Pre-Test Probability

Pre-Test Probability in Diagnostic Pathways and Test Evaluation

Pre-test probability is the starting estimate of how likely a person is to have the condition a test looks for, attached to a defined group of patients in a defined setting. A test result moves that estimate, and how far it moves depends on the test's accuracy and on where the estimate started. In health economics the pre-test probability is usually the first branch probability of a diagnostic decision tree, so it fixes how many true and false positives a testing strategy produces and the costs and QALYs that follow. The same test can be good value in one group of patients and poor value in another purely because their pre-test probabilities differ, so most of the practical difficulty lies in estimating the number for the right population.

Where the starting estimate comes from

The simplest estimate is the prevalence of the target condition among people who present in the same way and in the same setting as the patient. A finer estimate adjusts that figure for the patient's own features. For suspected coronary artery disease, Diamond and Forrester in 1979 estimated the pretest likelihood of disease by age, sex and symptoms from published data and combined it with the accuracy of four tests, including stress electrocardiography, through Bayes' theorem. They suggested the approach might help with decisions on the cost-effectiveness of tests.

$$p = \frac{D}{N}, \qquad O_{pre} = \frac{p}{1 - p}$$

where $p$ is the pre-test probability, $D$ is the number of people with the target condition among the $N$ people in the group to be tested, and $O_{pre}$ is the pre-test odds.

Clinical prediction rules give the estimate a formal structure. The NICE guideline on venous thromboembolic diseases (NG158, published March 2020 and last updated August 2023) asks clinicians to use the two-level PE Wells score to estimate the clinical probability of pulmonary embolism. The score adds points for clinical features, such as signs of deep vein thrombosis or a heart rate above 100 beats per minute, and more than 4 points places a patient in the PE likely group. A multivariable diagnostic model gives a continuous estimate that can serve as the pre-test probability for the next test.

When there are several risk strata, the overall prevalence in the tested population is a weighted average of the stratum values.

$$p = \sum_{k} w_k \, p_k$$

where $w_k$ is the share of tested patients who fall in stratum $k$ and $p_k$ is the pre-test probability in that stratum. A model that uses only the overall $p$ treats every patient as average.

How a test result moves the estimate

In a BMJ statistics note, Deeks and Altman give a likelihood ratio of 20.4 for a smoking history of 40 or more pack years, which takes a pre-test probability of obstructive airway disease of 0.1 to a post-test probability of 0.69, but takes 0.01 only to about 0.17. They also note that predictive values depend on the prevalence in the study sample and can rarely be generalised beyond the study, whereas likelihood ratios adapt to prior probabilities that differ between contexts. The positive predictive value and negative predictive value of an accuracy study are therefore tied to that study's pre-test probability.

For a negative result, the residual probability of disease follows from sensitivity, specificity and the pre-test probability.

$$P(D^{+} \mid T^{-}) = \frac{p\,(1 - Se)}{p\,(1 - Se) + (1 - p)\,Sp}$$

where $D^{+}$ is presence of the target condition, $T^{-}$ is a negative test result, $Se$ is sensitivity and $Sp$ is specificity. Whether a negative result can end investigation depends on this residual probability, which rises with $p$.

Why estimates differ between settings

Pre-test probability belongs to a population at a point in a care pathway, so it changes as referral filters patients. The group reaching a specialist clinic contains more people with the condition and often a different spectrum of disease, and accuracy can shift with it. Across 23 meta-analyses of 416 studies, Leeflang and colleagues found that specificity tended to be lower at higher prevalence and that the effect was statistically significant for sensitivity or specificity in 8 of the meta-analyses. They attributed this to mechanisms such as patient spectrum that affect prevalence and accuracy together.

Prediction rules also drift out of calibration. Genders and colleagues tested the Diamond and Forrester model on 2,260 patients with chest pain referred for coronary angiography at 14 hospitals and found that it overestimated the probability of coronary artery disease, especially in women. Predictions also varied across hospitals because disease prevalence differed.

Pre-test probability and the decision to test

Pauker and Kassirer set out the threshold approach in 1980. Treatment is withheld when the probability of disease is below a testing threshold, given without further testing above a test-treatment threshold, and the test is done only between the two. The clinical decision analysis page derives the thresholds. Outside the band, the expected gain from what the test can change in management is smaller than its cost and harm.

NG158 recommends that people with a likely PE Wells score be offered a CT pulmonary angiogram, and that people with an unlikely score be offered a D-dimer test first. When clinical suspicion is low and other diagnoses are feasible, it suggests the pulmonary embolism rule-out criteria to help decide whether further investigation is needed. For recent-onset chest pain, the NICE guideline CG95 was updated in November 2016 to remove references to an estimate of the likelihood of coronary artery disease. CT coronary angiography is now offered when clinical assessment indicates typical or atypical angina, or non-anginal chest pain with ST-T changes or Q waves on a resting ECG.

Pre-test probability as a parameter in economic evaluation

The NICE HealthTech programme manual (PMG48, section 2.3.14) notes that trials of tests are unusual and asks for a linked evidence modelling approach when direct data on final outcomes are missing, joining test results to the care decisions they trigger and then to outcomes. The pre-test probability enters at the first link, splitting the cohort into those who can be true positives or false negatives and those who can be false positives or true negatives. PMG48 (section 2.2.15) lists setting and patient population among sources of heterogeneity in accuracy results, so accuracy inputs should match the population of the pre-test probability.

In a cost-effectiveness analysis of imaging for stable chest pain, Genders and colleagues found that results were sensitive to the probability of coronary artery disease and to assumptions about false-positive results. A model can report results by pre-test stratum when practice can identify the strata, give the input a beta distribution in probabilistic sensitivity analysis when it comes from counts, and use threshold analysis to find where the preferred strategy changes. The NICE technology appraisal manual (PMG36, section 4.2.16) asks for net health benefits at GBP 25,000 and GBP 35,000 per QALY, so a threshold can be reported at both.

Worked example with a two-level score before a rule-out test

All numbers are illustrative and do not describe any real score or test. A service sees 1,000 patients with a suspected condition. A two-level clinical score places 300 of them in a high group with a pre-test probability of 40% and 700 in a low group with a pre-test probability of 8%. A rule-out blood test has sensitivity 0.95 and specificity 0.50 and costs GBP 20. Imaging costs GBP 200 and is assumed to be perfect and harmless. Each missed case loses 0.5 QALYs, and detected and missed cases are assumed to cost the same, so only testing costs differ.

1. Overall pre-test probability. The high group holds 0.40 × 300 = 120 cases and the low group 0.08 × 700 = 56, so the overall value is 0.3 × 0.40 + 0.7 × 0.08 = 0.176.

2. Residual probability after a negative blood test. In the low group, 56 × 0.05 = 2.8 cases test negative, as do 644 × 0.50 = 322 people without the condition, so the residual probability is 2.8 / 324.8 = 0.0086, or 0.86%. In the high group, 120 × 0.05 = 6 cases and 180 × 0.50 = 90 non-cases test negative, giving 6 / 96 = 0.0625, or 6.25%. Using the overall value of 0.176 gives 8.8 / 420.8 = 0.0209, or 2.09%, a figure that describes neither group.

3. Strategy A, blood test for everyone. Positive results number 375.2 in the low group and 204 in the high group, so 579.2 patients go on to imaging. The cost is 1,000 × GBP 20 + 579.2 × GBP 200 = GBP 20,000 + GBP 115,840 = GBP 135,840, and 2.8 + 6 = 8.8 cases are missed.

4. Strategy B, stratified. The high group is imaged without the blood test. Imaging falls on 300 + 375.2 = 675.2 patients, so the cost is 700 × GBP 20 + 675.2 × GBP 200 = GBP 14,000 + GBP 135,040 = GBP 149,040, and 2.8 cases are missed.

5. Compare. Strategy B costs GBP 149,040 minus GBP 135,840 = GBP 13,200 more, misses 6 fewer cases and gains 6 × 0.5 = 3.0 QALYs, an ICER of GBP 13,200 / 3.0 = GBP 4,400 per QALY. At GBP 25,000 per QALY its incremental net monetary benefit is 3.0 × 25,000 minus 13,200 = GBP 61,800 per 1,000 patients.

6. Find the threshold. Within a stratum, testing first instead of imaging everyone saves imaging for negative patients, less the blood test, and loses the QALYs of missed cases. Testing first is preferred while $p$ is below this value.

$$p^{*} = \frac{c_I \, Sp - c_T}{c_I \, Sp + (1 - Se)(\lambda q - c_I)}$$

where $p^{*}$ is the threshold pre-test probability, $c_I$ is the cost of imaging, $c_T$ is the cost of the rule-out test, $\lambda$ is the value placed on a QALY and $q$ is the QALY loss per missed case. At GBP 25,000 per QALY the numerator is 80, the imaging saving of 200 × 0.50 less the GBP 20 test, and the denominator is 100 + 0.05 × (12,500 minus 200) = 715, so the threshold is 80 / 715 = 0.112, or 11.2%. At GBP 35,000 the denominator is 100 + 0.05 × (17,500 minus 200) = 965 and the threshold is 80 / 965 = 0.083, or 8.3%. The negative likelihood ratio page finds a similar break-even between two referral populations, whereas here the split comes from a score within one service.

7. Interpret. The low group, at 8%, sits below both thresholds, and for its 700 patients testing first saves GBP 140,000 minus GBP 89,040 = GBP 50,960 against 2.8 × 0.5 = 1.4 QALYs lost, or GBP 36,400 per QALY forgone. The high group, at 40%, is far above both, so it is better imaged directly. A model using the overall 17.6% would place everyone above the threshold and miss the gain in the low group, and the narrow margin at GBP 35,000 shows how much rests on the low-group estimate.

Boundaries with nearby concepts

Prevalence describes a population, whereas pre-test probability applies to a patient or subgroup at one step, and the two coincide only when nothing distinguishes the patient from that population. Pre-test probability is a specific use of the general idea of a prior probability in diagnosis. It differs from a prior distribution in a Bayesian analysis, which describes uncertainty about a model parameter and not the chance that one patient has a condition. In a sequence of tests the post-test probability after one test becomes the pre-test probability for the next, which assumes the tests' errors are independent given disease status.

Common errors in estimating and using pre-test probability

Most errors come from taking the number from the wrong population, or from treating it as fixed when it is uncertain. Each passes into the model through the counts of false positives and missed cases.

• Borrowing the accuracy study's prevalence. A referral-centre study often has a higher prevalence than primary care, and its predictive values do not transfer.
• Using an uncalibrated prediction rule. The Diamond and Forrester model overestimated the probability of coronary artery disease in a later cohort, especially in women.
• Treating the input as certain. An estimate from a small series or expert judgement carries uncertainty that belongs in probabilistic and threshold analyses.

Sources

• Deeks JJ, Altman DG. Diagnostic tests 4: likelihood ratios. BMJ. 2004;329(7458):168-169. https://doi.org/10.1136/bmj.329.7458.168
• Diamond GA, Forrester JS. Analysis of probability as an aid in the clinical diagnosis of coronary-artery disease. New England Journal of Medicine. 1979;300(24):1350-1358. https://doi.org/10.1056/NEJM197906143002402
• Genders TSS, Steyerberg EW, Alkadhi H, et al. A clinical prediction rule for the diagnosis of coronary artery disease: validation, updating, and extension. European Heart Journal. 2011;32(11):1316-1330. https://doi.org/10.1093/eurheartj/ehr014
• Genders TSS, Petersen SE, Pugliese F, Dastidar AG, Fleischmann KE, Nieman K, Hunink MGM. The optimal imaging strategy for patients with stable chest pain: a cost-effectiveness analysis. Annals of Internal Medicine. 2015;162(7):474-484. https://doi.org/10.7326/M14-0027
• Leeflang MMG, Rutjes AWS, Reitsma JB, Hooft L, Bossuyt PMM. Variation of a test's sensitivity and specificity with disease prevalence. CMAJ. 2013;185(11):E537-E544. https://doi.org/10.1503/cmaj.121286
• National Institute for Health and Care Excellence. Recent-onset chest pain of suspected cardiac origin: assessment and diagnosis (CG95). London: NICE; 2010, last updated 30 November 2016. Recommendations 1.3.4.3 and update information. https://www.nice.org.uk/guidance/cg95
• National Institute for Health and Care Excellence. Venous thromboembolic diseases: diagnosis, management and thrombophilia testing (NG158). London: NICE; 2020, last updated 2 August 2023. Recommendations 1.1.16 to 1.1.21. https://www.nice.org.uk/guidance/ng158
• National Institute for Health and Care Excellence. NICE HealthTech programme manual (PMG48). London: NICE; 2025, last updated 17 December 2025. Sections 2.2.15 and 2.3.14. https://www.nice.org.uk/process/pmg48
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). London: NICE; 2022, last updated 13 October 2026. Section 4.2.16. https://www.nice.org.uk/process/pmg36
• Pauker SG, Kassirer JP. The threshold approach to clinical decision making. New England Journal of Medicine. 1980;302(20):1109-1117. https://doi.org/10.1056/NEJM198005153022003