Last month, we discussed the all important 2x2 table again and I gave you a quiz based on one of my long standing simple, but favorite papers putting the contingency table to use (Grayson et al: JAMA, March 1995). I know that I am repeating myself quite a bit here, but I can't emphasize enough how useful your mastery of the 2x2 table will be in years to come – especially when trying to keep things straight like sensitivity, specificity, positive predictive value, etc. - especially in your head as you're reading journal articles.
This month's Residency Insight will be rather brief – primarily because I want this technique of dealing with study numbers to sink in. Once it does, you will not forget how to properly lay out a 2x2 table.
Hopefully, I made it fairly simple enough to understand how to lay out and use the contingency table to determine the important parameters used in determining accuracy of tests based on gold standard definitions (criteria) for disease status. Osteomyelitis was the disease status in the example last month and the test was the probe to bone test (PTB). We were attempting to determine its utility in diagnosing osteomyelitis in a series of patients admitted with serious diabetic foot infections. Despite its weaknesses, (and the controversy surrounding this test) I find it extraordinarily useful in clinical practice. Much of its utility has been demonstrated by this study and the data presented in the table. Although not all cells were complete with values, you were given key values enabling completion of the table in its entirety – and thereby calculate the diagnostic parameters we sought.
Let's see how well you did. All the data presented last month in the table is in black – the answers are all in red. If you got any answers wrong, it was just a matter of arithmetic. Remember, this is all proportions and that is all it is. Figure it out and redo the numbers enough times so that you really do understand the appropriate formulation of the data in the table. You could actually figure it out with less cell values than I gave you- as long as you have a total number of study subjects.
So here is the completed table and the appropriate diagnostic parameters:
I made a mistake last month when I mentioned this: "Another Hint: a quick and easy way to calculate sensitivity is to find your false positive percent (FP/FP + TP). Sensitivity (%) is the complement of the false positive % - this means that the two added together must equal unity (100% or a probability of 1)" Instead of Sensitivity, I should have said SPECIFICITY is the complement of the False-positive frequency. In our table, there are 4 False Positive test results. These are people testing positive even though they do not have the disease. So they belong to the non-diseased population (total n=26). Our FP frequency is therefore 4/26 or .15 (15%). One minus .15 equals .85 (85%) - exactly what we calculated the specificity to be- it has to be, because 15% of the people without the disease yielded false positive test results – leaving the remaining 85% without disease who correctly tested negatively for the disease (true negative).
However, there is a relationship between PPV and sensitivity that becomes evident (and important). If you have a high PPV percentage (in this case 89%), there must be very few persons testing positively who do not have the disease (false positives). Here our denominator is the total number of positive tests (going across the Positive + test row) totaling n=37. Only 11% of the positive tests were in non-diseased persons using the total of positive tests as our denominator. It's all about numerators and denominators after all. But when we typically use the terminology "False positive rate" (even though it is not a rate), we are referring to the total population of non-diseased persons as our denominator (rather than the total number of positive tests going horizontally). It is an important point, although it can be confusing. Look carefully at the table and it will become clear- and allow you to better master the layout that will allow you to keep such terminology straight in your mind when you are reading your journal articles. I use it on a daily basis.
Until then, I hope you can appreciate the Power of the Numbers! ...
See you next time.
Robert Frykberg, DPM, MPH
PRESENT Editor,
Diabetic Limb Salvage
Suggested References:
- Grayson ML, Gibbons GW, Balogh K, Levin E, Karchmer AW. Probing to bone in infected pedal ulcers. A clinical sign of underlying osteomyelitis in diabetic patients. Jama. Mar 1 1995;273(9):721-723.
- Statistics. Cliffs Notes, Lincoln Nebraska. David Voelker and Peter Orton. 1993
- Online Statistics Education: An Interactive Multimedia Course of Study (https://onlinestatbook.com/)
- Stanton Glantz. Primer of Biostatistics. McGraw – Hill, Inc., New York
- Theodore Colton. Statistics in Medicine. Little, Brown, and Company. Boston
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