Tutorial:
The sensitivity of a screening test tells us how likely a screening test is to correctly identify those who have the condition/ disease under consideration. The computation of sensitivity requires comparing the results of the screening test with a gold standard test- the best available test. This helps answer the question, “How likely is the screening test to correctly identify those who have disease (or the condition under consideration)?”.
When determining the sensitivity of a screening test, one must administer both the gold standard test and the screening test to the same group of individuals. One then compares the performance of the screening test against the results of the gold standard test.
This process of obtaining test results from the gold standard test and the screening test could be undertaken simultaneously (where both tests are administered at the same time), or sequentially (where the screening test is administered after the gold standard test). Regardless of the approach, one would be able to construct a 2*2 contingency table as shown below:
You might have noticed from the 2*2 contingency table that the screening test results are not 100% accurate. Sometimes the test result indicates that there is disease, when in fact, there is no disease (false positive), and vice versa (false negative). It is not possible to devise a screening test that is 100% accurate (without any false positives or false negatives). Therefore, whenever we receive the result of a screening test, we cannot be 100% certain that the results are accurate.
What we are interested in, nevertheless, is answering the question, “If the screening test result is positive, what is the chance that the person actually has the disease?”.
Explanation: A person takes a test for a disease, and receives a test report. If the test report is positive (that is, the test result indicates presence of disease), one wants to know ‘what is the chance that the person actually has disease?’.
In order to determine the possibility that a person with a positive test result actually has the disease, one has to compute the predictive accuracy of a positive test, or Positive Predictive Value (PPV). To obtain the PPV, one has to ask the question, ‘Out of all those who were test positive, how many actually had the disease (True positive)?’. Thus, the denominator is the total number of test positives, and the numerator is the number of True Positives. To compute PPV, one simply expresses the ratio of the two values as a percentage:
PPV= (a/(a+b)) *100 (%)
The PPV is only useful when the test result is positive.
When the test result is negative, one has to ask a different question: ‘If the screening test result is negative, what is the chance that the person actually does not have the disease?’.
Explanation: A person takes a test for a disease, and receives a test report. If the test result is negative (that is the test result indicates absence of disease), one wants to know ‘what is the chance that the person actually does not have disease?’.
In order to determine the possibility that a person with a negative test result actually does not have the disease, one has to compute the predictive accuracy of a negative test, or Negative Predictive Value (NPV). To obtain the NPV, one has to ask the question, ‘Out of all those who were test negative, how many actually did not have the disease (True negative)?’. Thus, the denominator is the total number of test negatives, and the numerator is the number of True Negatives. To compute NPV, one simply expresses the ratio of the two values as a percentage:
NPV= (d/(c+d)) *100 (%)
The NPV is only useful when the test result is negative.
Unlike sensitivity and specificity, PPV and NPV are influenced by the prevalence of disease. When the prevalence of disease is high, PPV is high (when more people have the disease, a positive test result is more likely to be accurate). Conversely, when the prevalence of disease is low, NPV is high (when less people have the disease, a negative test result is more likely to be accurate).
Explanation: Assume you have a talking parrot that has been trained to say ‘white’ whenever you ask it, ‘What colour coin do I have in my hand?’. The objective is to detect the white coins in a bag- each time the parrot predicts the colour correctly counts as a true positive. You place equal number of white and black coins in a bag, and take out one coin at a time. Without revealing the colour, each time you ask the parrot, ‘What colour coin do I have in my hand?’ and the parrot says, ‘White’. In this scenario, the parrot will be correct 50% of the time. If you repeat the exercise with a bag containing only white coins, however, the parrot will be correct 100% of the time. The parrot gave the same answer consistently in both scenarios. What made the difference to its predictive accuracy was the proportion of white coins in the bag. The same is true of PPV, and the converse is true for NPV.
Knowing that test results are not 100% accurate, there are a few ways to minimize errors in diagnosis. One way is to sequentially administer additional tests to those who are positive on the first test. That is, persons positive on the first test will be administered a second (different) test. Those positive on the second test will be administered a third (different) test. If the third test result is also positive, the person will be declared as having disease. This approach is used in HIV diagnosis.
Another approach is to administer the same test multiple times, albeit after a lapse of time. For instance, if the first test was not positive but there is high suspicion of the condition, the same test may be repeated after two weeks (say). If the second test is positive, the person is considered to have the condition. An example of this approach is urine pregnancy testing.
Useful Link:
Link to previous tutorial on calculation of sensitivity:
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