For the last several months, we've been discussing some very basic, yet very important concepts about biostatistics that you need to know if you are to become educated consumers of medical literature. Very few of you learn this in college and even fewer learn it in Podiatry School (I know that I didn't). We've discussed descriptive statistics, p-values, 95% confidence intervals, and the incredibly useful 2 x 2 table. As was mentioned last month, the contingency table just makes numbers presented in journal articles more meaningful – and nicely lays out important parameters such as sensitivity, specificity, false positive, and positive predictive value. These are often mentioned in studies but, if you are anything like me, the true meaning of these statistical terms can be somewhat confusing. Remember that we are only talking about proportions here. You just need to figure out what proper numerators and denominators are to do your own calculations. Even when you don't have all the numbers, when you have the totals for a row or column and a total number of subjects, our parameters are easy to calculate.
Here is our handy 2 x 2 table that was presented last month that clearly illustrates a customary layout and defines our important parameters of interest (sensitivity, specificity, false positive, etc.):
As is evident in this layout, the central columns represent true disease status, while the central rows represent the results of some diagnostic test. Each cell would contain a crude number for that result (i.e. a positive test result in a diseased person would be a true positive, etc.). The last cell of each row or column represents the total for that test result or disease status, respectively. The lower right corner cell always represents the total number of patients in the study group. I think this is pretty clearly illustrated and it's important to understand how to lay out such a table. You also see how sensitivity, specificity, and positive predictive value are calculated based on the numbers in each appropriate cell – just determine the proper numerator (cell value of interest) and denominator (total numbers in the group of interest). Please read last month's ezine again to fully explain this again as a refresher.
Now we will have a quiz – the best kind because you are not being graded for it. But it will easily help you appreciate the value of the 2x2 table. To make it clinically relevant, I will take the numbers directly from a fairly well known paper from March 1995 (one of my favorites) dealing with validity of the probe to bone test in diabetic foot ulcers to determine the presence of osteomyelitis. You know the paper (or should know it (Grayson et al: JAMA). The famous 89% positive predictive value (PPV) for the probe to bone (PTB) test that you've all heard of. Now, I've given you the PPV probability (the probability of having the disease given a positive test result). The diseased individuals with a positive test (true positives) are the numerator here and the denominator is the total number of persons with a positive test. Hence, the value of testing positive. Now, with the numbers provided (based on the study results), it is your task to fill in the blanks and provide the values (percentages) for Sensitivity, Specificity, False Positives, and Negative Predictive Value (NPV = the value of a Negative test in detecting those persons without the disease in question). Hint: with the data given, first figure out the number of False Positive test results. Then it's all a simple matter of Math and proportions. Don't look at the original paper until you've completed the contingency table.
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)
This exercise should be simple, fun, and eye-opening. You should be then able to lay out a 2x2 table for any study in which data is presented (at least in part). Correct answers will be given next month along with another quiz, which we'll continue until we have mastered this tool.
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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