Lecture 2 : Diagnostic Testing : Sensitivity and Specificity

Diagnostic sensitivity

-Different from Analyic sensitity

VAlue of Sensitivity and specificity

-Not dependent on Prevalence or probability of Dz in a specific situation -Head to Head comparisons btwn diagnostic tests -Necessary for calculating predictive values.

DIAGNOSTIC SENSITIVITY

-Probability of a POSITIVE test in an animal KNOWN to HAVE the DZ+ the proportion of animals that test Positive out of a number of animals known to have the DZ

Specificity

-the probability of a NEGATIVE test in an animal known to NOT have the DZ(-) -the proportion of animals that test negative out of a number of animals known to NOT have the DZ(-)

DEFINE GOLD STANDARD : Comparing a new test to an Existing Gold Standard Test

1. 2 tests applied to each animal in the same population 2. The GS is assumed to reflect the Dz status "be correct" 3. The new test is often cheaper or faster than GS 4. Limitations -How ''gold" is the gold standard -is the population tested representative of your pop?

The perfect test would be

100%Se and 100%Sp Cow example: True dz. prevalence =50% Total pop 10, so 5 Dz+ and 5 Dz- After test 5 with Dz+ have + test and 5 with out Dz- have - test

Compare results with True prevalence =10% Pop=100

100X.10=10(DZ+) Sensitivity=80% .80X10=8 (TP) 10-8=2 (FN) (Dz-)100-10=90(Dz-) Specificity =80% 0.80 X 90=72(TN) 90-72=18=(FP)

A Highly Sensitive Test (100% Se and 80%Sp) cow example (10 total cows) Prevalence =50%

5 cows have Dz+ and 5 cows do not have Dz- -after test: Make 2x2 5 with Dz+ and 1 without Dz- = test + 4 with out Dz- test negative 5 TP 1 FP 4 TN 0 FN ***Highly Sensitive Test Have No False Negative, but worry about False positives.

(2/2)How can sensitivity and specificity be estimated?

Apply a test to known Dz+ or Dz- free population 1. Dz free areas -example:areas of the US where TB + cattle are very unlikely 2. Animals with diagnostic clinical signs -example: Cattle fromTB herds that have definitive lesions at slaughter **Limitation: is the pop similar to the one you would be testing

(1/2)How can sensitivity and specificity be estimated?

Compare a new test to an existing GOLD STANDARD

conceptual definition 10 Diseased (+) Cows -after test, you find that 8 cows have (+) test (True positives) and 2 cows have (-) test (False Negatives ) What is the sensitivity ?

Definition states it is the probability of a positive test in an animal KNOWN to have DZ(+) So take 8(+)/10 (total pop)=80%

A highly Specific Test 5 cow have Dz+ and 5 cows do not have Dz- Total pop=10 Se=80%, 100% sp Prevalence =50%

Make table Have 4 TP and 1 FN Have 5 TN and 0 FP ***Worry about False Negatives with highly specific test

Mathematical Definition of Sensitivity (formula)

Sensitivity TP/(TP + FN)

Mathematical Definition: Specificity

Specificity =TN/(FP+TN)

conceptual definition: Specificity 10 cows Known NOT to have DZ -After test : 2 test positive (False positive) 8 test negative (True Neg) -What is Specificity?

Specificity is TN/(TN+FP) =8/10= 80%

Cow example for Specificity

Specificity=TN(8)/ (TN(8) + FN(2)=0.80=80%

Math. Def. Of Sensitivity with Cow example

TP(8)/(TP(8)+FN(2)=0.80=80%

Basic Example: True Dz Prevalence =50%

TP=40 FN=10 Sensitivity =TP/TP+FN (40/50)=0.80=80% FP=18 TN=72 Specificity =TN/TN+FP (72/90)=0.80=80%

Analytic sensitivity

The smallest amount of a substance in a sample that can accurately be measured by an assay.