV and NPV have changed considerably!

 Note how the PPV and NPV have changed. In the first group the baseline prevalence of cod is 20%. This changes to 53% if you test +ve and 3% if you test negative. In the second group your baseline rate is 1% and this becomes only 4% if you test positive but 0.01% if negative. 

You can see with a specificity of 80% the likelihood of disease is multiplied by roughly 4 times (not exactly), but it isn't enough to make a diagnosis. A sensitivity of 90% means this test is useful for a screening. 

Therefore, when quoting the PPV and NPV, really you must define the cohort used, quoting its prevalence of disease. Exams will commonly ask you to modify the PPV with respect to a change in prevalence. So if you colleague asks you for the positive predictive value for their patient with a  raised d-dimer, ask them in which cohort are they would like the value quoted!

References

1. Department of Health. Disease Screening - Statistics Teaching Tools - New York State Department of Health. Available at: https://www.health.ny.gov/diseases/chronic/discreen.htm#:~:text=Sensitivity%20refers%20to%20a%20test’s,have%20a%20disease%20as%20negative. (Accessed: 27 September 2024).

2. Elliott Sharp·Statistics·June 30, G.M. (2021) Statistics: Sensitivity, specificity, PPV and NPV, Sensitivity-specificity-ppv-and-npv. Available at: https://geekymedics.com/sensitivity-specificity-ppv-and-npv/ (Accessed: 26 September 2024).