2 X 2 Table

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2 X 2 Table

		Disease
		+	-
Test	+	True Positive (TP)	False Positive (FP)	All with Positive Test TP+FP	Positive Predictive Value TP/(TP+FP)	Post-Test Probability Given Positive Test =PPV
	-	False Negative (FN)	True Negative (TN)	All with Negative Test FN+TN	Negative Predictive Value TN/(FN+TN)	Post-Test Probability Given Negative Test =100%-NPV
		All with Disease TP+FN	All without Disease FP+TN	Everyone=N TP+FP+FN+TN
		Sensitivity TP/(TP+FN)	Specificity TN/(FP+TN)	Pre-Test Probability (TP+FN)/(TP+FP+FN+TN)

A 2 X 2 table is a convenient way of summarizing and calculating all of the information about a diagnostic test.

How to fill out the table.
1) Assume a large N, total number of patients (10,000 usually means that you will not have fractions of people in any box... thatÕs the only reason for a large number.)
N = TP + FN + FP + TN

2) Use your best estimate of pretest probability (a.k.a. prevalence) for generating the total number of patients WITH (TP + FN) and WITHOUT (TN + FP) the disease.
Pretest probability = TP + FN / N

3) You now have TP+FN and TN+FP, so you can solve the next set of equations:
Use sensitivity to fill in the TP and FN boxes. Sensitivity = TP / TP+FN
Use specificity to fill in the TN and FP boxes. Specificity = TN / TN+FP

4) Calculation of PPV and NPV is now straightforward because you know the values for all the boxes in the table.

5) Wait, I donÕt know the pretest probability! ThatÕs one of the advantages of clinical experience -- your ability to estimate pretest probability accurately will improve with time. But, what if you remain with a certain range of uncertainty - I think that thereÕs a 5 to 35 percent chance that this patient (and all the patients who LOOK like this patient) has the target condition.
Well, you could calculate the 2 X 2 table for the lowest probability estimate, and then do it again for the highest estimate. But, wouldnÕt it be great if you could do the same thing without all those calculations. You can! ThatÕs one of the advantages of Likelihood Ratios (LRs). The Likelihood Ratios combine sensitivity and specificity into a single number for a positive test and a single number for a negative test. Using a nomogram (see the article III. How to Use an Article About a Diagnostic Test B. What are the Results and Will They Help Me in Caring for My Patients?JAMA 1994;271:703-7), you can quickly generate post-test probabilities by trying different pre-test probabilities.
LR positive = sensitivity / (1 - specificity)
LR negative = (1 - sensitivity) / specificity