S
& S
–
J
E XPLAIN THE CONCEPTS OF SENSITIVITY AND SPECIFICITY AS MEASURES OF TEST ACCURACY .............................. 1
U NDERSTAND THE BASIS FOR B AYES
’
THEOREM AND ITS USE IN THE CALCULATION OF LIKELIHOOD RATIOS AND
PREDICTIVE VALUES .................................................................................................................................................. 2
R EFERENCES .............................................................................................................................................................. 4
XPLAIN THE CONCEPTS OF SENSITIVITY AND SPECIFICITY AS MEASURES OF TEST ACCURACY
Sensitivity is a measure of the ability of a test to correctly identify people with disease. That is, the ability to correctly confirm the people who have a disease out of all the people who return a positive result on a test.
=
𝑇𝑟𝑢𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒𝑠
𝑇𝑟𝑢𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒𝑠 + 𝑓𝑎𝑙𝑠𝑒 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒𝑠
= 𝑎 𝑎 + 𝑐
Specificity is a measure of the ability of a test to correctly identify people without disease. That is, the ability to correctly confirm the people who do not have a disease out of all the people who return a negative result on a test.
=
𝑇𝑟𝑢𝑒 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒𝑠
𝑇𝑟𝑢𝑒 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒𝑠 + 𝑓𝑎𝑙𝑠𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒𝑠
= 𝑑 𝑏 + 𝑑
Positive test result
Negative test result
Disease present
True positive
False negative
Disease absent
False positive
True negative
Disease present a
Disease absent b Positive test result
Negative test result c d
Jess Q – Week 16 – Just My Annual Check Up Page 1

NDERSTAND THE BASIS FOR
AYES
THEOREM AND ITS USE IN THE CALCULATION OF LIKELIHOOD RATIOS AND
PREDICTIVE VALUES
(The parts that you really need are in bold – the rest is if you would like to know how it is calculated

)
Positive Predictive Value = a function that combines sensitivity, specificity and the prevalence of the condition
The extent to which the test identifies people with the disease (what proportion of people with a positive test results will have the disease
= 𝑡𝑟𝑢𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒𝑠 𝑡𝑟𝑢𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒𝑠 + 𝑓𝑎𝑙𝑠𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒𝑠
= 𝑎 𝑎 + 𝑏
NB: I have put down the explanation of how the PPV works in relation to Bayes theorem, however the lecturer specifically said that he never really understood the concept and that he just used the above formula for calculations.
But, if you would like to know, then……
Bayes’ theorem gives the relationship between the probabilities of A and B, where P(A) and P(B) are the probabilities of A and B occurring and P(A│B) is the probability of A occurring given that B does occur and P (B│A) is the probability of B occurring given that A does occur.
For example,
Suppose a drug test is 99% sensitive and 99% specific. That is, the test will produce 99% true positive results for drug users and 99% true negative results for non-drug users. Suppose that 0.5% of people are users of the drug. If a randomly selected individual tests positive, what is the probability he or she is a user?
Despite the apparent accuracy of the test, if an individual tests positive, it is more likely that they do not use the drug than that they do.
Jess Q – Week 16 – Just My Annual Check Up Page 2

Likelihood ratio
The likelihood ratio combines information about the sensitivity and specificity. It tells you how much a positive or negative result changes the likelihood that a patient would have the disease.
The likelihood ratio of a positive test result:
The likelihood ratio of a negative test result:
Once you have specified the pre-test odds, you multiply them by the likelihood ratio. This gives you the post-test odds.
The post-test odds represent the chances that your patient has a disease
Example
Consider an early test for developmental dysplasia of the hip. The test has 92% sensitivity and 86% specificity in boys
(AJPH 1998; 88(2): 285-288). The likelihood ratio for a positive result from this test is 0.92 / (1-0.86) = 6.6 for boys.
The likelihood ratio for a negative result from this test is (1-0.92) / 0.86 = 0.09 (or roughly 1/11).
If a male patient has a diagnostic test that is positive, what can we say about the chances that this boy will develop hip dysplasia? The prevalence of this condition is 1.5% in boys. This corresponds to odds of one to 66. Multiply the odds by the likelihood ratio, you get 6.6 to 66 or roughly 1 to 10. The post-test odds of having the disease is 1 to 10 which corresponds to a probability of 9%.
Suppose we had a negative result, but it was with a boy who had a family history of hip dysplasia. Suppose the family history would change the pre-test probability to 25%. How likely is hip dysplasia, factoring in both the family history and the negative test result? A probability of 25% corresponds to odds of 1 to 3. The likelihood ratio for a negative result is 0.09 or 1/11. So the post-test odds would be roughly 1 to 33, which corresponds to a probability of 3%.
Notice that a negative test seems to change things more than a positive test. There are two factors at work here. First, a positive result multiplies the pre-test odds by a factor of only seven whereas a negative result divides the pre-test odds by 11. This means that the test is better at ruling out a condition than ruling it in.
Second, the impact of a test is usually greatest for mid-sized probabilities. If a condition is either very rare, or very common, then only a very definitive test is likely to change things much. But mid-sized probabilities (say between
20% and 80%) will change greatly on the basis of even a moderately precise test
Jess Q – Week 16 – Just My Annual Check Up Page 3

The table below gives a general summary of likelihood ratios and what they indicate regarding likelihood of a condition to eventuate (or having a link to a condition)
EFERENCES
Screening Lecture – PPH Domain – Monday 28 th May
Epidemiology textbook (copy in PBL room)
Wikipedia when necessary for some formulas (sorry for that  )
Jess Q – Week 16 – Just My Annual Check Up Page 4