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Pre-test and post-test probability: When is the post-test probability sufficient for decision-making?

This study explores the estimation of pre-test and post-test probabilities in diagnostic tests and their impact on decision-making. It highlights the importance of considering test accuracy, prevalence, and subjective judgments in interpreting test results.

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Pre-test and post-test probability: When is the post-test probability sufficient for decision-making?

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  1. Pre-test and post-test probability. When is the post-test probability sufficient for decision-making? Agostino Colli Gargnano April 4-8 2017

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

  3. Imagine • 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. 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. LR+ 6.1 LR- 0.22 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. 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% AVERAGE VALUE which is typical of the study population. We need to estimate the value in our patients and in a single patient.

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

  12. a subjective estimate (opinion) of how much a hypothesis is probable is needed to calculate the effect of new information before test after test bayesian rule Probability of disease DIAGNOSIS 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. What is the probability of having the disease on the basis of the test results ? POST TEST PROBABILITY after test before test bayesian rule Probability of disease DIAGNOSIS

  15. 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) TSH LR+ 10 pre test ≈ 75% post test probability ≈ 97% odds 3 x 10 = 30

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

  18. judging by similarity and prevalence Pre test probability = an OPINION about the likelihood that your patient actually is affected by the target disease 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. (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) When you hear hoofbeats, don’t think zebras

  20. 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. FMF : judging only by prevalence < 1/100.000 judging only by similarity ? > 20% Finally you have to take into account ALTERNATIVE HYPOTHESES F A C D You have to judge if the (pretest) probability is low enough to rule out the FMF hypothesis or requires further testing. B E

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

  25. What can we do with all these probabilities ?

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

  27. Are you confident on the diagnosis? DECISIONAL THRESHOLDS PA no test - no treatment TREATMENT DO FURTHER TESTS NO TEST NO TREATMENT 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. 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 ! Archie Cochrane Effectiveness and Efficiency: Random Reflections on Health Services (p 43), 1972

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