More Details on Sensitivity and Specificity

Definition

Sensitivity refers to the proportion of people with disease who have a positive test result.

Specificity refers to the proportion of people without disease who have a negative test result.

SnNout is a mnemonic applied to the finding that when a sign, test or symptom has a high Sensitivity, a Negative result rules out the diagnosis.

SpPin is a mnemonic applied to the finding that when a sign, test or symptom has a high Specificity, a Positive result rules in the diagnosis.

How to Calculate SpPins and SnNouts

We can assume that there are four possible groups of patients, as indicated (a,b,c,d) in the table:

		Target Disorder
		Present	Absent
Diagnostic Test Result	+	a	b	a + b
	-	c	d	c + d
		a + c	b + d	a + b + c + d

From these we determine the sensitivity and specificity as follows:

Sensitivity = a/(a+c)
Specificity = d/(b+d)

Sample Calculation

Suppose you have a patient with anemia and a serum ferritin of 60 mmol/L. You come across a systematic review ( J Gen Intern 1992;7:145-53 ) of serum ferritin as a diagnostic test for iron deficiency anemia, with the results summarised in the table below.

		Target Disorder (iron deficiency anemia)
		Present	Absent
Diagnostic Test Result (serum ferritin)	+ (< 65 mmol/L)	731 a	270 b	1001 a + b
	- (≥65 mmol/L)	78 c	1500 d	1578 c + d
		a + c 809	b + d 1770	a + b + c + d 2579

The sensitivity and specificity are calculated as follows:

Sensitivity = a/(a+c) = 731/809 = 90%
Specificity = d/(b+d) = 1500/1770 = 85%

These results indicate that 90% of the patients with iron deficiency anemia have a positive test result (serum ferritin < 65 mmol/L), while 85% of patients who do not have the disorder test negative (serum ferritin ≥ 65 mmol/L). Since the specificity is high (≥ 80%) and your patient has a Positive test result, you can rule in the diagnosis of iron deficiency anemia.

Practice Calculation

The results of a blinded study (Stroke 1996;27:1516-1520 ) assessing the use of plasma D-dimer levels for diagnosing deep venous thrombosis (DVT) in patients hospitalised for stroke rehabilitation are summarised in the table below. The presence or absence of DVT was determined by positive or negative venous duplex ultrasound results.

		Target Disorder (DVT)
		Present	Absent
Diagnostic Test Result (Plasma D-dimer level)	+ (>1591 ng/mL)	13 a	19 b	32 a + b
	- (≤1591 ng/mL)	1 c	72 d	73 c + d
		a + c 14	b + d 91	a + b + c + d 105

What is the sensitivity and specificity for this example?

Sensitivity = _______
Specificity = _______

See our answer and compare

Sensitivity = a/(a+c) = 13/14 = 93% Specificity = d/(b+d) = 72/91 = 79%