The 5 x 5 table version of the 2 x 2

Now I am going to present to you how systematic this table is and how it clarifies the whole scenario for the following 5 things.

1. Sensitivity
2. Specificity
3. Negative predictive value
4. Positive predictive value
5. Odds ratio

Sensitivity = I am going to explain the sensitivity of a radio. There are 10 stations in the air. If it can only pick up 7 of them, it is 70% sensitive. Therefore if there are 10 cases of a disease in a population, and only 7 can be picked up by the test, it is 70% sensitive.

Specificity = Of all that are free of the disease, how many actually test negative. Now we think of a machine which opens oysters that have pearls inside. We feed it 20 oysters. It opens 8 of them.  2 out of the 8 did not have pearls. We then went on to open all those that it did not open and found 3 pearls but 9 were without pearls. Therefore the specificity is 9/11 - i.e. of the total without the pearls (11), it correctly identified 9.

Positive predictive value: We developed a test that can tell us with fair accuracy about a problem. It is - lets say for learning purposes sensitivity is 80% and specificity is 90%. Therefore if the test is done in a population of 20 people where the prevalence is 50%, 10 are without disease and 10 are with disease.

Of the 10 who have the disease, only 8 will turn positive on the test (because the sensitivity is 80%).

Of the 10 who do not have the disease, only 9 will be negative (because the specificity is 90%).

Therefore we have a total of 8 true positives and 1 false positive = 9 positives. Positive predictive value is used to tell us that if a person tests positive, what are the chances that he truly has the disease. In this case, it is 8/9.

Now to understand negative predictive value, of all those who tested negative, how many are truly negative? Easy?!!

2 out of the 10 who have the disease actually came out negative on the test (because it was only 80% sensitive) and 9 of those who do not have the disease turned out negative (because the specificity is 90%). Therefore a total of 11. Now how many of those who turned negative on the test are truly negative? This is the negative predictive value.

The answer is 9/11. So the prevalence, sensitivity and specificity are all key in this calculation. The 2 x 2 chart gives us the sensitivity and specificity but where examiners trick us is by not giving the prevalence and making us waste time in the test because without that, no prediction can be made.

Odds ratio: I am first going to cite an example for this. The likelihood that a case of lung cancer is a smoker divided by the likelihood that a person without lung cancer is a smoker.

So let us define it now. It is the likelihood of someone with the disease having the exposure divided by the likelihood of someone without the disease having the exposure.

If one replaces the test results with Risk factor exposure (as shown in the box below), one will be able to find out the odds ratio. It is like writing an "X" with the first stroke from box a to d (numerator) and the next stroke from box b to c (the denominator)