UCAT Question Analysis - Decision Making Q67
A laboratory can use Test A to find wheter a particular protein is contained in a blood sample. The probability that an individual's blood contains this kind of protein is 0.1%. The characteristics of Test A is as follows:
- If the protein is in the blood, Test A always detects it
- When Test A gives a negative result, it is 100% correct, i.e. it means the person does not have the protein in their blood.
- When 100 people with no protein in their blood were tested, for 5 of them the test showed a positive result.
The laboratory predicts the probability an individual who testes positive actually has the protein is very low (of the order of 2%). Which of the following applies?
A. No, it should be 95% since the test only gets it wrong in 5% of cases.
B. No, the probability should be far higher since the test has a low failure rate. But it is not 95%.
C. Yes, this is because the low prevalence of the protein presence makes the test very unreliable.
D. The lab cannot calculate a percentage using the data provided.
Answer and Explanation
C. Yes, this is because the low prevalence of the protein presence makes the test very unreliable.
We know that 0.1% of individuals will have the protein in question in their blood. So. if we take 1000 people, 1 person will have it and the rest will not.
Since the test accurately predicts the presence of the protein when it is there, we know that the 1 person who has it will have tested positive.
Out of the remaining 999 people, we know that 5% will be wrongly testing positive. So out of 1000 people, 1+0.05*999=51 people will have a positive test. But only one of them will actually have the protein. i.e. 1/51 (about 2%).
We can see that the problem is that the low prevalence means that the numerator is only 1. Had the protein been more prevalent, the rate would be higher. For example, if the protein was present in 70% of people, then the calculation would be 700 / (700+0.05*300)=700/715=98%.
Drafted by Quincy (UCAT PREP)