Sensitivity & SpecificitySensitivity & Specificity

Sam Thomson Sam Thomson

8/12/108/12/10

SensitivitySensitivity

• Proportion of people with the condition Proportion of people with the condition who have a positive test resultwho have a positive test result

= True Positives/(True Positives +False = True Positives/(True Positives +False Negatives) Negatives)

= TP/(TP+FN) = TP/(TP+FN)

Contingency TableContingency Table

   Disease PresentDisease Present Disease AbsentDisease Absent

Test PositiveTest Positive True Positive (TP)True Positive (TP) False Positive (FP)False Positive (FP)

Test NegativeTest Negative False Negative (FN)False Negative (FN) True Negative (TN)True Negative (TN)

QuestionQuestion• A new test to screen for pulmonary A new test to screen for pulmonary

embolism is used in 100 patients who embolism is used in 100 patients who present to the ED. The test is positive in 30 present to the ED. The test is positive in 30 of the 40 patients who are proven to have a of the 40 patients who are proven to have a PE. Of the remaining 60 patients, only 5 PE. Of the remaining 60 patients, only 5 have a positive test. What is the sensitivity have a positive test. What is the sensitivity of the new test?  of the new test?  

• A.8.33% A.8.33% 

• B.30% B.30%

• C.40%  C.40%  

• D.66.66% D.66.66%

• E.75%E.75%

AnswerAnswer• A contingency table can be constructed A contingency table can be constructed

from the above data:from the above data:

• Sensitivity = TP/(TP+FN)Sensitivity = TP/(TP+FN)• Sensitivity = 30/(30+10) Sensitivity = 30/(30+10) • E. 75%E. 75%

   PE PE DiagnoseDiagnose

dd

No PENo PE

Test positiveTest positive 3030 55

Test negativeTest negative 1010 55 55

SpecificitySpecificity

• Proportion of patients without the Proportion of patients without the condition who have a negative test resultcondition who have a negative test result

= True Negatives/(True Negatives +False = True Negatives/(True Negatives +False Positives) Positives)

= TN/(TN+FP) = TN/(TN+FP)

• High Specificity = Few False PositivesHigh Specificity = Few False Positives

QuestionQuestion• A rapid finger-prick blood test to help diagnose DVT is A rapid finger-prick blood test to help diagnose DVT is

developed. Comparing the test to current standard developed. Comparing the test to current standard techniques a study is done on 1,000 patients:techniques a study is done on 1,000 patients:What is the specificity of the new test? What is the specificity of the new test? 

• A.680/880  A.680/880  

• B.200/220 B.200/220

• C.680/780  C.680/780  

• D.680/700  D.680/700  

• E.200/300E.200/300   DVT DVT

presenpresentt

DVT absentDVT absent

New test positiveNew test positive 200200 100100

New test New test negativenegative

2020 680 680

AnswerAnswer

• Specificity = TN/(TN+FP)Specificity = TN/(TN+FP)

• = 680/(680+100)= 680/(680+100)

• C. 680/780C. 680/780