Disease Present	Disease Absent
Positive Test Result	True positive (TP)	False positive (FP)
Negative Test Result	False negative (FN)	True negative (TN)

The sensitivity of a test, given by TP / (TP + FN), is the probability that a patient with a given disease will have a positive result on that test; for a highly sensitive test, a negative result helps rule out a disease (SnNout).  Higher sensitivity means fewer FNs.  Similarly, the specificity of a test, given by TN / (TN + FP), is the probability that a patient without a given disease will have a negative test result on that test; for a highly specific test, a positive result helps rule in a disease (SpPin).  Higher specificity means fewer FPs.

Positive predictive value (PPV), given by TP / (TP + FP), is the probability that a positive test correctly identifies an individual with the disease.  Because higher specificity is associated with fewer FPs, higher specificity will, in the vast majority of cases, increase the PPV of the test (because FP is the denominator of PPV).  In this case, the test with highest specificity (97%) is the best choice as it will most likely also has the highest PPV.

PPV depends on prevalence and increases with increasing prevalence.  Although not necessary for this question, PPV can be calculated by constructing a 2x2 contingency table using the provided values for prevalence (10%), sensitivity (65%), and specificity (97%).  Taking a sample of 1000 women as an example, 100 will have breast cancer (10% prevalence) and 900 will not.  In addition:

• Sensitivity of 65% means that 65 out of the 100 patients with breast cancer will have a positive result for that serologic test; ie, TP = 65.  Therefore, 100 - 65 = 35 patients with breast cancer will have a negative result for that test; ie, FN = 35. 
• Specificity of 97% means that .97*900 = 873 patients out of the 900 patients without breast cancer will have a negative result for that serologic test; ie, TN = 873.  Therefore, 900 - 873 = 27 patients without breast cancer will have a positive test result for that test; ie, FP = 27.

PPV = TP / (TP + FP) = 65 / (65 + 27) = 0.706 (ie, 70.6%).  Similar calculations for the other values (not required to answer the question) yield PPVs of ~56% (Choice B), ~51% (Choice C), ~47% (Choice D), and ~48% (Choice E).  The latter test has the highest sensitivity, which increases its negative predictive value (NPV); NPV, given by TN / (TN + FN), represents the probability that a negative test correctly identifies an individual who does not have the disease.

Educational objective:
Good confirmatory tests must have a high specificity.  As specificity increases, the positive predictive value also increases and the number of false positives decreases.