1. Epidemiology made easy -or- “Lies, damn lies, and statistics”
Steven I McLaughlin DVM, MPH, ACVPM

2. “Epidemiology is just common sense,
…made complicated”
Dr. Jerry Gibson, State epidemiologist,
South Carolina Dept. of Health and Environmental Control

3. 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”

4. The only table that matters: The 2 x 2
Pos a b c d
Neg
Your test
“Truth” or “Gold Std” test
Sensitivity- a/a+c
% true pos, correctly identified by my test
Specificity- d/b+d
% true neg, correctly identified by my test
Predictive Val Pos - a/a+b
Of those my test says are pos, how many are truly pos ?
Predictive Val Neg - d/c+d
Of those my test says are neg, how many are truly neg?
Remember: You are comparing TWO TESTS when you calculate Sens, Spec, PVP, PVN You are comparing your test to a gold standard

5. 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+c
a/a+b

6. You serologically test 140 wallabies for a disease
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
PVP/PVN
Pos a c
Your test
“Gold Std” test
c+d
a+b
a+c
b+d
a+b+c+d d b
Neg
PVP=a/(a+b)=30/35 PVP = 86% 35 30 5
105 4
101
140

7. 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
Sens=a/(a+c)=24/34 Sens = 70%
Pos a c
Your test
“Gold Std” test
c+d
a+b
a+c
b+d
a+b+c+d d b
Neg
Sens/Spec 27 24 3 73 10 63
100 34 66

8. You serologically test 140 wallabies for a disease
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 b
Neg
Spec=d/(b+d)=101/106 Spec = 95%
Sens/Spec 35 30 5
105 4
101
140

9. 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 %
PVP/PVN
PVN=d/(c+d)=63/73 PVN = 86%
Pos a c
Your test
“Gold Std” test
c+d
a+b
a+c
b+d
a+b+c+d d b
Neg 27 24 3 73 10 63
100 34 66

10. 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. 886/900
B. 96/114
C. 882/886
D. 100/114
E. 882/1000
PVP/PVN
PVP=a/(a+b)=96/114 PVP = 84%
Pos a c
Your test
“Gold Std” test
c+d
a+b
a+c
b+d
a+b+c+d d b
Neg
114 96 18
886
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 4
882
1000
100
900

11. 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

12. 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%
PVP/PVN
PVN=d/(c+d)=882/886 PVN = 99%
Pos a c
Your test
“Gold Std” test
c+d
a+b
a+c
b+d
a+b+c+d d b
Neg
114 96 18
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
886 4
882
1000
100
900

13. 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

14. 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 b
Neg
And these 4 equations
Sensitivity - a/a+c
Specificity- d/b+d
Predictive Val Pos (PVP) - a/a+b
Predictive Val Neg (PVN) - d/c+d

15. (In case your brain hasn’t exploded yet.)
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

16. 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 negative B - Low Dose Dexamethasone Suppression (LDDS) C - Urine Cortisol Creatinine Ratio D - 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).

17. Where did that 900 come from ? 0.10 prev X 1000= 100 infected
Why high SPECIFICITY means you can trust a POSITIVE test result: Because false pos are LOW
Pos a b c d
Neg
Your test
“Truth” or “Gold Std” test
c+d
a+b
a+c
b+d
Total
a+b+c+d
Where did that 900 come from ? prev X 1000= 100 infected
= 900 Dz-free
True Pos
False Pos (1)
False Negs
True Negs (899)
900
Sensitivity
Specificity
If Spec =99.9%; Prev = 10% and test 1000 animals
Spec =d/(b+d)=899/(900) Only 1 False Pos A positive result by your test is likely correct
Sens = a
a+c
Spec = d
b+d
SENS

18. Where did that 100 come from ? 0.10 prev X 1000= 100 infected
Why high SENSITIVITY means you can trust a NEGATIVE test result : Because false negs are LOW
Pos a b c d
Neg
Your test
“Truth” or “Gold Std” test
c+d
a+b
a+c
b+d
Total
a+b+c+d
Where did that 100 come from ? prev X 1000= 100 infected
= 900 Dz-free
True Pos (99)
False Pos
False Negs (1)
True Negs
100
Sensitivity
Specificity
If Sens =99%; Prev = 10% and test 1000 animals
Sens =a/(a+c)=99/(100) Only 1 False Neg A negative result by your test is likely correct
Sens = a
a+c
Spec = d
b+d
SENS

19. As Prevalence decreases, PVP decreases too
Pos a c
Your test
“Gold Std” test
c+d
a+b
a+c
b+d
a+b+c+d d b
Neg
If Prev=30%, Sens and Spec=90%, 1000 turtles
PVP=a/(a+b)=270/(270+70) PVP = 79%
340
270 70
660 30
630
1000
300
700
Pos a c
Your test
“Gold Std” test
c+d
a+b
a+c
b+d
a+b+c+d d b
Neg
108
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%%. Hennekens and Buring, Epidemiology in Medicine 5th ed., pp ~9
~99
If Prev DECREASES to 1%, Sens and Spec=90%, 1000 turtles
PVP=a/(a+b)=9/(9+99) PVP decreases to ~1%
892 ~1
~891
1000 10
990

20. 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

21. You’re on your way!
“The art of epidemiological thinking is to draw conclusions from imperfect data” George W. Comstock

22. Extra practice questions, if you want them

23. You serologically test 140 wallabies for a disease
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 b
Neg
Sens=a/(a+c)=30/34 Sens = 88%
Sens/Spec 35 30 5
105 4
101
140

24. 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 %
Spec=d/(b+d)=63/66 Spec = 95%
Pos a c
Your test
“Gold Std” test
c+d
a+b
a+c
b+d
a+b+c+d d b
Neg
Sens/Spec 27 24 3 73 10 63
100 34 66

25. 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 %
PVP=a/(a+b)=24/27 PVP = 89%
Pos a c
Your test
“Gold Std” test
c+d
a+b
a+c
b+d
a+b+c+d d b
Neg
Sens/Spec 27 24 3 73 10 63
100 34 66

26. You serologically test 140 wallabies for a disease
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 %
PVP/PVN
Pos a c
Your test
“Gold Std” test
c+d
a+b
a+c
b+d
a+b+c+d d b
Neg
PVN=d/(c+d)=101/105 PVN = 96% 35 30 5
105 4
101
140

27. 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%
PVP/PVN
PVP=a/(a+b)=45/93 PVP = 48%
Pos a c
Your test
“Gold Std” test
c+d
a+b
a+c
b+d
a+b+c+d d b
Neg 93 45 48
907 5
902
1000 50
950