ANSWER
A differential diagnosis (abbreviated DDx) determines the correct diagnosis based on a patient’s history and physical examination. It entails distinguishing one disease or condition from others with similar clinical features. [1] Clinicians use differential diagnostic procedures to diagnose a patient’s specific disease or, at the very least, to consider any potentially life-threatening conditions. A differential diagnosis is often used to refer to each option of a possible disease (e.g., acute bronchitis could be a differential diagnosis in evaluating a cough, even if the final diagnosis is a common cold).

A differential diagnostic procedure, in general, is a systematic diagnostic method used to determine the presence of a disease entity when multiple alternatives are possible. This method may employ algorithms similar to the process of elimination, or at the very least, a method of obtaining information that reduces the “probabilities” of candidate conditions to negligible levels by using evidence such as symptoms, patient history, and medical knowledge to adjust epistemic confidences in the diagnostician’s mind (or, for computerized or computer-assisted diagnosis, the software of the system).

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Differential diagnosis can be thought of as implementing aspects of the hypothetico-deductive method. The potential presence of candidate diseases or conditions can be viewed as hypotheses that clinicians then determine as true or false.

A differential diagnosis is also commonly used in psychiatry/psychology, where two different diagnoses can be assigned to a patient exhibiting symptoms that could be classified as either. Given the similarities in the symptoms of both conditions, a patient diagnosed with bipolar disorder may also be given a differential diagnosis of borderline personality disorder.

The strategies used in preparing a differential diagnosis list vary depending on the healthcare provider’s experience. While inexperienced providers may work systemically to assess all possible explanations for a patient’s concerns, those with more experience frequently rely on clinical experience and pattern recognition to protect the patient from the delays, risks, and costs associated with ineffective strategies or tests. Effective providers use an evidence-based approach, supplementing their clinical experience with clinical research knowledge. [2]

Components in general

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More information: Detection procedure
There are four general steps to a differential diagnosis. The clinician will do the following:

Compile pertinent patient information and a list of symptoms.

[3]
Make a list of potential causes (candidate conditions) for the symptoms.
[4] The list does not have to be in writing.
Prioritize the list by weighing the risks of a diagnosis against its likelihood. These are subjective rather than objective parameters.
Tests should be performed to determine the correct diagnosis. The phrase “to Rule Out” is used to describe this. Even after the procedure, the diagnosis remains ambiguous. The clinician reconsiders the risks and may treat them empirically, a practice known as “Educated Best Guess.”
VINDICATE’M a mnemonic for considering multiple possible pathological processes:
[Citation required]
[clarification required]

Vascular Inflammatory / Infectious Neoplastic Degenerative / Drugs
Idiopathic / Iatrogenic / Intoxication
Autoimmune / Allergic / Anatomic Traumatic Endocrine / Environmental Metabolic Congenital
[5]
Specific procedures
There are several methods for differential diagnostic procedures and variations of those methods. A differential diagnostic procedure can also be used with or in place of protocols, guidelines, or other diagnostic procedures (such as pattern recognition or medical algorithms). [Citation required]

For example, there may need to be more time to perform detailed calculations or estimate various probabilities in a medical emergency. The ABC protocol (Airway, Breathing, and Circulation) may be more appropriate. Later, a more thorough differential diagnostic procedure may be used when the situation is less critical.

The differential diagnostic procedure may be shortened if a “pathognomonic” sign or symptom is discovered (in which case the target condition is almost certainly present) or if a sine qua non-sign or symptom is absent (in which case it is almost sure that the target condition is absent).

A diagnostician can be selective, focusing on disorders that are more likely to occur (a probabilistic approach), more severe if left undiagnosed and untreated (a predictive approach), or more responsive to treatment if offered (a predictive approach) (a pragmatic approach).

[6] Because the subjective probability of a condition’s presence is never precisely 100% or 0%, the differential diagnostic procedure may aim to specify these various probabilities to form indications for further action.

The methods of differential diagnosis listed below are based on epidemiology and likelihood ratios, respectively.

A method based on epidemiology
One method of performing a differential diagnosis by epidemiology aims to estimate the probability of each candidate condition occurring in the first place in the individual by comparing their probabilities of occurring in the first place. It is based on probabilities associated with the presentation (such as pain) and the various candidate conditions (such as diseases). [Citation required]

Theory
Bayes’ theorem provides the statistical foundation for differential diagnosis. For example, when a die is thrown, the outcome is 100% certain, but the probability that it would have happened in the first place (hereafter abbreviated WHOIFP) remains 1/6. Similarly, the probability that a presentation or condition would have occurred in an individual in the first place (WHOIFPI) is not the same as the probability that the presentation or condition has occurred in the individual because the presentation has occurred in the individual with 100% certainty. Nonetheless, the contributing probability fractions of each condition are assumed to be the same:

Pr ( Individual condition causes presentation )
Pr ( Presentation has occurred in individual ) = Pr ( WHOIFPI Presentation by condition )
Pr ( WHOIFPI Presentation )
display style beginaligned&frac Pr(text presentation caused by condition in individual)Pr(text presentation has occurred in individual)=frac Pr(text presentation WHOIFPI caused by condition)
Pr(text presentation WHOIFPI)end aligned where:

Pr(A condition in the presentation of the individual cause) is the probability that a condition in the particular condition causes the presentation without further qualification.
Pr(Presentation has occurred in individual) is the probability that the presentation has occurred in the individual and can thus be set to 100%.
Pr(Presentation WHOIFPI by condition) is the likelihood that the presentation would have occurred in the first place in the individual under the given conditions.
The probability that the presentation would have occurred in the first place in the individual is given by Pr(Presentation WHOIFPI).
When an individual presents with a symptom or sign, Pr(Presentation in individual) is 100% and can thus be replaced by 1, and can be ignored because division by 1 has no effect:

Pr ( Individual condition causes presentation ) = Pr ( Individual condition causes presentation WHOIFPI )
Pr ( WHOIFPI Presentation ) Pr(a condition in individual causes text presentation) = frac Pr(text presentation WHOIFPI by condition)
PR (text presentation WHOIFPI)
The sum of the individual candidate conditions can be used to approximate the total probability of the presentation occurring in the individual:

Pr ( Presentation WHOIFPI ) = Pr ( Presentation WHOIFPI by condition 1 ) + Pr ( Presentation WHOIFPI by condition 2 ) + Pr ( Presentation WHOIFPI by condition 3 ) + etc. begin align Pr(text presentation WHOIFPI) & = Pr(text presentation WHOIFPI by condition 1 ) & + Pr(text presentation WHOIFPI by condition 2 ) & + Pr(text presentation WHOIFPI by condition 3 ) + text
Furthermore, the probability of the presentation being caused by any candidate condition is proportional to the condition’s probability, depending on how frequently it causes the presentation:

Pr ( Presentation WHOIFPI by condition ) = Pr ( Condition WHOIFPI ) condition presentation, Pr(textPresentation WHOIFPI by condition ) = Pr(textCondition WHOIFPI) cdot r textcondition r textpresentation, where:

Pr(Presentation WHOIFPI by condition) is the likelihood that the presentation would have occurred in the first place in the individual under the given conditions.
The probability that the condition would have occurred in the first place in the individual is given by Pr(Condition WHOIFPI).
r
The rate at which a condition causes the presentation, that is, the fraction of people with conditions who manifest with the presentation, is referred to as condition presentation.
The probability that a condition would have occurred in the first place in an individual is approximately equal to that of a population that is as similar to the individual as possible except for the current presentation, with relative risks provided by known risk factors that distinguish the individual from the population compensated where possible:

Pr ( Condition WHOIFPI ) condition Pr ( Condition in population ), Pr(textCondition WHOIFPI) approx RR text condition cdot Pr(textCondition in population), where:

The probability that the condition would have occurred in the first place in the individual is given by Pr(Condition WHOIFPI).
The relative risk for a condition conferred by known risk factors in the individual not present in the population is referred to as RRcondition.
Pr(Condition in Population) is the likelihood that the condition will occur in a population that is as close to the individual as possible except for the presentation.
The table below shows how these relationships can be established for a variety of candidate conditions:

Candidate situation 1 Candidate circumstance 3rd Candidate Condition
Pr(Population Condition) Pr(Population Condition 1) Pr(Population Condition 2) Pr (Condition 3 in population)
RRcondition RR1 RR2 RR3
Pr(WHOIFPI Condition) Pr(WHOIFPI Condition 1) Pr(WHOIFPI Condition 2) P (Condition 3 WHOIFPI)
presentation condition one presentation condition two presentation r
3rd condition presentation
Pr(Presentation WHOIFPI by condition) (Presentation WHOIFPI by condition)
Pr(WHOIFPI Presentation by Condition 1) Pr(WHOIFPI Presentation by Condition 2) Pr (Presentation WHOIFPI by condition 3)
Pr(Presentation WHOIFPI) = the sum of the probabilities in the preceding row
Pr(Presentation is caused by individual condition) Pr(Presentation is caused by individual condition 1) Pr (Presentation is caused by condition 2 in individual)
Pr(Presentation is caused by condition 3 in individual) (Presentation is caused by condition 3 in individual)
Another “candidate condition” is when there is no abnormality, and the presentation is simply a (usually unlikely) appearance of a normal state. Its population probability (P(No abnormality in population)) is additive to the sum of the probabilities of “abnormal” candidate conditions.

Example
This example case demonstrates how this method is used, but it is intended to be something other than a guideline for dealing with similar real-world cases. Also, the example uses relatively specific numbers with sometimes several decimals. In contrast, in reality, the probabilities are often simply rough estimates, such as very high, high, low, or very low, but the method’s general principles are still used. [Citation required]

A blood test of, say, serum calcium for an individual (who becomes the “patient” in this example) reveals a result above the standard reference range, which most definitions classify as hypercalcemia, which becomes the “presentation” in this case. A clinician (who becomes the “diagnostician” in this example) who is not currently seeing the patient learns of his discovery.

For practical reasons, the clinician believes there is sufficient test indication to review the patient’s medical records. Let’s pretend that the only information in the medical records is a family history of primary hyperparathyroidism (here abbreviated as PH), which could explain hypercalcemia. Assume that the resulting hereditary risk factor confers a relative risk of ten (RRPH = ten) for this patient.

The clinician believes there is sufficient motivation to perform a differential diagnostic procedure for hypercalcemia. Because the most common causes of hypercalcemia are primary hyperparathyroidism (PH) and cancer, the clinician’s list of candidate conditions can be as follows:

Cancer caused by primary hyperparathyroidism (PH)
Other diseases that the clinician may consider (which are termed “other conditions” for the rest of this example)
There is no disease (or abnormality), and the finding is due to statistical variability.
The probability that the individual would have developed ‘primary hyperparathyroidism’ (PH) in the first place (P(PH WHOIFPI)) can be calculated as follows:

Assume that the patient’s most recent blood test was routine and that the incidence of primary hyperparathyroidism in a general population that matches the individual (except for the presentation and mentioned heredity) is 1 in 4000 per year. Ignoring more detailed retrospective analyses (including disease progression speed and lag time of medical diagnosis), the time-at-risk for developing primary hyperparathyroidism can be roughly regarded as the previous half-year because the previous blood test would have most likely caught up with previously developed hypercalcemia. This equates to a likelihood of primary hyperparathyroidism (PH) in the population of:

Pr ( PH in the population ) = 0.5 years 1 4000 per year = 1 8000

Pr(textPH in the population) = 0.5text years cdot frac1text4000 per year = frac18000
With the relative risk conferred by the family history, the probability that primary hyperparathyroidism (PH) would have occurred in the individual in the first place based on the currently available information becomes:

Pr ( PH WHOIFPI ) = 10 1 8000 = 1 800 = 0.00125 Pr ( PH in population ) = 10 1 8000 = 1 800 = 0.00125

Pr(text WHOIFPI) = approximately RR PHcdot Pr(textPH in population) = 10 cdot frac 18000 = frac 1800 = 0.00125
Because primary hyperparathyroidism (PH) is assumed to cause hypercalcemia almost always (rPH hypercalcemia = 1), this independently calculated probability of PH is assumed to be the same as the probability of being a cause of the presentation:

PH hypercalcemia = 0.00125 1 = 0.00125 beginalign Pr ( Hypercalcemia WHOIFPI by PH ) = Pr ( PH WHOIFPI ) PH hypercalcemia = 0.00125 1 = 0.00125

Pr(textHypercalcemia WHOIFPI by PH) & = Pr(text WHOIFPI) dot r text right arrow texthypercalcemia& = 0.00125 cdot 1 = 0.00125 ending
For the sake of simplicity, let’s assume that the incidence of cancer in the area is estimated to be 1 in 250 per year, giving a population probability of cancer of:

Pr ( cancer in the population ) = 0.5 years 1 250 per year = 1 500

Pr(text cancer in population) = 0.5 text years cdot frac1text250 per year = frac1500
For the sake of simplicity, assume that any relationship between a family history of primary hyperparathyroidism and cancer risk is ignored and that the individual’s relative risk of contracting cancer in the first place is similar to that of the population (RRcancer = 1):

Cancer Pr ( WHOIFPI )
Pr ( cancer in the population ) = 1 1 500 = 1 500 = 0.002.
Pr(text cancer WHOIFPI) = approximately RR text cancer cdot Pr(text cancer in population) = 1 cdot frac1500 = frac1500 = 0.002.
However, hypercalcemia occurs in only about 10% of cancers[7] (rcancer hypercalcemia = 0.1), so:

Pr ( Hypercalcemia WHOIFPI by cancer ) = Pr ( cancer WHOIFPI ) cancer hypercalcemia = 0.002 0.1 = 0.0002. beginalign & Pr(textHypercalcemia WHOIFPI by cancer) = & Pr(textcancer WHOIFPI) cdot r textcancer rightarrow texthypercalcemia = & 0.002 0.1 = 0.0002. ending
Other candidate conditions’ probabilities of causing hypercalcemia in the first place can be calculated similarly. However, for the sake of simplicity, let us assume that the probability of any of these happening in the first place is calculated at 0.0005 in this example.

In the case of no disease, the corresponding population probability is additive to the sum of probabilities for other conditions:

Pr ( no disease in the population ) = 1 Pr ( PH in the population ) Pr ( cancer in the population ) Pr ( other conditions in the population ) = 0.997.

Pr(techno disease in a population) & = 1 – Pr(textPH in population) & quad – Pr(text cancer in population) & quad – Pr(text other conditions in population) & = 0.997.
The likelihood of the individual being healthy in the first place can be assumed to be the same:

Pr ( no disease WHOIFPI ) = 0.997.

Pr(no disease WHOIFPI text) = 0.997.
The rate at which a case with no abnormal condition results in serum calcium measurement being above the standard reference range (thus classifying as hypercalcemia) is less than 2.5%, according to the definition of the standard reference range. However, this probability can be further specified by considering how far the measurement deviates from the mean in the standard reference range. Assume the serum calcium measurement was 1.30 mmol/L, which corresponds to a standard score of 3 and a corresponding probability of 0.14% that such degree of hypercalcemia would have occurred in the first place in the absence of any abnormality:

no disease hypercalcemia = 0.0014 r techno disease right arrow text hypercalcemia = 0.0014
As a result, the probability that hypercalcemia would have occurred in the absence of disease can be calculated as follows:

Pr ( Hypercalcemia WHOIFPI by no disease ) = Pr ( no disease WHOIFPI ) no disease hypercalcemia = 0.997 0.0014 0.0014 beginning & Pr(textHypercalcemia WHOIFPI by no disease) = & Pr(techno disease WHOIFPI) dot r techno disease right arrow text hypercalcemia = & 0.997 dot 0.0014approx 0.0014 ending
Thus, the likelihood that hypercalcemia would have occurred in the first place in the individual can be calculated as follows:

Pr ( hypercalcemia WHOIFPI ) = Pr ( hypercalcemia WHOIFPI by PH ) + Pr ( hypercalcemia WHOIFPI by cancer ) + Pr ( hypercalcemia WHOIFPI by other conditions ) + Pr ( hypercalcemia WHOIFPI by no disease ) = 0.00125 + 0.0002 + 0.0005 + 0.0014 = 0.00335
As a result, the likelihood that the individual’s hypercalcemia is caused by primary hyperparathyroidism (PH) can be calculated as follows:

Pr ( hypercalcemia caused by PH in individual ) = Pr ( hypercalcemia caused by PH in WHOIFPI )
Pr ( hypercalcemia WHOIFPI ) = 0.00125 0.00335 = 0.373 = 37.3 %beginalign & Pr(text hypercalcemia caused by PH in individual) = & frac Pr(text hypercalcemia caused by PH)
Pr(text hypercalcemia WHOIFPI) = & frac 0.001250.00335 = 0.373 = 37.3% end alignment
Similarly, the likelihood that an individual’s hypercalcemia is caused by cancer can be calculated as follows:

Pr ( hypercalcemia caused by cancer in individual ) = Pr ( hypercalcemia WHOIFPI by cancer ) Pr ( hypercalcemia WHOIFPI ) = 0.0002 0.00335 = 0.060 = 6.0 %, beginning & Pr(text hypercalcemia caused by cancer in individual) = & frac Pr(text hypercalcemia WHOIFPI by cancer)

Pr(texthypercalcemia WHOIFPI) = & frac 0.00020.00335 = 0.060 = 6.0%, endalign, and for other candidate conditions:

Pr ( hypercalcemia caused by other conditions in the individual ) = Pr ( hypercalcemia caused by other conditions in the individual )
Pr ( hypercalcemia WHOIFPI ) = 0.0005 0.00335 = 0.149 = 14.9 %, beginning & Pr(text hypercalcemia is caused by other conditions in individual) = & frac Pr(text hypercalcemia WHOIFPI is caused by other conditions)
Pr(text hypercalcemia WHOIFPI) = & frac 0.00050.00335 = 0.149 = 14.9%, ending, and the probability that no disease exists:

Pr ( hypercalcemia is present despite no disease in individual ) = Pr ( hypercalcemia WHOIFPI by no disease ) Pr ( hypercalcemia WHOIFPI ) = 0.0014 0.00335 = 0.418 = 41.8 %beginalign &Pr(text hypercalcemia is present despite no disease in individual) = & frac Pr(text hypercalcemia WHOIFPI by no disease)

Pr(texthypercalcemia WHOIFPI) = & frac 0.00140.00335 = 0.418 = 41.8 % endalign
For clarity, the following calculations are provided in the method described as a table:

Other conditions PH Cancer

There is no disease.
P(Condition in population) (Condition in population)
0.000125 0.002 – 0.997 RRx 10 1 – – P(Condition WHOIFPI) 0.00125 0.002 – – hypercalcemia
1 0.1 – 0.0014 \sP(hypercalcemia WHOIFPI by condition) (hypercalcemia WHOIFPI by condition)
P(hypercalcemia WHOIFPI) = 0.00335 P(hypercalcemia WHOIFPI) = 0.00125 0.0002 0.0005 0.0014 (hypercalcemia is caused by condition in individual)
37.3% 6.0% 14.9% 41.8%
Thus, the probability that the hypercalcemia is caused by primary hyperparathyroidism, cancer, other conditions, or no disease at all is estimated to be 37.3%, 6.0%, 14.9%, and 41.8%, respectively, and can be used to estimate further test indications.

This case is continued in the following section’s example of the method.

The likelihood ratio method
The differential diagnosis procedure can become highly complex when additional tests and treatments are considered. One method that uses likelihood ratios to derive subsequent post-test likelihoods is a tradeoff between being clinically perfect and relatively simple to calculate.

Theory
Various methods can be used to estimate the initial likelihoods for each candidate condition, including:

As described in the preceding section, by epidemiology.
By clinic-specific pattern recognition, such as statistically knowing that patients presenting to a specific clinic with a specific complaint have a statistically significant likelihood of each candidate’s condition.
One method of estimating likelihoods even after additional tests is multiplying likelihood ratios (derived from sensitivities and specificities) after each test or procedure. In an ideal world, sensitivities and specificities for all tests for all possible pathological conditions would be established. However, in practice, these parameters may only be established for one of the candidate conditions. When multiplying with likelihood ratios, likelihoods must be converted from probabilities to odds in favour (hereafter referred to as “odds”) by:

odds \s= \sprobability
1 probability fractextodds = fractextprobability
{1-\text{probability}}
However, only the candidate conditions with a known likelihood ratio require this conversion. Following multiplication, the conversion back to probability is calculated as follows:

text probability = fractextoddstextodds+1 text probability = odds odds + 1
For simplicity, the remaining candidate conditions (for which there is no established likelihood ratio for the test at hand) can be adjusted by multiplying all candidate conditions by a common factor to yield a sum of 100%.

The probabilities that result are used to estimate the indications for additional medical tests, treatments, or other actions. If an additional test is indicated and returns a result, the procedure is repeated using the likelihood ratio of the additional test. The indications for additional tests, treatments, or other actions change with updated probabilities for each candidate condition. The procedure can be repeated until there is no longer any indication for performing further actions. Such an endpoint occurs primarily when one candidate condition becomes so sure that no test is found that is powerful enough to change the relative probability profile sufficiently to motivate any change in subsequent actions. Making tests with high specificity for conditions of already outstandingly high-profile-relative probability is a tactic for reaching such an endpoint with as few tests as possible because the high likelihood ratio positive for such tests is very high, bringing all less likely conditions to relatively lower probabilities. On the other hand, tests with high sensitivity for competing candidate conditions have a high likelihood ratio negative, potentially reducing the probabilities for competing candidate conditions to negligible levels. If such negligible probabilities are obtained, the clinician can rule out these conditions and proceed with only the remaining candidate conditions in the differential diagnostic procedure.

Example
This example continues with the same patient as in the epidemiology-based method example. As with the previous example of an epidemiology-based method, this example case is provided to demonstrate how the method is used but is not intended to serve as a guideline for dealing with similar real-world cases. Furthermore, the example uses relatively specific numbers, whereas, in reality, these are frequently just rough estimates. In this example, an epidemiology-based method determined the probabilities for each candidate condition to be as follows:

Other conditions PH Cancer

There is no disease.
Probability
37.3% 6.0%
14.9% 41.8%
These percentages could also have been determined through experience at the specific clinic, as these are the percentages for final diagnosis for people presenting to the clinic with hypercalcemia and a family history of primary hyperparathyroidism.

Primary hyperparathyroidism (PH) is the condition with the highest profile-relative probability (except “no disease”). However, cancer is still a significant concern because, if it is the actual cause of hypercalcemia, the decision of whether to treat or not likely means life or death for the patient, potentially putting the indication for further tests for both of these conditions at a similar level.

Let’s say the clinician considers the profile-relative probabilities of being of sufficient concern to send the patient a call for a clinician visit, with an additional visit to the medical laboratory for an additional blood test complemented with additional analyses, including parathyroid hormone for the suspicion of primary hyperparathyroidism.

For the sake of simplicity, assume that the clinician first receives the blood test (abbreviated as “BT”) result for the parathyroid hormone analysis, which reveals an elevated parathyroid hormone level compared to what would be expected based on the calcium level.

A sensitivity of approximately 70% and a specificity of approximately 90% for primary hyperparathyroidism can be estimated for such a constellation.

[8] This results in a positive likelihood ratio of 7 for primary hyperparathyroidism.

The possibility of primary hyperparathyroidism is now referred to as Pre-BTPH because it occurs before the blood test (the Latin preposition pre means before). It was calculated to be 37.3%, corresponding to odds of 0.595. With a positive likelihood ratio of 7 for the blood test, the post-test odds are calculated as follows:

Odds ( PostBT ) = Odds ( PreBT ) ( ) = 0.595 7 = 4.16, operatornameOdds(textPostBT PH) = operatornameOdds(textPreBT PH) = operatornameOdds(textPreBT PH) Where: cdot LH(BT) = 0.595 cdot 7 = 4.16

Odds(PostBTPH) is the probability of having primary hyperparathyroidism following a parathyroid hormone blood test.
Odds (PreBTPH is the probability of primary hyperparathyroidism before a parathyroid hormone blood test).
LH(BT) is the likelihood ratio for a positive parathyroid hormone blood test.
A probability of 4.16 is converted from an Odds(PostBTPH) of 4.16 by:

Pr \s( \sPostBT \s� \s� \s) \s= \sOdds \s⁡ \s( \sPostBT \s� \s� \s) \sOdds \s⁡ \s( \sPostBT \s� \s� \s) \s+ \s1 \s= \s4.16 \s4.16 \s+ \s1 \s= \s0.806 \s= \s80.6 \s% \ Pr(textPostBT PH) = fracoperatornameOdds(textPostBT PH) operatornameOdds(textPostBT PH) + 1 = frac4.164.16+1 = 0.806 = 80.6 %
As a result, the sum of the probabilities for the remaining candidate conditions should be:

Pr ( PostBT ) = 100% 80.6 % = 19.4 % Pr(textPostBT rest) = 100% – 80.6 % = 19.4 %
Before the parathyroid hormone blood test, the sum of their probabilities was:

Pr (PreBT rest ) = 6.0 % + 14.9 % + 41.8 % = 62.7 % Pr(textPreBT textrest ) = 6.0 % + 14.9 % + 41.8 % = 62.7 %
As a result, to achieve a total of 100% for all candidate conditions, each other candidate must be multiplied by a correcting factor:

Correcting factor = Pr ( PostBT rest ) Pr ( PreBT rest ) = 19.4 62.7 = 0.309 textCorrecting factor = fracPr(textPostBT textrest)Pr(textPreBT textrest) = frac19.462.7 = 0.309 text
For example, the probability of cancer following the test is calculated as follows:

Pr ( PostBT cancer ) = Pr ( PreBT cancer ) Correcting factor = 6.0 % 0.309 = 1.9 % cdot textCorrecting factor = 6.0% cdot 0.309 = 1.9% Pr(textPostBT textcancer) = Pr(textPreBT textcancer)
The following table shows the probabilities for each candidate’s condition before and after the blood test:

Other conditions PH Cancer

There is no disease.
P(PreBT)
37.3% 6.0% 14.9% 41.8% \sP(PostBT)
80.6% 1.9% 4.6% 12.9%
These “new” percentages, which include an 80% profile-relative probability of primary hyperparathyroidism, underpin any recommendations for additional tests, treatments, or other actions. Let us assume that the clinician keeps the patient’s appointment for a follow-up checkup focusing on primary hyperparathyroidism.

A clinician visit can be viewed as a series of tests, including medical history questions and physical examination components, where the post-test probability of the previous test can be used as the pre-test probability of the next. The results of previous tests dynamically influence the indications for selecting the next test.

Let’s say the patient in this example has more severe symptoms and signs of depression, bone pain, joint pain, or constipation than would be expected from hypercalcemia, supporting the suspicion of primary hyperparathyroidism [9], and let’s say the likelihood ratios for the tests when multiplied together, result in a product of 6 for primary hyperparathyroidism.

The presence of unspecific pathologic symptoms and signs in the history and examination is frequently suggestive of cancer. The tests revealed an overall likelihood ratio of 1.5 for cancer. For other conditions, as well as the case of not having any disease, let’s say it’s unknown how the tests will affect them, as is often the case in reality. The following are the results of the history and physical examination (abbreviated as P&E):

PH Cancer

Other circumstances

There is no disease.
P(PreH&E)
80.6% 1.9% 4.6% 12.9% \sOdds(PreH&E)
4.15 0.019 0.048 0.148
H&E’s likelihood ratio
6 1.5 – – \sOdds(PostH&E)
24.9 0.0285 – – \sP(PostH&E)
96.1% 2.8% – – Total known P(PostH&E) 98.9%
P is the sum of the rest (PostH&E)
1.1%
P is the sum of the rest (PreH&E)
4.6% + 12.9% = 17.5%
Factor of correction
1.1% / 17.5% = 0.063
P after correction – – 0.3% 0.8% (PostH&E)
96.1% 2.8% 0.3% 0.8%
Following the history and examination, the physician may feel confident enough to schedule the patient for a parathyroidectomy to resect the affected tissue.

At this point, the likelihood of “other conditions” is so low that the physician cannot think of any test that could make a significant enough difference to form an indication for such a test. The physician thus practically regards “other conditions” as ruled out, in this case not primarily by any specific test for other adverse conditions, but rather by the absence of positive tests thus far.

Because of the severe consequences of missing it, the cutoff for confidently ruling out “cancer” may be more stringent. The physician may consider that at least a histopathologic examination of the resected tissue is indicated.

This example is continued in the section below with the example of Combinations.

Candidate condition coverage
The validity of the initial estimation of probabilities by epidemiology and the subsequent workup by likelihood ratios is dependent on the inclusion of candidate conditions that are responsible for as much of the probability of developing the condition as possible. It is clinically significant to include those where relatively rapid initiation of therapy is most likely to result in the most significant benefit. Each differential diagnosis method will only provide the correct conclusion if a necessary candidate condition is included. The need to find more candidate conditions for inclusion grows in direct proportion to the severity of the presentation itself. For example, if the only presentation is a deviating laboratory parameter and all common harmful underlying conditions have been ruled out, it may be acceptable to stop looking for more candidate conditions; however, this would be much more likely unacceptable if the only presentation was severe pain.

Combinations
If two conditions have high post-test probabilities, particularly if the sum of the probabilities for conditions with known likelihood ratios exceeds 100%, the actual condition is a combination of the two. In such cases, the combined condition should be added to the list of candidate conditions, and the calculations should begin again.

To continue with the previous example, suppose the history and physical examination were also suggestive of cancer, with a likelihood ratio of 3, resulting in an Odds(PostH&E) of 0.057, corresponding to a P(PostH&E) of 5.4%. This equates to a “sum of known P(PostH&E)” of 101.5%. This indicates that a combination of primary hyperparathyroidism and cancer, such as parathyroid hormone-producing parathyroid carcinoma, should be considered. Recalculation may be required, with the first two conditions divided into “primary hyperparathyroidism without cancer,” “cancer without primary hyperparathyroidism,” and “combined primary hyperparathyroidism and cancer,” and likelihood ratios applied to each condition separately. However, in this case, the tissue has already been resected, allowing for a histopathologic examination that includes the possibility of parathyroid carcinoma (which may entail appropriate sample staining). Assume the histopathologic examination confirms primary hyperparathyroidism while also revealing a malignant pattern. An initial epidemiological method estimates the incidence of parathyroid carcinoma at 1 in 6 million people per year,[10] giving a very low probability before any tests are performed.
In comparison, the probability of non-malignant primary hyperparathyroidism occurring concurrently with an unrelated non-carcinoma cancer presenting with malignant cells in the parathyroid gland is calculated by multiplying the two probabilities. The resulting probability is much lower than one in six million. As a result, despite the low probability of occurrence in the first place, the probability of parathyroid carcinoma after histopathologic examination may still be close to 100%.

Differential diagnosis by machine
More information: System for clinical decision support
The use of computer software to make a partial or complete differential diagnosis is known as machine differential diagnosis. It could be an application of artificial intelligence. It may also be considered “Augmented Intelligence” if it meets the FDA criteria of:
Revealing the underlying data.
Revealing the underlying logic.
Leaving the clinician in charge of shaping and making the decision.
The FDA considers Machine Learning AI a device, whereas Augmented Intelligence applications are not.

Many studies show that decision support systems improve care quality and reduce medical errors. Some of these systems are intended to treat a specific medical condition, such as schizophrenia, Lyme disease, or ventilator-associated pneumonia. [13] Others are designed to cover all significant clinical and diagnostic findings to assist physicians with a faster and more accurate diagnosis.

However, these tools still require advanced medical skills to rate symptoms and select additional tests to determine the likelihood of various diagnoses. Machine differential diagnosis can also not diagnose multiple concurrent disorders at the moment. [14] As a result, non-professionals should still seek a proper diagnosis from a healthcare provider.