What a Test Actually Tells You — An Introduction to Sensitivity, Specificity, and Pretest Probability

The phrase "a test with 99% accuracy" tells a person who just received their results, by itself, nothing at all.

The numbers on the test report are facts about the test. The person holding the results wants to know facts about themselves. The two are not the same. To cross over from the former to the latter, one more piece of information—which is written nowhere on the test report—must be present. That information is the pretest probability, that is, the probability that this person has the disease before taking the test.

This article follows only that path across. The terms placed along the path are all familiar ones, but at the place where each term first appears, its definition is established anew once.

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Same Test, Two Populations

We create an imaginary test. Before that, we define two ratios that describe test performance.

Sensitivity is the proportion of people who actually have the disease whom the test correctly catches as positive. If sensitivity is 99%, when you give this test to 100 people with the disease, 99 test positive and one is missed. Specificity is the proportion of people who do not have the disease whom the test correctly filters out as negative. If specificity is 99%, out of 100 people without the disease, 99 test negative and one is misjudged.

The two ratios share something in common. Both are values counted backward with the knowledge of who already has the disease. You gather people with the disease on one side first, and count what the test said for those people. In the clinic, the direction is reversed. You receive the result first without knowing which group the person sitting in front of you belongs to.

A separately established standard decides who has the disease. A reference standard is the criterion that judges who is counted as having the disease and who is counted as not having it. It may be a biopsy, imaging, or the consensus of multiple clinicians. You first divide the population into disease and non-disease using the reference standard, and then measure how well the test being evaluated (the index test) separates the two groups (PMID 33876780). Therefore, if this standard wavers, both sensitivity and specificity waver along with it.

Now we apply this test to two populations. Counting by the number of people rather than percentages makes calculation faster, and multiple studies have shown that probability estimation improves when presented in terms of person counts (PMID 26220870).

Population A — 10 out of 1,000 people have the disease (1%)

• Out of 10 people with the disease, about 10 test positive
• Out of 990 people without the disease, about 10 test positive (1% misjudgment)
• Total positives are 20, of which the true ones are 10 → probability that a positive person actually has the disease ≈ 50%

Population B — 300 out of 1,000 people have the disease (30%)

• Out of 300 people with the disease, about 297 test positive
• Out of 700 people without the disease, about 7 test positive
• Total positives are 304, of which the true ones are 297 → ≈ 98%

The test is the same. Neither sensitivity nor specificity changed. Yet the exact same positive result is fifty-fifty in Population A, and close to certainty in Population B. A result that comes out positive even though there is no disease is called a false positive, and in Population A, half of the positives are false positives.

This difference has a name. Positive predictive value is the probability that a person who tests positive actually has the disease. Negative predictive value is the probability that a person who tests negative actually does not have the disease. The 1% and 30% that divided the two populations are the pretest probability defined earlier. When looking at the population as a whole, the prevalence in that population—that is, the proportion of people who have the disease—becomes the pretest probability.

The calculation that moves from the pretest probability to the post-result probability also has a name. Bayes' rule is the rule that incorporates test results into the pretest probability to move to the post-test probability. The post-test probability is also called the posterior probability. According to this rule, the pretest probability (= prevalence) and the measurement properties of the test (sensitivity and specificity) together determine the post-test probability (PMID 33741123). The distinction that forms the backbone of this entire article comes from here.

What the patient wants to know is always the bottom row. And the bottom row cannot be calculated from the top row alone.

A classic review summarizing the principles of screening summarizes this as follows. In situations with low prevalence, even a very excellent test has a poor positive predictive value. Therefore, knowing the approximate prevalence is a prerequisite for interpreting screening test results (PMID 11897304).

Training Does Not Erase the Illusion

Diagnostic accuracy metrics confuse even physicians. When 326 residents were asked the meanings of these metrics, the median score was 3 out of 7. When asked to calculate the post-test probability of appendicitis, 30 people (11.8%) estimated it correctly, and 86.6% estimated it higher than the actual value. Training year, acute care surgery experience, and the format in which information was presented failed to change the results (PMID 26306891). The authors write that most people overestimated the probability of disease, which correspondingly increases the risk of unnecessary procedures and treatments.

Other studies point in the same direction. In a systematic review pooling 24 papers, looking at 6 papers that asked for definitions, healthcare professionals more frequently got the definition of the likelihood ratio—a value measuring how much a test result shifts probability—wrong than the definitions of sensitivity and specificity. They tended to overestimate the probability following a positive result. Whether presentation as likelihood ratios improves estimation remains inconclusive. Three studies showed improved accuracy, while 3 studies showed decreased accuracy. On the other hand, 5 studies showed that presenting information using natural frequencies rather than probabilities improved estimation and calculation. The authors suggest that combining natural frequencies and visual aids can aid understanding (PMID 26220870).

Statistical training also fails to clear away this illusion. A 1982 study posed conditional probability problems to four groups of individuals: physicians with statistical training, private practice physicians, nurses, and hospital staff. The group that gave the most biased answers was the physicians with statistical training. On problems requiring prevalence information, they were clearly better than the other groups, yet only 34% of their responses were accurate, and 37% ignored the concept of prevalence (PMID 7157027). The authors concluded that intensive statistical and decision-making training has limited value in improving clinicians' judgment.

Recent data share the same texture. In a survey of medical students, the correct answer rate for Bayesian reasoning tasks was 41.1%, and the correct answer rate for a scenario distinguishing stroke from migraine was 48.3%. Students ranked pathophysiology and symptoms at the very top as important factors in diagnosis, placing epidemiology dead last out of 9 factors (mean rank 8.8) (PMID 41840426).

The habit of placing epidemiology dead last contains the entire problem this article addresses. Epidemiology is the primary ingredient of pretest probability, and without pretest probability, you cannot read what a test result means for this person.

That Is Also How It Shows Up in Real Data

The 1% and 30% earlier were invented numbers. In real data as well, when the prevalence is low, a significant portion of positives turns out to be a misfire.

Out of 19,597 respiratory specimens handled by a laboratory over one month, SARS-CoV-2 RNA was detected for the first time in 52 specimens (0.27%). When these 52 specimens were retested with a different platform, only 29 (56%) were reconfirmed and 23 (44%) were not confirmed (PMID 33068757).

Even when specificity is very high, the positive predictive value can be low. In this data, the estimates varied depending on the assumed conditions; one commercial test had a positive predictive value of 61.8% to 89.8% even though its specificity was 99.91% to 99.98%. In a laboratory-developed test (specificity 97.4% to 99.1%), the positive predictive value dropped down to 20.1% to 73.8%. The authors conclude that nucleic acid amplification tests are highly specific. At the same time, they write that when prevalence is low, a significant portion of initial positives are not reconfirmed, so confirmatory testing greatly reduces false-positive detections. Conversely, they add that for specimens with a high pretest probability of detection, additional tests can be omitted to concentrate testing where it is clinically meaningful and reduce delays (PMID 33068757).

When prevalence is extremely low, the positive predictive value can drop all the way to the floor. Early in the pandemic, a hospital in Tokyo performed both PCR and chest CT on 292 asymptomatic patients scheduled for surgery under general anesthesia. PCR was positive in 3 patients, and the CT scans of all 3 patients were negative. Thus, in this data, both the sensitivity and the positive predictive value of CT were 0%. The specificity was 96.9%, and the negative predictive value was 98.9%. However, this negative predictive value was almost equal to the proportion of people who had no disease even before the test, so a negative CT essentially contributed nothing to shifting the probability. The authors concluded that CT screening was not useful in low-prevalence settings like Tokyo at that time, and that the criteria for implementing CT screening should be established based on prevalence (PMID 33172767).

How Far It Moves — The Likelihood Ratio

Up to this point, the story has been about how the pretest probability changes the meaning of a result. The remaining half is the task of measuring how much a single result moves that probability.

A likelihood ratio is a value that shows how many times more likely a given test result is to occur in a person with the disease than in a person without the disease. If a likelihood ratio is 1, that result does not move the probability at all. If it is greater than 1, it pushes the probability toward the side with the disease; if smaller, it pushes it the other way.

Likelihood ratios can be carried over and used between populations. Predictive values contain the prevalence, so if you take a value measured in another study and bring it as-is to the person in front of you, it will be wrong. Likelihood ratios are not like that, so you can combine a likelihood ratio measured in another population with your patient's pretest probability to obtain the posttest probability (PMID 36202637). Methodological overviews also pick out the likelihood ratio as the value that best connects pretest probability and posttest probability (PMID 15827842).

Likelihood ratios do not even need to be assigned as just two values, positive and negative. If a test is one where the result comes out as a number, a likelihood ratio can be assigned separately for each range of values. Then, you can rescue the information that was thrown away by crushing the results into positive and negative.

Likelihood ratios by range show the axis of this article most clearly. After pooling the individual patient raw data from five studies on diagnosing pulmonary embolism, dividing the D-dimer values into eight ranges (cutoffs of 250, 500, 750, 1,000, 1,500, 2,500, and 5,000 ng/mL), and estimating the likelihood ratio for each range, the results are as follows.

• The likelihood ratio for the 1,000 to 1,499 ng/mL range was 0.98 (95% confidence interval 0.82–1.18), which was essentially 1. Values in this range hardly move the probability at all.
• In a model assuming that the likelihood ratio increases by a constant multiple for every step up in range, that multiple was about 2-fold (constant between ranges 2.0, 95% confidence interval 1.9–2.1).
• For a person with a pretest probability of 15%, their D-dimer had to be below 500 for their posttest probability to drop below 3%. For a person with a pretest probability of 5%, 1,000 was that cutoff (PMID 28370759).

Even for the exact same test value, which value should be considered "negative" depends not on the test kit, but on that person's pretest probability. However, these numbers are approximations calculated from the data of those five studies. The authors also conclude on the note that judgment strategies based on these values generally agree with several strategies already published.

Thresholds Are Defined by Purpose and Value

To divide a numerical test result into positive and negative, a line must be drawn somewhere. That line is called a threshold, or cutoff. An ROC curve is a graph created by plotting sensitivity and (1−specificity) for every possible threshold as it moves from low to high. The value in parentheses is the proportion of people without disease who test positive. The area under the curve is a single number summarizing how well a test separates two groups.

In a continuous numerical test, sensitivity and specificity move in opposite directions. Lowering the threshold catches more cases but makes more false alarms; raising it does the reverse. Therefore, where to draw the line must be determined by looking at the clinical costs of incorrect results (PMID 11897304). The curve is only a list of possible combinations, and it does not tell you which point among them to pick.

Which point to choose is formally organized. The optimal threshold is the one that maximizes expected utility. That threshold is determined by the pretest probability of the disease (expressed as an odds ratio) and "how much more important sensitivity is compared to specificity," and the threshold is the point on the ROC curve where the slope equals that value (PMID 21570638). The higher the probability of disease, and the greater the cost of missing the disease, the more the threshold shifts toward the more sensitive side. Pretest probability is factored into the calculation not only when interpreting results, but also when choosing a threshold.

A line connecting combinations of sensitivity and specificity that have equal value is called an indifference curve. The authors' formulation stands on these two curves. The ROC curve shows what is possible, and the indifference curve shows what is desirable. Overlapping the two reveals what should be chosen (PMID 21570638).

The tuberculin skin test illustrates this in actual numbers. In a study that recalculated epidemiological survey data using a model rather than an original accuracy study, the positive predictive value based on the general U.S. population ranged from 0.44 to 1.0 depending on the cutoff. Even though the resulting area under the curve was exceptionally high at 0.997, the optimal cutoff varied widely from 2 mm to 16 mm depending on the prevalence and the purpose of the test (PMID 8583267). Having a good test and deciding where to draw the line are separate issues.

A recent example points in the same direction. In a computer-aided detection system assisting in the reading of silicosis, two criteria were applied to data from 501 chest X-rays of former gold miners. One was the Youden index (a criterion choosing the point where the sum of sensitivity and specificity is greatest), and the other was guaranteeing a sensitivity of at least 90%. The thresholds derived from the two criteria differed from each other, and also varied depending on the definition of silicosis and the reader. Changing the assumed prevalence altered the positive predictive value significantly, changing the proportion of false positives accordingly. The authors explain the implications by dividing them into three uses: routine screening for active miners, outreach screening for retired miners, and compensation claim review, and conclude that users must first determine the purpose, whether they prioritize sensitivity or specificity more, the definition of silicosis, and also weigh the impact of prevalence (PMID 40188380). Even with the same system and the same images, a different purpose requires a different threshold.

Determining the threshold is about who uses the test and for what purpose.

Pretest Probability Also Dictates Test Selection

Pretest probability changes not only how results are interpreted, but also which test is chosen.

In stable angina, each noninvasive test has a separate pretest probability range within which significant coronary stenosis can be confirmed (post-test probability >85%) or excluded (<15%). In a meta-analysis of 132 studies and 28,664 patients that used invasive coronary angiography as the reference standard, exercise electrocardiography could be used for confirmation only when the pretest probability was ≥80%, and for exclusion only when it was ≤19%. This means that for patients with a pretest probability in between, it can neither confirm nor exclude the condition. Coronary CT angiography could confirm the diagnosis at a pretest probability of ≥58% and exclude it at ≤80%.

Up to this point, these values are based on anatomical stenosis judged visually on angiography. When the criterion was changed to functional stenosis—namely, stenosis measured by fractional flow reserve (a value measuring how much the stenosis actually reduces blood flow)—the ranges for the same CT narrowed to ≥75% and ≤57%. The authors conclude that test selection must be based on that patient's pretest probability range and which reference standard is used (PMID 29850808).

What Tests Actually Do — Shrinking the "I Don't Know" Zone

Saying that a test moves probabilities sounds abstract, but doing it well changes what a patient experiences.

A blood test that monitors for rejection after a kidney transplant (donor-derived cell-free DNA) is an example. Out of 922 samples, among 345 samples whose pre-test risk was in the intermediate zone (10–30%), 253 were reclassified into different zones after the test. Among those that moved in the correct direction, 72% (117/162) moved toward the low-risk side, and 36% (33/91) toward the high-risk side. If the biopsy threshold was set at 10%, calculations showed that 482 biopsies could have been safely avoided, 91% of which were routine protocol biopsies. These values are from a cohort with a relatively low prevalence of rejection (PMID 42133430).

What this test did was shrink the "I don't know" zone rather than make a diagnosis.

Screening tests also pull their weight when well-designed. A study comparing periods with and without newborn hearing screening, alternated by hospital, included 53,781 babies. During the screening periods, babies with moderate or worse hearing loss were referred before 6 months of age at a rate of 71 more per 100,000 than during the non-screening periods. The false-negative rate—the proportion of results where a baby had the disease but tested negative—was also 4%, lower than the conventional surveillance examination (27%) (PMID 10626585). The authors suggest this screening may be particularly useful for babies with moderate-to-profound hearing loss, for whom early management can yield the greatest benefit.

What False Positives Stir Up

Just as tests can translate probabilities well, false positives cause trouble in settings where the pretest probability is low.

This problem becomes clear in incidentally discovered adrenal and pituitary masses. Clinically diagnosed hormone-secreting tumors are much rarer than incidentally discovered masses. Effective hormone screening requires a pretest probability high enough to limit the number of false positives. Otherwise, costs and harms follow while chasing false positives. The authors of this review call this, borrowing an expression from Mold and Stein, "a cascade of events—one that accelerates as it proceeds, making it harder to stop the further it goes" (PMID 9074861).

This cascade is actually observed. In a systematic review of 38 studies using serum tumor markers for cancer screening in asymptomatic people, the positive predictive value in the general asymptomatic population was consistently low. False positives frequently led to imaging tests, invasive procedures, and surgeries, with a complication rate of up to 15%. No mortality benefit was confirmed in large randomized trials. While noting that the positive predictive value improved in certain subgroups (e.g., elevated CA 19-9 in newly onset diabetes), the authors conclude that evidence is insufficient to support population screening (PMID 42522803).

Screening also carries inherent risks. It means finding a disease that would not have caused harm even if it had not been detected, which is called overdiagnosis. In a 1994 review examining infant neuroblastoma screening in Japan, false positives prompting additional tests were less than 0.1%, and the survival rate of children found by screening exceeded 90% (about 50% when found by symptoms). However, viewed through biological markers, the tumors caught by screening tended to have a favorable prognosis from the start, and some tumors with poor prognosis slipped right past screening. The authors reported that, based on the evidence at that time, screening prevented few deaths while the potential for overdiagnosis was large, and concluded that screening could not be recommended before additional evidence emerged (PMID 8790511).

Looking like survival has improved and actually reducing deaths are two different stories. Simply bringing forward the time of diagnosis lengthens the period from diagnosis to death, and slow-growing diseases are more easily caught by screening. The only way to avoid these two optical illusions is through randomized trials. The screening review that cited the relationship between prevalence and positive predictive value earlier also notes that screening can improve health. The indirect evidence linking cervical cytology programs and reductions in cervical cancer mortality is strong (PMID 11897304).

Common Misunderstandings

The first misunderstanding is that "if accuracy is high, it is reliable." Even in a test with a specificity in the 99.9% range, the positive predictive value dropped to 61.8–89.8% (PMID 33068757), and in 292 asymptomatic preoperative patients, the positive predictive value of CT became 0% (PMID 33172767). Accuracy is an attribute of a test, but whether its results are reliable is determined together with who it is used on (PMID 11897304).

The second misunderstanding is that "if it is negative, it is not the disease." How well a negative result rules out a disease depends on a person's pretest probability. According to an overview summarizing the likelihood ratios of various tests for pulmonary embolism, in a person with a high pretest probability, the post-test probability still exceeds 10% even if CT pulmonary angiography is negative. Conversely, in a person with a pretest probability of less than 17%, if the D-dimer is negative (negative likelihood ratio 0.05), the post-test probability drops below 1%. The same overview adds that as the post-test probability of one test becomes the pretest probability of the next, the interval to the final diagnosis narrows with repeated testing (PMID 16091094).

Tests used for definitive diagnosis can also miss disease. In a study where both ultrasound and temporal artery biopsy were performed on 381 patients newly suspected of having giant cell arteritis, the sensitivity of biopsy was 39% (specificity 100%), which is significantly lower than previous reports. In the same study, a strategy combining clinical judgment at the 2-week time point with biopsy showed a sensitivity of 91% and a specificity of 81%. A combination accomplishes what a single test cannot, but it trades away some specificity as the price; because the reference diagnosis in this study itself uses clinical findings and biopsy together, this value must be read alongside the limitations of the reference standard covered later in "An Honest Unresolved Problem" (PMID 27925577).

Conversely, even for a test with high sensitivity, the weight of a negative result can be lighter than expected. In a meta-analysis of the straight leg raise test that gathered entirely non-primary care surgical case series (reference standard = surgery), sensitivity was high at 0.91, but specificity was 0.26 (PMID 10788860). When specificity is this low, the extent to which a negative result lowers probability is reduced just as much. What a negative result tells you is "the probability has gone down by this much."

The third misunderstanding is that "sensitivity and specificity are fixed constants attached to a test," which is the point most frequently missed. Sensitivity and specificity are learned in textbooks as properties of a test, but in real-world data, they move according to prevalence.

Out of 6,909 papers extracted from diagnostic accuracy meta-analyses in the Cochrane Database, the highest prevalence quartile had an odds of sensitivity 1.47 times higher and an odds of specificity 0.47 times that of the lowest quartile (PMID 37460126). Odds is the value obtained by dividing the probability that an event will happen by the probability that it will not happen. Here, the "severalfold" value is the value obtained by dividing the two odds, in other words, an odds ratio. To spell it out, studies with higher prevalence estimated sensitivity higher and specificity lower.

The reason is twofold. One is clinical variation. Populations with higher prevalence may include more severe patients, and tests work better on them. The other is artificial variation. Study design, particularly who was confirmed with the reference standard depending on the index test result, shakes up prevalence and accuracy together (PMID 18778913). Therefore, the authors advise clinicians to select studies from populations most similar to their own situation to use as the basis for their judgment.

That does not mean there is a rule that "it is always like this in primary care." In a meta-epidemiological study comparing pre-referral and post-referral care, the differences in sensitivity and specificity across 13 tests varied widely in both direction and magnitude. The authors concluded that there is no universal pattern, as it simply varies depending on the test and the target disease (PMID 40339825).

The fourth misunderstanding is that "the more tests you do, the safer you are." Gathering 35 papers and 118 instances evaluating the overuse of diagnostic tests, overuse estimates scatter from 0.09% to 97.5% (median 11.0% based on indication criteria). Most were under 25%. Among the 33 instances that came out high at 25% or more, the most frequently evaluated subjects were preoperative tests (7 instances) and imaging for simple lower back pain (6 instances) (PMID 33972387). The authors believe that these estimates are scattered like this because what defines overuse and how it is measured differ from study to study.

Repeated testing is in the same vein. In a cohort looking at prostate-specific antigen testing in English primary care using 2000–2018 data, among 1.52 million people who received at least one test, 48.4% were tested multiple times. Among them, 72.8% had never crossed the age-specific referral threshold even once. The median retesting interval was 12.6 months (PMID 41062172). The authors note that a substantial portion of those tested multiple times were tested more frequently than recommended, raising concerns about over-testing.

The fifth misunderstanding is that "results finalize the probability." Test results merely update probability, they do not finalize it. The previous D-dimer data shows that exact saying. The same value acts as a rule-out for some people, but falls short of a rule-out for others. This is because what a result does is shift the probability from its starting point.

Honest Unresolved Problems

The first unresolved problem is that the reference standard is not perfect. Sensitivity and specificity are values measured on top of the reference standard, which is the criterion that decides who is sick. If that criterion shakes, the values on top of it shake too.

When the reference standard is incomplete, ROC curve estimation is biased, and even the likelihood ratio connecting the pretest probability and posttest probability is biased. A simulation study showed in the example of diagnosing iron deficiency with transferrin saturation that, depending on the prevalence and the correlation between the index test and the reference standard, the likelihood ratio can be skewed enough to be clinically meaningful (PMID 40650984).

The giant cell arteritis study from earlier is an example of that. The authors stated as a limitation that there is no independent gold standard. A gold standard refers to the most reliable reference standard that confirms the disease independently of other tests. The reference diagnosis of that study itself was a classification criterion using clinical findings and biopsy results together. The authors noted that the finding where both ultrasound and biopsy had moderate inter-observer agreement casts doubt on the assumption that a positive biopsy always means the disease (PMID 27925577).

The design of accuracy studies also shakes the values. Who received the reference standard changes the values. The values are distorted when only some participants are confirmed with the reference standard, especially when people with a positive index test are more likely to receive the confirmatory test (= reference standard). The conclusion of a paper that dealt with this problem hits the nail on the head. "If a finding was already used to determine who would receive a confirmatory test, the usefulness of that finding cannot be evaluated by looking only at the people who received the confirmatory test." (PMID 35124189)

This problem appears in actual studies as well. In the meta-analysis of the straight leg raise test from earlier, studies with more valid designs, such as those that blinded both the index test and the reference standard, showed lower discriminatory power. The authors conclude that the included studies cannot validly evaluate the accuracy of these tests (PMID 10788860).

The Biggest Unresolved Question — "Should This Test Be Done?"

Everything discussed so far is about probability. Whether or not to perform a test cannot be answered by probability alone.

An overview covering the rational use of diagnostic tests summarizes this point. Most accuracy studies are cross-sectional designs measuring the test and reference standard at the same time, and randomized trials comparing diagnostic strategies are rare. The accuracy measures captured by cross-sectional studies are indirect and insufficient to define the actual benefit returning to the patient. Among those measures, positive and negative likelihood ratios are the most useful for clinical management. The authors conclude that knowing the methodology is fundamental but not sufficient. And they note that costs, turnaround time, and patient preferences and values are better included in decisions (PMID 30994847).

To Go Deeper

• When reading an accuracy paper, look for four things first: ① Who was gathered (what is the disease prevalence in that group, and are they similar to the person in front of me?) ② What was the reference standard? ③ Who received that reference standard (everyone, or mainly those who tested positive on the index test)? ④ How was the threshold determined (is its intended use the same as mine)? (PMID 33876780).
• When looking at numbers, convert percentages into the number of people. Framing it as "how many out of 1,000 people" makes the magnitude of false positives visible (PMID 26220870).
• Distinguish between predictive value and likelihood ratio. The positive predictive value from another study cannot be transferred to your own population, but the likelihood ratio can be used by combining it with your patient's pretest probability (PMID 36202637). However, likelihood ratios are also constructed from sensitivity and specificity, and as seen in the third common misconception, those two shift according to prevalence. Therefore, likelihood ratios are not completely free either, and here too, it is correct to choose the value from the group most similar to your situation (PMID 18778913).
• If only one thing remains, it is this: A test is not an answer, but a tool that shifts probability. How much it shifts is determined by the test, and where it starts is determined by the person.

What this article leaves behind is an understanding of why a single number on a report cannot be the answer on its own. Therefore, an individual's result finally gains meaning when read together with their pretest probability. What the probability shifted by the test ultimately means for the patient is followed by "Better Numbers, Better Patients? — An Introduction to Surrogate Endpoints".

Finally, there is a space this article intentionally left blank. The starting point, namely the pretest probability, is not written anywhere on the test result sheet. It comes from the person's age, symptoms, clinical course, other findings, and the path by which they arrived at this test. The work of gathering those materials and turning them into a single number—how history taking and physical examination shift probability, and how clinical prediction rules are derived and validated—is taken over by "Where Does Pretest Probability Come From? — History, Physical Examination, and Clinical Prediction Rules".

Source Papers

Study designs and cohorts are noted together. Grades are in review-notes.md.

Concepts — PMID 33741123 (2021) Commentary on Bayes' theorem · PMID 11897304 (2002) Overview of screening. Also notes that screening can improve health (cervical cytology–reduction in mortality, strong indirect evidence) · PMID 15827842 (2005) Methodological overview · PMID 36202637 (2023) Overview of palliative care, also covers the limitations of likelihood ratios · PMID 33876780 (2022) Overview of study designs.

How Often They Are Wrong — PMID 26306891 (2016) 326 resident physicians · PMID 26220870 (2015) 24 literature reviews. The effect of presenting likelihood ratios is mixed (3 studies more accurate / 3 studies less accurate) · PMID 7157027 (1982) 169 subjects in four groups · PMID 41840426 (2026) Cross-sectional survey of medical students (sample size not reported).

Low-Prevalence Real-World Data — PMID 33068757 (2021) Single laboratory, 1 month, 19,597 specimens (the above figures are point estimate ranges by assumption parameter) · PMID 33172767 (2021) Single hospital in Tokyo, retrospective analysis of 292 asymptomatic patients scheduled for surgery.

Likelihood Ratios — PMID 28370759 (2017) Synthesis of 5 pulmonary embolism studies · PMID 16091094 (2005) Overview.

Thresholds — PMID 21570638 (2011) Methodology. Two widely used rules of thumb are optimal only in special cases · PMID 8583267 (1995) Recalculation of epidemiological data and Bayesian analysis (U.S. Navy recruits and WHO survey). Sensitivity 0.59 to 1.0 · PMID 40188380 (2025) Analytical methodology, existing ROC data from 501 chest X-rays of miners. States that silicosis CAD is at an earlier stage of development than tuberculosis CAD and is validated by relying on expert reading.

In Clinical Practice — PMID 29850808 (2018) Meta-analysis, 132 papers referencing invasive angiography and 23 papers referencing fractional flow reserve totaling 28,664 and 4,131 patients respectively · PMID 42133430 (2026) Observational cohort, 922 specimens, low prevalence of rejection. Area under the curve: test alone 0.79 to 0.80, combined with clinical information 0.82 to 0.87 · PMID 10626585 (1999) Crossover comparison study, 53,781 infants. False alarm rate 1.5%, yield 90 cases per 100,000 for bilateral hearing loss of 40 dB or greater (80% of expected prevalence) · PMID 9074861 (1997) Endocrinology overview. Also notes that the primary justification for additional evaluation is often closer to reassuring individuals who test negative · PMID 42522803 (2026) Systematic review of 38 papers (asymptomatic populations). Positive predictive value improves in some subgroups, but evidence for population screening is insufficient · PMID 8790511 (1994) Overview of evidence from a nationwide Japanese program (urine VMA and HVA).

Why Values Fluctuate — PMID 37460126 (2023) 6,909 papers from 552 Cochrane meta-analyses · PMID 18778913 (2009) Mechanisms · PMID 40339825 (2025) Meta-epidemiology, 9 papers, 13 types (7 signs and symptoms sensitivity +0.03 to +0.30, 4 biomarkers −0.11 to +0.21, 1 imaging modality −0.22).

What Misunderstandings Produce in the Clinic — PMID 27925577 (2016) TABUL, 381 referred patients in secondary care. Ultrasound has a higher sensitivity and lower specificity (54% sensitivity and 81% specificity) than biopsy (39% sensitivity and 100% specificity). When all patients undergo ultrasound first and only those with negative results undergo biopsy, biopsies are reduced by 43% · PMID 10788860 (2000) Systematic review of 11 papers (reference standard = surgery). Crossed straight leg raise has the exact opposite values with a sensitivity of 0.29 and specificity of 0.88 · PMID 33972387 (2022) 118 evaluations from 35 papers · PMID 41062172 (2025) 10.23 million primary care men in England.

Unresolved Issues in Reference Standards and Study Design — PMID 35124189 (2022) Methodology (the solution is to refer all positives + randomly sample negatives) · PMID 40650984 (2025) Simulated data · PMID 30994847 (2019) Overview.

Values Omitted from the Main Text — PMID 27548805 (2016) proposes a diagnostic yield framework that counts the number of individuals who undergo unnecessary additional tests among false positives when accuracy alone cannot yield a conclusion, and uses expected utility as accuracy weighted by prevalence and the relative importance of the two types of errors · PMID 23798453 (2013) reports across 23 meta-analyses (416 papers) that moving prevalence from lowest to highest shifted sensitivity or specificity by 0 to 40 percentage points, but only specificity remained consistent while sensitivity showed no systematic effect—which contrasts with the findings of the 6,909-paper study above · PMID 23958378 (2013) finds evidence of consistent effects across design, observer variation, clinical information, reference standards, verification bias, and prevalence and severity, reporting that the effect was stronger in sensitivity than in specificity.