Epidemiology made easy-or-

“Lies, damn lies, and statistics”

Steven I McLaughlin DVM, MPH, ACVPM

steve@zukureview.com www.zukureview.com

“Epidemiology is just common sense,

Dr. Jerry Gibson, State epidemiologist,

South Carolina Dept. of Health and Environmental Control

…made complicated”

Lies, damn lies, and statistics

• You WILL see a couple questions on:– Sens, Spec– Predictive Val Pos, Predictive Val Neg

• The key is to draw a 2x2 table

• And remember your “ABCs”

The only table that matters: The 2 x 2

Pos

a b

c d

Pos

Neg

Neg

Your test

“Truth” or “Gold Std” test

Remember: You are comparing TWO TESTS when you calculate Sens, Spec, PVP, PVN

You are comparing your test to a gold standard

For reference:

• Sensitivity- a/a+c

% true pos, correctly identified by my test

• Specificity- d/b+d

% true neg, correctly identified by my test

• Predictive Value Pos - a/a+b

Of those my test says are pos, how many are truly pos ?

• Predictive Value Neg - d/c+d

Of those my test says are neg, how many are truly neg?a/a+b

a/a+c

You serologically test 140 wallabies for a disease.

35 wallabies test seropositive and 105 test seronegative.

However, postmortem data reveals 5/35 of the seropositive wallabies are disease free and 4/105 of the seronegative wallabies are diseased.

What is the predictive value positive (PVP) of this serologic test?

 A. 39/101  B. 35/39  C. 105/140  D. 30/35 E. 101/105

Pos

a

c

Your test

“Gold Std” test

c+d

a+b

a+c b+d a+b+c+d

d

bPos

Neg

Neg

140

35

105

5

4

30

101

PVP=a/(a+b)=30/35

PVP = 86%

PVP/PVN

You serologically test 100 Siberian box turtles for galloping halitosis.

27 turtles test seropositive and 73 test seronegative.

However, molecular testing reveals 3/27 of the seropositive turtles are disease free and 10/73 of the seronegative turtles are diseased.

What is the sensitivity of your serologic test?

 A. 66/73  B. 63/66  C. 27/100  D. 10/63 E. 24/34

Pos

a

c

Your test

“Gold Std” test

c+d

a+b

a+c b+d a+b+c+d

d

bPos

Neg

Neg

100

27

73

3

10

24

63

34 66

Sens=a/(a+c)=24/34

Sens = 70%

Sen

s/Sp

ec

You serologically test 140 wallabies for a disease.

35 wallabies test seropositive and 105 test seronegative.

However, postmortem data reveals 5/35 of the seropositive wallabies are disease free and 4/105 of the seronegative wallabies are diseased.

What is the specificity of this serologic test?

 A. 101/106  B. 105/140  C. 30/34  D. 30/35 E. 106/140

Pos

a

c

Your test

“Gold Std” test

c+d

a+b

a+c b+d a+b+c+d

d

bPos

Neg

Neg

140

35

105

5

4

30

101

Spec=d/(b+d)=101/106

Spec = 95%Sen

s/Sp

ec

You serologically test 100 Siberian box turtles for galloping halitosis.

27 turtles test seropositive and 73 test seronegative.

However, molecular testing reveals 3/27 of the seropositive turtles are disease free and 10/73 of the seronegative turtles are diseased.

What is the predictive value negative (PVN) of your serologic test?

 A. 91%  B. 89%  C. 86%  D. 73% E. 70 %

Pos

a

c

Your test

“Gold Std” test

c+d

a+b

a+c b+d a+b+c+d

d

bPos

Neg

Neg

100

27

73

3

10

24

63

34 66

PVN=d/(c+d)=63/73

PVN = 86%

PVP/PVN

You are using a SLAP® heartworm antigen test with a reported sensitivity 96% and specificity of 98%.

Assuming the prevalence of heartworm in your area is 10%, what is the predictive value positive (PVP) of your test ?

A. 886/900B. 96/114C. 882/886D. 100/114E. 882/1000

Pos

a

c

Your test

“Gold Std” test

c+d

a+b

a+c b+d a+b+c+d

d

bPos

Neg

Neg

1000

114

886

18

4

96

882

100 900

PVP=a/(a+b)=96/114

PVP = 84%

PVP/PVN

Correct: PVP is 92%. The trick with this kind of question is to pick an imaginary number of animals that you test, like 1000, and fill out your 2x2 table from there. Follow the links to see diagrams step by step.

If prev is 10% then there must be 100/1000 dogs w/ heartworm and 900 dogs that are disease-free.

A 96% sensitive test will correctly call 96/100 positive (box "a"), and IN-correctly call 4/100 negative, (box "c": these are the false negs).

If 100/1000 animals are infected, then 900/1000 are Dz-free. Your 98% specific test will correctly call 882/900 Dz-free(box "d": 0.98 X 900=882) and IN-correctly call 18/900 positive, (box "b": these are the false pos).

Now your a,b,c,d boxes are all filled, it is easy to calculate PVP =a/(a+b)=96/(96+18)=84%

Ref: Hennekens and Buring, Epidemiology in Medicine 5th ed., pp. 332-39.

You are using a SLAP® heartworm antigen test with a reported sensitivity 96% and specificity of 98%.

Assuming the prevalence of heartworm in your area is 10%, what is the predictive value negative (PVN) of your test ?

A. 80%B. 85%C. 88%D. 92%E. 99% Pos

a

c

Your test

“Gold Std” test

c+d

a+b

a+c b+d a+b+c+d

d

bPos

Neg

Neg

1000

114

886

18

4

96

882

100 900

PVN=d/(c+d)=882/886

PVN = 99%

PVP/PVN

Correct: PVN is 99%. The trick with this kind of question is to pick an imaginary number of animals that you test, like 1000, and fill out your 2x2 table from there. Follow the links to see diagrams step by step.

If prev is 10% then there must be 100/1000 dogs w/ heartworm and 900 dogs that are disease-free.

A 96% sensitive test will correctly call 96/100 positive (box "a"), and IN-correctly call 4/100 negative, (box "c": these are the false negs).

If 100/1000 animals are infected, then 900/1000 are Dz-free. Your 98% specific test will correctly call 882/900 Dz-free(box "d": 0.98 X 900=882) and IN-correctly call 18/900 positive, (box "b": these are the false pos).

Now your a,b,c,d boxes are all filled, it is easy to calculate PVN =d/(c+d)=882/(882+4)=99%

Ref: Hennekens and Buring, Epidemiology in Medicine 5th ed., pp. 332-39.

Congratulations!You can now handle the most common epi questions you are

likely to see

All you need is a 2x2 table

Pos

a

c

Your test

“Gold Std” test

c+d

a+b

a+c b+d a+b+c+d

d

bPos

Neg

Neg

And these 4 equations

Sensitivity - a/a+c Specificity- d/b+dPredictive Val Pos (PVP) - a/a+bPredictive Val Neg (PVN) - d/c+d

Three extra concepts (In case your brain hasn’t exploded yet.)

If your head is about to pop,just try to remember the next slide.

Then go home and pet your dog

You suspect hyperadrenocorticism in a 9-year old female spayed dog with a two-month history of increased appetite, thirst and urinary accidents.

Which diagnostic test do you trust the most if it has a positive result?

Urine Cortisol Creatinine Ratio (UCCR). Sensitivity=90% , Specificity =25%ACTH Stimulation. Sensitivity=80% , Specificity =85%Low Dose Dexamethasone Suppression. Sensitivity=95% , Specificity =50%

A - Cannot say without knowing the predictive value negativeB - Low Dose Dexamethasone Suppression (LDDS)C - Urine Cortisol Creatinine RatioD - ACTH Stimulation E - Cannot say without knowing the predictive value positive

Remember your Ps and Ns.

ACTH Stim is most sPecific (fewer false Pos, so trust a POS test more).

LDDS is more seNsitive (fewer false Negs, so trust NEG test more).

Why high SPECIFICITY means you can trust a POSITIVE test result: Because false pos are LOW

Pos

a b

c d

Pos

Neg

Neg

Your test

“Truth” or “Gold Std” test

c+d

a+b

a+c b+d

Totala+b+c+d

Sens = a a+c

Spec = d b+d

SE

NS

True Pos

False Negs

False Pos (1)

True Negs (899)

If Spec =99.9%; Prev = 10% and test 1000 animals

Spec =d/(b+d)=899/(900)

Only 1 False PosA positive result by your test is likely correct

900

Where did that 900 come from ?

0.10 prev X 1000= 100 infected

1000-100= 900 Dz-free

Why high SENSITIVITY means you can trust a NEGATIVE test result : Because false negs are LOW

Pos

a b

c d

Pos

Neg

Neg

Your test

“Truth” or “Gold Std” test

c+d

a+b

a+c b+d

Totala+b+c+d

Sens = a a+c

Spec = d b+d

SE

NS

True Pos (99)

False Negs (1)

False Pos

True Negs

If Sens =99%; Prev = 10% and test 1000 animals

Sens =a/(a+c)=99/(100)

Only 1 False NegA negative result by your test

is likely correct

Where did that 100 come from ?

0.10 prev X 1000= 100 infected

1000-100= 900 Dz-free

100

Pos

a

c

Your test

“Gold Std” test

c+d

a+b

a+c b+d a+b+c+d

d

bPos

Neg

Neg

660

70

30

270

630

340

As Prevalence decreases, PVP decreases too

If Prev=30%, Sens and Spec=90%, 1000 turtles

PVP=a/(a+b)=270/(270+70)

PVP = 79%

If Prev DECREASES to 1%, Sens and Spec=90%, 1000 turtles

PVP=a/(a+b)=9/(9+99)

PVP decreases to ~1%

Pos

a

c

Your test

“Gold Std” test

c+d

a+b

a+c b+d a+b+c+d

d

bPos

Neg

Neg

1000

892

~99

~1

~9

~891

10 990

108

1000

700300

As prevalence of a disease goes DOWN, PVP of your serologic test also goes DOWN. That is, as your disease becomes more and more rare, the predictive value of your same old test gets WORSE. That’s all you need to know. Read more only if you want to see the math, (but you don’t need it.) >>>>>>>>

Lets say prevalence of pedunculated giblet disease is 30% in 1000 turtles (that’s 300 infected, 700 dz-free, then).

A test w/ 90% sensitivity would correctly Dx 270 (cell "a") with the dz (true pos) and INcorrectly say 30 were negative (cell "c"); a test w/ 90% specificity would correctly Dx 630 (cell "d") as dz-free (true negs) and INcorrectly say 70 were positive (cell "b"): PVP=a/(a+b)=270/(270+70)= 79%.

Now, do the same math on 1000 turtles, but assume prevalence is now only 1% (0.01) after your vaccination program. You will see PVP goes down to ~1%.

Ref: Hennekens and Buring, Epidemiology in Medicine 5th ed., pp. 332-39.

“The art of epidemiological thinking is to draw conclusions from imperfect data”

George W. Comstock

You’re on your way!

Extra practice questions, if you want them

You serologically test 140 wallabies for a disease.

35 wallabies test seropositive and 105 test seronegative.

However, postmortem data reveals 5/35 of the seropositive wallabies are disease free and 4/105 of the seronegative wallabies are diseased.

What is the sensitivity of this serologic test?

 A. 95%  B. 96%  C. 88%  D. 86% E. 77 %

Pos

a

c

Your test

“Gold Std” test

c+d

a+b

a+c b+d a+b+c+d

d

bPos

Neg

Neg

140

35

105

5

4

30

101

Sens=a/(a+c)=30/34

Sens = 88%Sen

s/Sp

ec

You serologically test 100 Siberian box turtles for galloping halitosis.

27 turtles test seropositive and 73 test seronegative.

However, molecular testing reveals 3/27 of the seropositive turtles are disease free and 10/73 of the seronegative turtles are diseased.

What is the specificity of your serologic test?

 A. 95%  B. 91%  C. 86%  D. 73% E. 70 %

Pos

a

c

Your test

“Gold Std” test

c+d

a+b

a+c b+d a+b+c+d

d

bPos

Neg

Neg

100

27

73

3

10

24

63

34 66

Spec=d/(b+d)=63/66

Spec = 95%

Sen

s/Sp

ec

You serologically test 100 Siberian box turtles for galloping halitosis.

27 turtles test seropositive and 73 test seronegative.

However, molecular testing reveals 3/27 of the seropositive turtles are disease free and 10/73 of the seronegative turtles are diseased.

What is the predictive value positive (PVP) of your serologic test?

 A. 91%  B. 89%  C. 86%  D. 73% E. 70 %

Pos

a

c

Your test

“Gold Std” test

c+d

a+b

a+c b+d a+b+c+d

d

bPos

Neg

Neg

100

27

73

3

10

24

63

34 66

PVP=a/(a+b)=24/27

PVP = 89%

Sen

s/Sp

ec

You serologically test 140 wallabies for a disease.

35 wallabies test seropositive and 105 test seronegative.

However, postmortem data reveals 5/35 of the seropositive wallabies are disease free and 4/105 of the seronegative wallabies are diseased.

What is the predictive value negative (PVN) of this serologic test?

 A. 95%  B. 96%  C. 88%  D. 86% E. 77 %

Pos

a

c

Your test

“Gold Std” test

c+d

a+b

a+c b+d a+b+c+d

d

bPos

Neg

Neg

140

35

105

5

4

30

101

PVN=d/(c+d)=101/105

PVN = 96%

PVP/PVN

You are using an FeLV test with a sensitivity of 90% and a specificity of 95%.

Assuming the prevalence of feline leukemia in your area is 5%, what is the predictive value positive (PVP) of your test ?

A. 45%B. 48%C. 55%D. 88%E. 90%

Pos

a

c

Your test

“Gold Std” test

c+d

a+b

a+c b+d a+b+c+d

d

bPos

Neg

Neg

1000

93

907

48

5

45

902

50 950

PVP=a/(a+b)=45/93

PVP = 48%

PVP/PVN