Pre-test probability: how to read tests

A test comes back positive and the first reaction is to treat the result as a diagnosis. At the bedside, however, the same positive D-dimer can mean very different things in two patients, and the same negative test can end the investigation in one case and say almost nothing in the other. The difference lies in what you thought before ordering the test.

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This text explains pre-test probability and how it changes the interpretation of tests: the calculation with odds and likelihood ratio, an example with D-dimer in suspected deep vein thrombosis, the thresholds that tell when a test changes management, and the most common estimation errors. The shortcut for using likelihood ratios in your head and the use of history and physical exam findings as tests are in the text on differential diagnosis with clues; here the focus is the next step, the complementary test.

Key points

• Pre-test probability is the chance that the disease is present before the test, estimated from history, physical exam and epidemiology.
• The result of a test does not say whether the disease exists; it multiplies the chance you already had by the likelihood ratio of the result.
• The same result leads to very different final probabilities depending on the starting probability.
• Predictive values depend on the prevalence of the studied group; sensitivity and specificity alone do not tell the probability of disease in your patient.
• A test only helps when the probability is between two thresholds: below the first, it is not worth testing; above the second, you already treat.
• Professionals tend to overestimate the probability before and after tests, and training estimation is part of clinical reasoning.

Summary

• What pre-test probability is
• From probability to odds and back
• The D-dimer example
• Sensitivity, specificity and predictive values
• When the test does not change management
• Why we get the estimate wrong
• How to train estimation
• Frequently asked questions
• Checklist for interpreting a test

What pre-test probability is

Pre-test probability is your estimate that the patient has a disease before knowing the result of a test. It comes from what you already know: age, sex, context, symptoms, physical exam findings and the frequency of the disease where you practice. After the test, this estimate is updated and becomes the post-test probability.

Diagnosis, in this view, is a hypothesis, and absolute certainty is not achievable no matter how many tests are ordered (Kassirer, 1989). The task is to reduce uncertainty enough to make the best therapeutic decision (Kassirer, 1989). Thinking in terms of pre-test probability is the practical way to know how much uncertainty exists and how much a test can reduce it.

Where the estimate comes from

There are three main sources. The first is prevalence in the context: the same complaint has different distributions of diseases in primary care, the emergency department and the ward of a tertiary hospital. The second is the patient's own findings, each with its weight. The third is clinical prediction rules, which combine several findings into a score and have been validated in groups of patients.

When a validated rule exists, it is usually the safest anchor. In the study by Wells and colleagues, doctors used a clinical model to classify patients with suspected deep vein thrombosis as likely or unlikely before any test (Wells et al., 2003). The example below shows what happens with the same test in each group.

Estimate is not a guess

An estimate can be rough and still be useful. Saying "low", "intermediate" or "high" already changes the way you read a result, and with practice you can reach reasonable numerical ranges. What does not work is skipping this step and letting the test decide alone, because, as the next sections show, the test cannot do that.

Hypothesis before the test

In practice, pre-test probability only exists for a defined hypothesis. You do not estimate the probability of "something"; you estimate the probability of deep vein thrombosis, of pneumonia, of urinary tract infection. That is why the list of hypotheses comes before ordering tests, and each test should answer a question about a hypothesis on the list. How to build and order that list is in the text on clinical reasoning.

From probability to odds and back

The tool that links pre-test probability to the result is the likelihood ratio. It is the proportion of people with the disease who have a given result divided by the proportion of people without the disease who have the same result (Grimes and Schulz, 2005). Values greater than 1 indicate that the result is associated with the presence of the disease, and values less than 1, with its absence (Deeks and Altman, 2004).

The calculation in three steps

The likelihood ratio does not apply directly to probability, but to odds. Pre-test odds multiplied by the likelihood ratio gives the post-test odds, which then converts back to probability (Deeks and Altman, 2004). The three steps are:

1. Pre-test odds = probability ÷ (1 − probability).
2. Post-test odds = pre-test odds × likelihood ratio.
3. Post-test probability = post-test odds ÷ (1 + post-test odds).

In the example from the Deeks and Altman article, smoking 40 pack-years or more had a likelihood ratio of 20.4 for obstructive airway disease (Deeks and Altman, 2004). Starting from a probability of 0.1, the odds are 0.11; multiplied by 20.4, they become 2.27; and the final probability is 0.69 (Deeks and Altman, 2004).

The same result, three starting points

Now the same likelihood ratio of 20.4, from the Deeks and Altman article (Deeks and Altman, 2004), applied to other starting probabilities. The numbers below are an editorial calculation, made with the formula from the article.

Pre-test and post-test probability	Calculation via odds (editorial calculation)
From 1% to about 17% (editorial calculation with the likelihood ratio from Deeks and Altman, 2004)	Pre-test odds 0.01 ÷ 0.99 = 0.0101; post-test odds 0.0101 × 20.4 = 0.206; probability 0.206 ÷ 1.206 ≈ 0.17 (ratio and formula from Deeks and Altman, 2004)
From 10% to about 69% (the example from the article itself by Deeks and Altman, 2004)	Pre-test odds 0.1 ÷ 0.9 = 0.111; post-test odds 0.111 × 20.4 = 2.27; probability 2.27 ÷ 3.27 ≈ 0.69 (ratio and formula from Deeks and Altman, 2004)
From 50% to about 95% (editorial calculation with the likelihood ratio from Deeks and Altman, 2004)	Pre-test odds 0.5 ÷ 0.5 = 1; post-test odds 1 × 20.4 = 20.4; probability 20.4 ÷ 21.4 ≈ 0.95 (ratio and formula from Deeks and Altman, 2004)

Editorial calculation based on the likelihood ratio and the formula from Deeks and Altman, 2004; the starting points of 1% and 50% and the rounding are the editor's.

The lesson from the table: a result with a high likelihood ratio, considered strong, still leaves the disease unlikely when the starting probability is very low (editorial calculation above). That is why the same information can confirm the diagnosis in one patient and only raise a doubt in another.

The Fagan nomogram

To avoid the conversions, there is a nomogram: a ruler with three columns in which a straight line links pre-test probability to the likelihood ratio and shows the post-test probability (Fagan, 1975). The Deeks and Altman article includes the nomogram with the same smoking example, from 0.1 to about 0.7 (Deeks and Altman, 2004). For the mental shortcut without a nomogram, see the simplified method in the text on differential diagnosis.

Strength of a likelihood ratio

Ratios above 10 and below 0.1 are considered strong evidence to confirm or rule out a diagnosis in most situations (Deeks and Altman, 2004). Ratios close to 1 barely change the decision, while very high or very low ratios change the estimate considerably (Grimes and Schulz, 2005). "Strong" here is always relative to the starting point, as the table showed.

Results with multiple levels

Not every test is positive or negative. Tests with results in ranges can have a likelihood ratio for each range (Grimes and Schulz, 2005). In the example by Deeks and Altman, each smoking load range has its own ratio: 20.4 for 40 pack-years or more, 1.01 for 20 to 40, and 0.55 for up to 20 (Deeks and Altman, 2004). Reading a greatly altered value as equal to a slightly altered one throws away information.

The D-dimer example

The trial by Wells and colleagues is a good example of pretest probability in practice, because it shows the same test in two groups with different starting probabilities (Wells et al., 2003). The numbers below were checked in the full text of the article.

The study design

Outpatients with suspected deep vein thrombosis in the lower limbs were classified by a clinical model as likely (score of 2 or more) or unlikely (less than 2) and randomized to ultrasound alone or D-dimer followed by ultrasound (Wells et al., 2003). In the D-dimer group, those who were unlikely and had a negative D-dimer did not undergo ultrasound (Wells et al., 2003).

The starting probability in each group

Among the 1,082 patients who completed follow-up, the prevalence of proximal deep vein thrombosis or pulmonary embolism was 15.7% (Wells et al., 2003). In the likely group, it was 27.9%; in the unlikely group, 5.5% (Wells et al., 2003). Within the D-dimer arm, the proportions were 28.7% among the likely and 5.1% among the unlikely (Wells et al., 2003).

The same test, two results

Group (D-dimer arm)	Starting probability	Negative predictive value	Positive predictive value
Unlikely	5.1% (Wells et al., 2003)	99.1% (Wells et al., 2003)	14.1% (Wells et al., 2003)
Likely	28.7% (Wells et al., 2003)	89.0% (Wells et al., 2003)	38.6% (Wells et al., 2003)

Source of all numbers in the table: Wells et al., 2003.

In the unlikely group, the negative predictive value was 99.1% and the positive predictive value was 14.1% (Wells et al., 2003). In the likely group, the negative was 89.0% and the positive was 38.6% (Wells et al., 2003). Read another way (editorial calculation: 100% minus the negative predictive value from Wells et al., 2003), after a negative D-dimer about 0.9% of disease remained in the unlikely group and about 11% in the likely group.

This is the core of pretest probability: the same negative test almost ruled out the disease in those who already started low and left a chance in about nine in those who started high (editorial calculation from Wells et al., 2003). Not by chance, the study protocol called for ultrasound for every likely patient, with or without a negative D-dimer (Wells et al., 2003).

What the article does not report

The article by Wells and colleagues does not report the sensitivity or specificity of D-dimer in this sample. It provides the prevalence by group and the predictive values, and mentions that the two tests used had similar negative predictive values in a previous study by the authors (Wells et al., 2003). Therefore, this text does not assign sensitivity or specificity numbers to the study.

Implied likelihood ratios (editorial calculation)

It is possible to estimate, approximately, the likelihood ratio that would lead from the starting probability to the final probability in each group. This is an editorial calculation, with the numbers from Wells et al. (2003), and not a result published by the article.

• Unlikely, negative D-dimer: pretest odds 0.051 ÷ 0.949 ≈ 0.054; post-test odds 0.009 ÷ 0.991 ≈ 0.009; implied ratio 0.009 ÷ 0.054 ≈ 0.17 (editorial calculation with the numbers from Wells et al., 2003 and the formula from Deeks and Altman, 2004).
• Unlikely, positive D-dimer: post-test odds 0.141 ÷ 0.859 ≈ 0.164; implied ratio 0.164 ÷ 0.054 ≈ 3.1 (editorial calculation with the numbers from Wells et al., 2003 and the formula from Deeks and Altman, 2004).
• Likely, negative D-dimer: pretest chance 0.287 ÷ 0.713 ≈ 0.40; posttest chance 0.11 ÷ 0.89 ≈ 0.12; implicit ratio 0.12 ÷ 0.40 ≈ 0.31 (editorial calculation with the numbers from Wells et al., 2003 and the formula from Deeks and Altman, 2004).
• Likely, positive D-dimer: posttest chance 0.386 ÷ 0.614 ≈ 0.63; implicit ratio 0.63 ÷ 0.40 ≈ 1.6 (editorial calculation with the numbers from Wells et al., 2003 and the formula from Deeks and Altman, 2004).

The implicit ratios differ between the groups (editorial calculation above). One possible explanation is that the ability of a test to separate sick from not sick patients can vary with the type of patient evaluated, the so-called spectrum bias, which is one of the caveats pointed out for accuracy studies (Pewsner et al., 2004). The lesson for the study is twofold: the starting probability matters, and the performance of a test depends on the group in which it was measured.

The practical gain

Using the pretest probability together with the D-dimer reduced the average number of ultrasounds per patient from 1.34 to 0.78 (Wells et al., 2003). Two hundred and eighteen patients in the D-dimer group, 38.8% of those who completed follow-up, did not need an ultrasound (Wells et al., 2003). Among the patients in the D-dimer group in whom thrombosis was ruled out by the initial strategy, 0.4% had a thromboembolic event within three months, versus 1.4% in the control group, a difference without statistical significance (Wells et al., 2003).

Sensitivity, specificity and predictive values

Sensitivity and specificity describe how the presence or absence of the disease predicts the test result; they do not, on their own, tell the probability of disease given a result (Deeks and Altman, 2004). Predictive values give that probability, but they depend on the prevalence in the group studied (Deeks and Altman, 2004). The likelihood ratio brings the two things together: it comes from the performance of the test and applies to your patient's probability.

Why the predictive value does not travel

The D-dimer example showed this in practice: the same test had quite different predictive values in the likely and unlikely groups (Wells et al., 2003). A published predictive value holds for patients similar to those in the study. If your patient starts from a quite different probability, the predictive value from the article is not theirs.

SnNOut and SpPIn with care

Two memory rules are popular: a very sensitive test, when negative, rules out the disease (SnNOut); a very specific test, when positive, confirms it (SpPIn) (Pewsner et al., 2004). Pewsner and colleagues show that the power to rule out does not depend only on sensitivity and falls when specificity is low; likewise, the power to confirm depends on both measures (Pewsner et al., 2004). The authors recommend critically evaluating accuracy studies and calculating posttest probabilities, with confidence intervals, before treating a test as SnNOut or SpPIn (Pewsner et al., 2004).

Combining test and clinical findings

The likelihood ratios of complementary tests, when added to a good clinical assessment, improve diagnostic accuracy synergistically (Grimes and Schulz, 2005). In practice, this means that the test does not replace the history and physical examination: it starts from the point where they left the probability.

When the test does not change management

A test is worth it when the result can change what you do. Pauker and Kassirer described two probability thresholds for this decision: the testing threshold and the test-treatment threshold (Pauker and Kassirer, 1980).

The two thresholds

If the probability of disease is below the testing threshold, you neither treat nor test; if it is above the test-treatment threshold, you treat without further tests; the test should only be done between the two thresholds (Pauker and Kassirer, 1980). The threshold values depend on the reliability and risks of the test and the benefits and risks of treatment (Pauker and Kassirer, 1980).

A published example of a threshold

Kline and colleagues estimated the testing threshold for ordering D-dimer in suspected pulmonary embolism at 1.8%, using the method of Pauker and Kassirer (Kline et al., 2004). With eight clinical criteria, among them age under 50 years and pulse under 100 beats per minute, the authors derived a rule to justify not ordering the test (Kline et al., 2004). Among low-risk patients who met all the criteria, the prevalence of pulmonary embolism was 1.4%, below the threshold (Kline et al., 2004).

The authors themselves point out the limitation: the specificity of the rule was 27% in the low-risk group and 15% in the very low-risk group (Kline et al., 2004). The value of the example, for those who study, is to show the reasoning: when the probability is already below the testing threshold, the test result should not change management.

The search for certainty

Kassirer pointed to the stubborn search for diagnostic certainty as a cause of excess testing and recalled that the task is to reduce uncertainty enough to decide, not to eliminate it (Kassirer, 1989). In a meta-analysis of 15 years of studies, the average rate of overuse of laboratory tests was 20.6% (Zhi et al., 2013). The same meta-analysis found average underuse of 44.8%, which is a reminder that the problem is also failing to order the test that would change management (Zhi et al., 2013).

Questions before ordering

A simple way to apply the thresholds on the ward, as editorial guidance:

1. Which hypothesis will this test examine?
2. What is my pre-test probability for it, even as a range?
3. If the result comes back positive, what do I do? And if it comes back negative?
4. If both answers are the same, the test does not change management.

Editorial guidance; the decision to order a test or not is always up to the physician responsible for the patient.

Why we get the estimate wrong

Estimating probability is hard, and studies show that error is common even among trained professionals.

Overestimating before and after

In a survey of 553 professionals from outpatient clinics in eight American states, with scenarios common in primary care, the pre-test probability was overestimated in all four scenarios presented (Morgan et al., 2021). After a positive radiograph for pneumonia, the estimated probability was 95%, against 46% to 65% in the evidence (Morgan et al., 2021). After a positive mammogram, the estimate was 50%, against 3% to 9% in the evidence (Morgan et al., 2021). The authors suggest that these overestimates contribute to overdiagnosis and overuse of tests (Morgan et al., 2021).

The classic false-positive question

In 1978, Casscells and colleagues asked physicians, residents and students what the chance of disease was after a positive test, in a disease with a prevalence of 1 in 1,000 and a false-positive rate of 5% (Manrai et al., 2014). When repeating the same question in 2013, Manrai and colleagues found 23% correct answers, with no significant difference compared with the 18% of the original study (Manrai et al., 2014). The most common answer in both studies was 95%, given by 44% of participants in 2013 (Manrai et al., 2014).

The calculation, as editorial calculation with the prevalence and the false-positive rate from the question reported by Manrai et al., 2014 and assuming the test detects every sick person: in 1,000 people, 1 has the disease and tests positive; of the 999 without the disease, about 5%, or 50, test positive; so 1 in about 51 positives has the disease, close to 2%, the same answer that Manrai and colleagues considered correct (Manrai et al., 2014). The distance between the most common answer, 95%, and the correct one, close to 2%, is the distance between ignoring and considering the pre-test probability (Manrai et al., 2014).

Natural frequencies help

Replacing percentages with counts, as in the calculation above, makes reasoning easier. In a study with 48 physicians, the positive predictive value was estimated correctly 10% of the time when the information came as probabilities, and 46% when it came as natural frequencies (Hoffrage and Gigerenzer, 1998). Thinking "in every 1,000 patients like this" is a simple tool for the ward.

Very different estimates for the same case

In a study with emergency and internal medicine residents and attending physicians, pretest probability estimates for the same written case varied widely; in one of the cases, answers ranged from 3% to 98% (Phelps and Levitt, 2004). The authors warn that this variation can limit the consistency of post-test probabilities calculated with likelihood ratios (Phelps and Levitt, 2004). So whenever one exists, a validated prediction rule or local prevalence data helps anchor the estimate.

Mistakes worth avoiding

• Forgetting the starting point: reading the result as if it were enough on its own.
• Using the predictive value of another group: applying the number from the article to a patient very different from those studied.
• Treating a range result as binary: losing the information about how abnormal the test came back.
• Trusting the memory rule too much: applying SnNOut to a test with low specificity.
• Ordering a test that does not change management: when any result leads to the same decision.

How to train the estimate

The estimate improves with repetition and feedback, like any clinical reasoning skill. The key point is to write down a number before seeing the result and compare afterward.

On the ward

Before looking at a test, tell yourself the main hypothesis and a probability range. After the result, redo the estimate and see if the change matches the strength of the test. When there is a validated prediction rule for the situation, compare your estimate with the rule's. Discuss with the resident or the attending physician not only the diagnosis, but the probability each of you had before the test.

With training cases

Staged cases are good for this exercise because the data arrive little by little, as on the ward. With each new piece of information, write down the main hypothesis and the probability you assign to it; at the end, see at what point the estimate changed and why.

Training on NEXO

On NEXO, each case arrives in up to six clues, and this format is a good field for training pretest probability: with each clue you form hypotheses and can estimate how much you trust the main one before the next. Each guess shows the proximity in ICD-10 across five levels, which tells you whether your hypothesis was in the right group of diseases. On the third clue the case area appears and, on the fifth, the ICD range; you can skip a clue whenever you want to move ahead.

A simple exercise to do in the Daily mode, with the case of the day, the same for everyone: before each guess, write down your hypothesis and a probability range; at the end, compare with the group at which clue each person felt most confident. The Archive gathers previous cases, Multimedia brings cases with image and audio, and Continents, cases linked to Africa, the Americas, Asia, Europe and Oceania, where epidemiology changes the starting probability. Adrenaline, with the dose chosen beforehand, trains the estimate under time pressure.

The Anki button creates the card straight from NEXO and opens it in the Anki app, searches the cards you already have and, when the case has an image, takes the image to the card; it is worth saving the finding that most changed your estimate. To understand the limits of each mode, see the NEXO economy page. To get to know the game, read what NEXO is.

With the group

The ranking has the Global, Universities and Group tabs, the latter with an invite code. With the league or the group playing the same case, comparing estimates shows in practice the variation that studies describe and helps each person calibrate their own number. If you coordinate a medical school, league or residency and want to use cases like these in teaching, get to know NEXO Closer. Researchers who want to study how students calibrate the estimate can get to know NEXO Researcher, physicians who want to review cases, NEXO Curator, and those who produce Medicine content, NEXO Creators.

Frequently asked questions

What is pretest probability?

It is the estimate that the patient has a disease before the result of a test, based on history, physical examination, epidemiology and, when they exist, validated prediction rules. After the test, it is updated and becomes the post-test probability.

How do you calculate post-test probability?

Convert the pretest probability into odds, multiply by the likelihood ratio of the result and convert back into probability (Deeks and Altman, 2004). The Fagan nomogram does the same calculation without math (Fagan, 1975).

Why does the same positive test mean different things?

Because the result multiplies the chance that already existed. With the same likelihood ratio of 20.4, a probability of 10% goes to about 69% (Deeks and Altman, 2004), while one of 1% goes to about 17% (editorial calculation with the same formula).

What is the difference between predictive value and likelihood ratio?

Predictive value is already a probability of disease, but it depends on the prevalence of the group in which it was measured (Deeks and Altman, 2004). The likelihood ratio measures the strength of the result and can be applied to your patient's probability.

Does a negative D-dimer always rule out thrombosis?

In the study by Wells and colleagues, a negative D-dimer safely ruled out thrombosis in clinically unlikely patients, but it was not used alone in the likely ones, who underwent ultrasound (Wells et al., 2003). The decision for each patient belongs to the responsible physician.

When is it not worth ordering a test?

When the probability is below the testing threshold or above the test-treatment threshold, because the result does not change management (Pauker and Kassirer, 1980).

How to train the estimation of pretest probability?

Write a probability range before each result and compare afterward. Stepwise cases, such as those in NEXO with up to six clues, help practice forming hypotheses and estimating with each new piece of information.

Checklist for interpreting a test

1. Define the hypothesis the test will examine.
2. Estimate the pretest probability, even if only as a range.
3. Look for a prediction rule validated for the situation.
4. Ask whether the result changes management, positive or negative.
5. Use the likelihood ratio, not just sensitivity or specificity.
6. Do the math using odds or use the nomogram.
7. Read results as a range by level, not just as positive or negative.
8. Think in natural frequencies: out of every 1,000 patients like this one.
9. Check whether the study of the test had patients similar to yours.
10. Compare your estimate with that of colleagues and with the case outcome.

Want to train today? Play the case of the day on NEXO.

References

1. Kassirer JP. Our stubborn quest for diagnostic certainty. A cause of excessive testing. N Engl J Med. 1989. https://doi.org/10.1056/NEJM198906013202211
2. Wells PS, Anderson DR, Rodger M, et al. Evaluation of D-dimer in the diagnosis of suspected deep-vein thrombosis. N Engl J Med. 2003. https://doi.org/10.1056/NEJMoa023153
3. Grimes DA, Schulz KF. Refining clinical diagnosis with likelihood ratios. Lancet. 2005. https://pubmed.ncbi.nlm.nih.gov/15850636/
4. Deeks JJ, Altman DG. Diagnostic tests 4: likelihood ratios. BMJ. 2004. https://pubmed.ncbi.nlm.nih.gov/15258077/
5. Fagan TJ. Letter: Nomogram for Bayes's theorem. N Engl J Med. 1975. https://pubmed.ncbi.nlm.nih.gov/1143310/
6. Pewsner D, Battaglia M, Minder C, et al. Ruling a diagnosis in or out with "SpPIn" and "SnNOut": a note of caution. BMJ. 2004. https://pubmed.ncbi.nlm.nih.gov/15271832/
7. Pauker SG, Kassirer JP. The threshold approach to clinical decision making. N Engl J Med. 1980. https://pubmed.ncbi.nlm.nih.gov/7366635/
8. Kline JA, Mitchell AM, Kabrhel C, et al. Clinical criteria to prevent unnecessary diagnostic testing in emergency department patients with suspected pulmonary embolism. J Thromb Haemost. 2004. https://pubmed.ncbi.nlm.nih.gov/15304025/
9. Zhi M, Ding EL, Theisen-Toupal J, et al. The landscape of inappropriate laboratory testing: a 15-year meta-analysis. PLoS One. 2013. https://pubmed.ncbi.nlm.nih.gov/24260139/
10. Morgan DJ, Pineles L, Owczarzak J, et al. Accuracy of Practitioner Estimates of Probability of Diagnosis Before and After Testing. JAMA Intern Med. 2021. https://pubmed.ncbi.nlm.nih.gov/33818595/
11. Manrai AK, Bhatia G, Strymish J, et al. Medicine's uncomfortable relationship with math: calculating positive predictive value. JAMA Intern Med. 2014. https://pubmed.ncbi.nlm.nih.gov/24756486/
12. Hoffrage U, Gigerenzer G. Using natural frequencies to improve diagnostic inferences. Acad Med. 1998. https://pubmed.ncbi.nlm.nih.gov/9609869/
13. Phelps MA, Levitt MA. Pretest probability estimates: a pitfall to the clinical utility of evidence-based medicine? Acad Emerg Med. 2004. https://pubmed.ncbi.nlm.nih.gov/15175211/