1. When is the post-test probability sufficient for decision-making?
Pre-test and post-test probability.
When is the post-test probability sufficient for decision-making?
Agostino Colli
Gargnano April

2. new information = test results
When do we order a diagnostic test?
When we are uncertain about the diagnosis and need new information.
new information = test results

3. Imagine always positive in patient with the disease
a diagnostic test for a disease:
always positive in patient with the disease
never positive in patient without the disease
Clinical judgement would not be required to diagnose the disease :
it would be sufficient to know the test result

4. the enrolled patients are not enough to see a FALSE RESULT
disease +
disease -
test +
100
test -
inadequate sample size:
the enrolled patients are not enough to see a FALSE RESULT

5. Diagnostic tests are not perfect and always produce FALSE RESULTS
There are no actually pathognomonic signs or test results
Just because diagnostic tests are imperfect,
ACCURACY HAS TO BE ESTIMATED.
accuracy= the proportion of TRUE RESULTS

6. disease + disease - 5 25 75 Predictive value 20/30 65/70
test + 20 10
test - 5 65 25 75
Predictive value
20/30
65/70
LR+ 6.1 LR
Sensitivity 20/25=80%
Specificity 65/75=87%
PREDICTIVE VALUE
POSITIVE: How many patients with positive test have the disease ?
NEGATIVE: How many patients with negative test do not have the disease?

7. 20/30 65/70 disease + disease - Predictive value test + 20 10 test - 525 75
Predictive values depend on:
test accuracy
proportion of patients with disease (prevalence)
A posteriori estimate:
PREVALENCE : 25/(25+75)= 25% = PRETEST PROBABILITY

8. ..but for physicians and for patients the main concern is not the average accuracy of a test.
Physicians would like to know whether a patient with a positive test has or has not a disease .
The clinical questions are :
How many patients with positive test have the disease ?
What is the probability of having the disease after testing?

9. from a diagnostic study into clinical practice:
Post-test probabilities obtained in a diagnostic study can be transferred into another context only if the patients are very similar, that is the pre-test probability is the same.
facing an individual patient :
before ordering a test, the pre-test probability and the consequent post-test probabilities in the case of positive or negative results should be estimated.

10. Prevalence (pre test probabilty): 25/(25+75)= 25%
disease +
disease -
Predictive value
test + 20 10
66%
test - 5 65
93% 25 75
AVERAGE VALUE which is typical of the study population.
We need to estimate the value in our patients and in a single patient.
Prevalence (pre test probabilty): 25/(25+75)= 25%

11. So we are uncertain about the diagnosis, have only imperfect tests and have to move in twilight of probability
The effect of new information on uncertainty can be assessed expressing uncertainty as a probability

12. Probability of disease
before test
after test
bayesian rule
Probability of disease
DIAGNOSIS
a subjective estimate (opinion) of how much a hypothesis is probable is needed to calculate the effect of new information
For the INTERPRETATION of a test result you have to estimate the probability before the test

13. pretest probability
the probability of the target disease before diagnostic tests result is known
Subjective probability: a subjective judgment in the minds of those involved in the diagnostic at hands
experience
scientific background

14. Probability of disease
before test
after test
bayesian rule
Probability of disease
DIAGNOSIS
POST TEST PROBABILITY
What is the probability of having the disease on the basis of the test results ?

15. POST TEST PROBABILITY and PREDICTIVE VALUE
PREDICTIVE VALUE IS NOT A PROPERTY OF THE INDEX TEST, such as sensitivity and specificity (operative characteristics)
POST TEST PROBABILITY and PREDICTIVE VALUE
positive predictive value ≡ post test probability
negative predictive value = 1- post test probability
( which sounds somehow counterintuitive)

16. The interpretation of a test result according to the bayesian rule
PRE TEST ODDS x LR = POST TEST ODDS
then transform in probability :
probability = odds /(1+odds) ; odds = probability/(1-probabilty)
pre test ≈ 75% post test probability ≈ 97%
odds 3 x 10 = 30
TSH LR+ 10

17. Pre test probability: poor reproducibility
but people have different opinions
Da: Phelps M, Levitt A. Acad Emerg Med 2004; 11: 692-4 17

18. Pre test probability = an OPINION
about the likelihood that your patient actually is affected by the target disease
judging by similarity and prevalence
by prevalence
Taking into account the frequency of the suspected diseases. Even with typical presentation a rare disease remains rare (i.e. improbable)
by similarity
How much does your patient seem to have symptoms and signs (or also preliminary test results) typical of a suspected disease?

19. When you hear hoofbeats, don’t think zebras
(only) by similarity → over-estimation of the probability of rare disease (zebras)
judging
(only) by prevalence → failure to search and detect the peculiarity of the individual patient (reductionism)

20. Sensitivity 57% specificity 99% LR+ 57 LR - 043
A boy (of Northern Italian ascendant) with recurrent (>3 in the last two year) episodes of abdominal pain with fever > 38° lasting >48h, sometimes accompanied by mono-arthritis.
Familiar Mediterranean Fever (FMF) was suspected and genetic test performed.
His presentation: 3 out of 4 major criteria for Familiar Mediterranean Fever (Livneh A, Langevitz P, Zemer D, et al. Arthritis Rheum 1997; 40:1879. ).
Sensitivity 57% specificity 99% LR+ 57 LR - 043
FMF is a rare disease, and if 3 typical symptoms/signs are present (judging by similarity), the hypothesis that this boy is affected by the disease still remains quite improbable (judging by prevalence).

21. The clinical scenario :
Let’s discuss this case
A boy (of Northern Italian ascendant) with recurrent (>3 in the last two year) episodes of abdominal pain with fever > 38° lasting >48h, sometimes accompanied by mono-arthritis.
This presentation suggests some diagnostic hypotheses (A; B; C ; D; F…)
The sum of the probability of having A + B+ C +D + E + F.. MUST be 100%
A . ASPECIFIC COLLECTION OF SYMPTOMS
B . CONNECTIVE DISEASE (LES..)
C. CROHN DISEASE
D. REITER SYNDROME
E. STILL DISEASE of adults.
F. FAMILIAR MEDITERRANEAN FEVER

22. FAMILIAR MEDITERRANEN FEVER
by PREVALENCE: a very rare disease (with a prevalence in Italy < 1/300,000)
Judging
by SIMILARITY: the presentation is TYPICAL 3/4 major symptoms LR+ 57)
The pretest probability of FMF should be
100 – p [concurrent hypotheses]
F= 100 – (A+B+C+D+E)

23. A B C D E F
FMF :
judging only by prevalence < 1/
judging only by similarity ? > 20%
Finally you have to take into account
ALTERNATIVE HYPOTHESES
You have to judge if the (pretest) probability is low enough to rule out the FMF hypothesis or requires further testing.

24. good question, good answer
post-test probability %
Test informative effect
pre-test probability %
good question, good answer
> 25% <75%

25. What can we do with all these probabilities ?

26. When the harm of being wrong is acceptable.
Informally and intuitively :
When the harm of being wrong is acceptable.

27. DECISIONAL THRESHOLDSPA
no test - no treatment
TREATMENT
NO TEST
NO TREATMENT
DO FURTHER TESTS
Are you confident on the diagnosis? p*
treatment threshold 0%
100 % PB
test - treatment
N Engl J Med 1980; 302:1109

28. Lancet 2012; 380:307
To the Hippocratic Oath might be added:
I will not request an investigation unless I am confident that the answer, and the actions I take on its basis, will substantially improve my patient’s life

29. Archie Cochrane Before ordering a test decide what you will do if
(a) it is positive, or
(b) it is negative,
and if both answers are the same
don’t do the test !
Effectiveness and Efficiency: Random Reflections on Health Services (p 43), 1972