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Sensitivity and specificity explained: A Cochrane UK Trainees blog

Posted on 28th November 2019 by

Tutorials and Fundamentals
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This blog has been written by Saul Crandon, an Academic Foundation Doctor at Oxford University Hospitals NHS Foundation Trust, former S4BE blogger and now one of the members of the Cochrane UK & Ireland Trainees Advisory Group (CUKI-TAG). The blog, originally posted on Cochrane UK’s website, explains what we mean by – and how to calculate – ‘sensitivity’, ‘specificity’, ‘positive predictive value’ and ‘negative predictive value’ in the context of diagnosing disease. 


The diagnostic process is a crucial part of medical practice. Some consider the diagnosis process an art, as described by its Merriam Webster definition; “the art or act of identifying a disease from its signs and symptoms”.

In order to arrive at a diagnosis, one must consider a myriad of information, often in the form of the history (which describes the symptoms the patient is experiencing) and a clinical examination (which elicits the signs related to the disease process). This usually provides a sensible list of differential diagnoses, which can be confirmed or reputed with the use of diagnostic testing. This may be in the form of a blood sampling, radiological imaging, urine testing and more.

Here is the crux; tests are never 100% accurate. We must consider the statistics around testing to determine what makes a good test and what makes a not-so-good test.

Consider the following example:

A company creates a blood test for Disease X.

                                                    Has Disease X         Doesn’t have Disease X

Blood test POSITIVE          True Positives (TP)     False Positives (FP)

Blood test NEGATIVE        False Negatives (FN)  True Negatives (TN)

Now let’s look at the same table, inserting some values to work with.

                                                    Has Disease X         Doesn’t have Disease X

Blood test POSITIVE                   134                                   7

Blood test NEGATIVE                  11                                    245

Sensitivity

Sensitivity is the proportion of people WITH Disease X that have a POSITIVE blood test. A test that is 100% sensitive means all diseased individuals are correctly identified as diseased i.e. there are no false negatives. Importantly, as the calculation involves all patients with the disease, it is not affected by the prevalence of the disease.

“If I have Disease X, what is the likelihood I will test positive for it?”   

Mathematically, this is expressed as:

Sensitivity = True Positives / (True Positives + False Negatives)

= TP / (TP + FN)
= 134 / (134 + 11)
= 134 / 145
= 0.924  x 100
Sensitivity = 92.4%

In other words, the company’s blood test identified 92.4% of those WITH Disease X.

A sensitive test is used for excluding a disease, as it rarely misclassifies those WITH a disease as being healthy. An example of a highly sensitive test is D-dimer (measured using a blood test). In patients with a low pre-test probability, a negative D-dimer test can accurately exclude a thrombus (blood clot).

Specificity

Specificity is the proportion of people WITHOUT Disease X that have a NEGATIVE blood test. A test that is 100% specific means all healthy individuals are correctly identified as healthy, i.e. there are no false positives.

“If I do not have disease X, what is the likelihood I will test negative for it?”

Mathematically, this is expressed as:

Specificity = True Negatives / (True Negatives + False Positives)

= TN / (TN + FP)
= 245 / (245 + 7)
= 245 / 252
= 0.972 x 100
Specificity = 97.2%

In other words, the company’s blood test identified 97.2% of those WITHOUT Disease X.

A specific test is used for ruling in a disease, as it rarely misclassifies those WITHOUT a disease as being sick. A perfectly specific test therefore means no healthy individuals are identified as diseased.

Additional measures

We can take this a step further. The predictive value of tests can be calculated with similar statistical concepts. For the sake of simplicity, we will continue to use the example above regarding a blood test for Disease X.

Positive Predictive Value

Positive Predictive Value (PPV) is the proportion of those with a POSITIVE blood test that have Disease X.

“If I have a positive test, what is the likelihood I have disease X?”

PPV = True Positives / (True Positives + False Positives)

= TP / (TP + FP)
= 134 / (134 + 7)
= 134 / 141
= 0.950 x 100
PPV = 95%

In other words, the blood test identified 95% of those with a POSITIVE blood test, as having Disease X.

As the calculation for PPV and NPV includes individuals with and without the disease, it is affected by the prevalence of the disease in question. Therefore you must ensure that the same population is used (or the incidence of the disease is the same between the populations) when comparing PPV and NPV for different tests.

Negative Predictive Value

Negative Predictive Value (NPV) is the proportion of those with a NEGATIVE blood test that do not have Disease X.

“If I have a negative test, what is the likelihood I do not have Disease X”

NPV = True Negatives / (True Negatives + False Negatives)

= TN / (TN + FN)
= 245 / (245 + 11)
= 245 / 256
= 0.957
NPV = 95.7%

In other words, the blood test identified 95.7% of those with a NEGATIVE blood test, as not having Disease X.

Note

The example used in this article depicts a fictitious test with a very high sensitivity, specificity, positive and negative predictive values. In real scenarios, it is often challenging to create a test with maximal precision in all four areas and often improvements in one area are subject to sacrificing accuracy in other areas.

Summary

Diagnostic testing is a fundamental component of effective medical practice. You should now feel comfortable with the concepts behind binary clinical tests. Both sensitivity and specificity as well as positive and negative predictive values are important metrics when discussing tests. If you would like to read further into this topic, we recommend starting with Receiver Operating Characteristic (ROC) curves. This concept is beyond the scope of this article.


If you found this article helpful, feel free to share it and keep an eye out for other blogs by the Cochrane UK and Ireland Trainee Group (CUKI-TAG).

References (pdf)

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Saul Crandon

Saul is an Internal Medicine Trainee at NHS Greater Glasgow & Clyde. He also holds Honorary Clinical Lecturer status at the University of Glasgow as part of his role within the Glasgow Academic Training Environment (GATE). He has previously worked as a doctor in both the UK and Australia. He graduated from the University of Liverpool in 2018 after being awarded an intercalated Masters of Research degree (Distinction) from the University of Leeds in 2017. Saul is currently serving his fourth year on the committee for the Cochrane UK & Ireland Trainees Advisory Group. Before joining CUKI-TAG, he was a Students4BestEvidence Pioneer, producing a catalogue of articles and tutorials on research methodology. He has a strong interest in the education and promotion of evidence-based medicine. View more posts from Saul

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No Comments on Sensitivity and specificity explained: A Cochrane UK Trainees blog

  • Regina Agbulu

    Hi,
    Thanks for this.
    Please a quick question – I’m doing a dta and I come across an systematic review article with a series of sensitivities and specificities etc from other publications and studies which had been brought together by the current authors.
    A) is it possible for one to find “an average” of these sensitivities / spec/ npv /ppv

    B)if it is possible, how can I do this.

    Thanks and regards,
    Gina

    23rd February 2022 at 2:46 pm
    Reply to Regina
    • Emma Carter

      Hi Regina. This is a very specialist topic and one that I’m afraid wouldn’t be a straight forward answer (and certainly not from me!). However, there is a specific chapter within the Cochrane Diagnostic Test Accuracy Handbook on this topic, which you can find details of here: https://methods.cochrane.org/sdt/handbook-dta-reviews Apparently chapter 10 will be the most useful to you. We would recommend expert statistician input if you are looking to do a DTA with meta analysis. Best of luck! Emma.

      24th February 2022 at 2:42 pm
      Reply to Emma

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