Answer

a—The likelihood that the patient has streptococcal pharyngitis if the rapid streptococcal antigen test is positive is termed the positive predictive value of the test. In general, the positive predictive value of any test indicates the likelihood that someone with a positive test result actually has the disease.

Predictive values are useful to the clinician as they indicate the likelihood of disease in a patient when the test result is positive (positive predictive value) or the likelihood that the patient does not have the disease when the test result is negative (negative predictive value). The predictive values of a test depend on the sensitivity and the specificity of the test, as well as the prevalence of the disease. The positive predictive value of a test would be higher if the prevalence of disease was higher, and would be lower if the prevalence was lower.

Using a 2x2 table to calculate the positive predictive value (table), the first step is to calculate the expected number of patients with or without streptococcal pharyngitis in a given pharyngitis population. The 10% prevalence of streptococcal pharyngitis in adults with pharyngitis means a clinician may see 10 patients with streptococcal pharyngitis among 100 adult patients with pharyngitis. Assuming a population of 1000 (arbitrary), 100 patients with streptococcal pharyngitis may be seen among 1000 patients with pharyngitis. Streptococcal pharyngitis will probably not be seen in 900 (1000 minus 100) patients who have pharyngitis. The calculation of predictive values would not be any different if you assume a population of 10 000 or 1 million, as we are dealing with ratios of values.

View this table: [in this window] [in a new window]   Calculating positive predictive value

 
Next, calculate the numbers in the "streptococcal pharyngitis" column of the table. The sensitivity of the rapid streptococcal antigen test is 80%, which means that 80 out of 100 patients with streptococcal pharyngitis will have a positive rapid streptococcal antigen test. The number of patients with streptococcal pharyngitis who have a positive rapid streptococcal antigen test is calculated by multiplying 0.80 (sensitivity) and 100 (number of patients with the disease). A negative rapid streptococcal antigen test would be seen in 20 (100 minus 80) patients with streptococcal pharyngitis.

Then, calculate numbers in the "no streptococcal pharyngitis" column of the table. The specificity of the rapid streptococcal antigen test is 95%, which means that 95 out of 100 patients who do not have streptococcal pharyngitis will have a negative rapid streptococcal antigen test. The number of patients without streptococcal pharyngitis who have a negative rapid streptococcal antigen test is calculated by multiplying 0.95 (specificity) and 900 (number of patients without the disease). Therefore, 855 out of 900 patients will have a negative rapid streptococcal antigen test. A total of 45 (900 minus 855) patients who do not have streptococcal pharyngitis will have a positive rapid streptococcal antigen test.

Lastly, the positive predictive value is the proportion of patients with a positive rapid streptococcal antigen test who have streptococcal pharyngitis. Therefore, it is 80/(80+45), which equals 0.64 or 64%. This means the likelihood that the case patient has streptococcal pharyngitis if the rapid streptococcal antigen test is positive is 64%.

The sensitivity and specificity of the test (80% (b) and 95% (c), respectively) do not indicate the likelihood of disease in the patient when the test result is positive or negative but merely represent the characteristics of the test. The sensitivity of a test represents the proportion of patients with disease who would have a positive test result, whereas the specificity of a test represents the proportion of patients without the disease who would have a negative test result.

The negative predictive value (d) is the proportion of the patients with a negative test result who do not have disease. This value is 855/(855+20), which equals 0.98 or 98%. This means the likelihood that the case patient does not have streptococcal pharyngitis if the rapid streptococcal antigen test is negative is 98%.

Cite this as: BMJ 2009;339:b3835