2x2 Table for Diagnostic Studies

Clinical Parameters

1. Prevalence of Disease (Prev) = (a+c)÷(a+b+c+d)

The prevalence of disease is the probability of any individual in the study having the disease of interest. The total number of individuals with disease and total number of study patients are located at the bottom of the 2x2 table, as we've set it up. Looking at the prevalence is a good first step in examining a diagnostic 2x2 table to determine generalizability of certain clinical parameters to other patient groups.

2. Test Level (TL) = (a+b)÷(a+b+c+d)

The test level is the proportion of those with a positive test result among all study subjects. The total with a positive test and total number of subjects are located on the extreme right side of the 2x2 table, as we've set it up.

3. Clinical Sensitivity (Sens) = a÷(a+c)

The sensitivity is the probability of a positive test result given that the individual is known to have the disease or condition of interest. Since sensitivity only involves those with disease, we only need the left column of the 2x2 table (cells "a" and "c") to determine the clinical sensitivity of the test. There are diagnostic accuracy studies that have been carried out without a control (non-diseased) group for which only the clinical sensitivity can be calculated. Unfortunately, the sensitivity alone greatly limits the usefulness of the study. Generally speaking, a high degree of clinical sensitivity makes for a good screening test.

4. Clinical Specificity (Spec) = d ÷(b+d)

In contrast to the sensitivity, the specificity is the probability of a negative test result given that the individual is known not to have the disease or condition of interest. In evaluating the specificity, we only consider those without disease; consequently, only the right column of the 2x2 table is considered (cells "b" and "d"). Tests with high clinical specificities are generally good as confirmatory tests in screening programs.

5. Positive Predictive Value (PPV) = a ÷(a+b)

The positive predictive value (PPV) is the probability that the individual has the disease of interest given that the test result is positive. Only those with a positive test result are considered in calculating the PPV; as a result, only the upper row of the 2x2 table is needed to calculate the PPV. Unfortunately, the PPV is sensitive to changes in the prevalence of disease. Consequently, these studies must be carefully evaluated to ensure that the disease prevalence is the same as that found in the patient population to which the results of the study might be applied. Furthermore, if the study is a case control study, the prevalence is selected by the study investigators (e.g., 4 controls for every case; prevalence would be 20% in that case). As a result, the prevalence, PPV and NPV would almost certainly not be useful in the real clinical world.

6. Negative Predictive Value (NPV) = d ÷(c+d)

The negative predictive value (NPV) is the probability that the individual does not have the disease of interest if the test result is negative. Those with a negative test result are considered in calculating the NPV; consequently, only the lower row of the 2x2 table is needed to calculate the PPV (cells "c" and "d"). Unfortunately, like the PPV, the NPV is sensitive to changes in the prevalence of disease. These studies must be carefully evaluated to ensure that the disease prevalence is the same as that found in the patient population to which the results of the study might be applied. In addition, if the study is a case control study, the prevalence is selected by the study investigators (e.g., 2 controls for every case; prevalence would be 33% in that case). In these studies, the prevalence, PPV and NPV would almost certainly could not be generalized for use in the real clinical world.

7. False Positive Rate (FPR) = b ÷(b+d)

The false positive rate (FPR) is the probability that an individual will have a positive test result given that he/she does not have the disease of interest. It is essentially the rate of misclassification for those without disease. The FPR is the complement of the clinical specificity, i.e., FPR = 1-spec. The FPR is used in the calculation of the positive likelihood ratio.

8. False Negative Rate (FNR) = c ÷(a+c)

The false negative rate (FNR) is the probability that an individual will have a negative test result given that he/she has the disease of interest. It is essentially the rate of misclassification for those with disease. The FNR is the complement of the clinical sensitivity, i.e., FNR = 1-sens. The FNR is used in the calculation of the negative likelihood ratio.

9. Positive Likelihood Ratio (LR+) = sens÷FPR = sens÷(1+spec)

The positive likelihood ratio is the ratio of the probability of a positive test for those with disease (sens) to that of a positive test for those without disease (FPR). The positive likelihood ratio is used to calculate the posterior probability of disease for those with a positive test result.

10. Negative Likelihood Ratio (LR-) = FNR ÷spec = (1-sens) ÷spec

The negative likelihood ratio is the ratio of the probability of a negative test for those with disease (FNR) to that of a negative test for those without disease (spec). The negative likelihood ratio is used to calculate the posterior probability of disease for those with a negative test result.

11. Odds Ratio [for a positive test] (OR) = (a÷c)÷(b÷d)

The simple odds ratio is not commonly used in the evaluation of diagnostic test results, however, it may be used in meta-analyses to combine the results of several studies.

Parameters of Overall Diagnostic Accuracy

12. Diagnostic Accuracy = (a+d)÷(a+b+c+d)

The diagnostic accuracy is nothing more than the proportion of those individuals correctly categorized by the test (those with disease who had a positive test plus those without disease who had a negative test result). Unfortunately, the diagnostic accuracy one would expect by chance alone would be 50%; consequently, the diagnostic accuracy must be evaluated with a baseline value of 0.5 instead of 0.

13. Misclassification Rate = (b+c)÷(a+b+c+d)

The misclassification rate is the proportion of those individuals incorrectly categorized by the test (those with disease who had a negative test plus those without disease who had a positive test result). The misclassification rate is the complement of the diagnostic accuracy of the test, i.e., misclassification rate = 1 - diagnostic accuracy. Unfortunately, like the diagnostic accuracy, one would expect by chance alone that the misclassification rate would be 50%; consequently, the diagnostic accuracy must be evaluated with a baseline value of 0.5 instead of 1.

14. Youden's Index = (sens+spec)-1

Youden's index is an overall measure to summarize the sensitivity and specificity. It ranges up to a "perfect" value of 1.0.

15. Diagnostic Odds Ratio (DOR) = (LR+)÷(LR-)

The diagnostic odds ratio (DOR) is an overall measure to summarize test performance. It is the positive likelihood ratio divided by the negative likelihood ratio. The DOR is being used increasingly often as a clinical parameter for meta-analysis to combine the results of multiple studies.

16. Cohen's Kappa index (κ)

The kappa index uses the expected value for each of the cells in the 2x2 table and corrects for agreement by chance alone. The kappa index is a lot like a diagnostic accuracy except that in accounting for agreement by chance, the baseline is 0 rather than 0.5.

Terms Used with Likelihood Ratio Calculations

17. Pretest Probability (Prior Probability)

The probability that the patient has the disease or condition of interest just prior to performing the test. The information for this probability may come from demographic studies, patient history, presentation, and physical examination as well as any results from tests performed prior to the test of interest.

18. Pretest Odds (Prior Odds)

The odds that the patient has the disease or condition prior to performing the test. The pretest probability must be converted to a pretest odds using the following equation: odds = probability÷(1-probability).

19. Posttest Odds (Posterior Odds)

The odds that the patient has the disease of interest given the result of the test of interest. Posttest odds = (pretest odds)*(likelihood ratio) [LR+ for a positive test result and LR- for a negative test result].

20. Posttest Probability (Posterior Probability)

The probability that the patient has the disease or condition after incorporating information from the test result. The posttest odds must be converted to a posttest probability using the following equation: probability = odds÷(1+odds).