8.7 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Differential diagnosis | 2/6 | https://en.wikipedia.org/wiki/Differential_diagnosis | reference | science, encyclopedia | 2026-05-05T07:27:56.437702+00:00 | kb-cron |
Pr(Presentation is caused by condition in individual) is the probability that the presentation is caused by condition in the individual; condition without further specification refers to any candidate condition Pr(Presentation has occurred in individual) is the probability that the presentation has occurred in the individual, which can be perceived and thereby set at 100% Pr(Presentation WHOIFPI by condition) is the probability that the presentation Would Have Occurred in the First Place in the Individual by condition Pr(Presentation WHOIFPI) is the probability that the presentation Would Have Occurred in the First Place in the Individual When an individual presents with a symptom or sign, Pr(Presentation has occurred in individual) is 100% and can therefore be replaced by 1, and can be ignored since division by 1 does not make any difference:
Pr
(
Presentation is caused by condition in individual
)
=
Pr
(
Presentation WHOIFPI by condition
)
Pr
(
Presentation WHOIFPI
)
{\displaystyle \Pr({\text{Presentation is caused by condition in individual}})={\frac {\Pr({\text{Presentation WHOIFPI by condition}})}{\Pr({\text{Presentation WHOIFPI}})}}}
The total probability of the presentation to have occurred in the individual can be approximated as the sum of the individual candidate conditions:
Pr
(
Presentation WHOIFPI
)
=
Pr
(
Presentation WHOIFPI by condition 1
)
+
Pr
(
Presentation WHOIFPI by condition 2
)
+
Pr
(
Presentation WHOIFPI by condition 3
)
+
etc.
{\displaystyle {\begin{aligned}\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{etc.}}\end{aligned}}}
Also, the probability of the presentation to have been caused by any candidate condition is proportional to the probability of the condition, depending on what rate it causes the presentation:
Pr
(
Presentation WHOIFPI by condition
)
=
Pr
(
Condition WHOIFPI
)
⋅
r
condition
→
presentation
,
{\displaystyle \Pr({\text{Presentation WHOIFPI by condition}})=\Pr({\text{Condition WHOIFPI}})\cdot r_{{\text{condition}}\rightarrow {\text{presentation}}},}
where:
Pr(Presentation WHOIFPI by condition) is the probability that the presentation Would Have Occurred in the First Place in the Individual by condition Pr(Condition WHOIFPI) is the probability that the condition Would Have Occurred in the First Place in the Individual rCondition → presentation is the rate at which a condition causes the presentation, that is, the fraction of people with conditions that manifests with the 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, compensated where possible by relative risks given by known risk factor that distinguish the individual from the population:
Pr
(
Condition WHOIFPI
)
≈
R
R
condition
⋅
Pr
(
Condition in population
)
,
{\displaystyle \Pr({\text{Condition WHOIFPI}})\approx RR_{\text{condition}}\cdot \Pr({\text{Condition in population}}),}
where:
Pr(Condition WHOIFPI) is the probability that the condition Would Have Occurred in the First Place in the Individual RRcondition is the relative risk for condition conferred by known risk factors in the individual that are not present in the population Pr(Condition in population) is the probability that the condition occurs in a population that is as similar to the individual as possible except for the presentation The following table demonstrates how these relations can be made for a series of candidate conditions:
One additional "candidate condition" is the instance of there being no abnormality, and the presentation is only a (usually relatively unlikely) appearance of a basically normal state. Its probability in the population (P(No abnormality in population)) is complementary to the sum of probabilities of "abnormal" candidate conditions.
==== Example ==== This example case demonstrates how this method is applied but does not represent a guideline for handling similar real-world cases. Also, the example uses relatively specified numbers with sometimes several decimals, while in reality, there are often simply rough estimations, such as of likelihoods being very high, high, low or very low, but still using the general principles of the method. For an individual (who becomes the "patient" in this example), a blood test of, for example, serum calcium shows a result above the standard reference range, which, by most definitions, classifies as hypercalcemia, which becomes the "presentation" in this case. A clinician (who becomes the "diagnostician" in this example), who does not currently see the patient, gets to know about his finding. By practical reasons, the clinician considers that there is enough test indication to have a look at the patient's medical records. For simplicity, let's say that the only information given in the medical records is a family history of primary hyperparathyroidism (here abbreviated as PH), which may explain the finding of hypercalcemia. For this patient, let's say that the resultant hereditary risk factor is estimated to confer a relative risk of 10 (RRPH = 10). The clinician considers that there is enough motivation to perform a differential diagnostic procedure for the finding of hypercalcemia. The main causes of hypercalcemia are primary hyperparathyroidism (PH) and cancer, so for simplicity, the list of candidate conditions that the clinician could think of can be given as:
Primary hyperparathyroidism (PH) Cancer Other diseases that the clinician could think of (which is simply termed "other conditions" for the rest of this example) No disease (or no abnormality), and the finding is caused entirely by statistical variability The probability that 'primary hyperparathyroidism' (PH) would have occurred in the first place in the individual (P(PH WHOIFPI)) can be calculated as follows: Let's say that the last blood test taken by the patient was half a year ago and was normal and that the incidence of primary hyperparathyroidism in a general population appropriately matches the individual (except for the presentation and mentioned heredity) is 1 in 4000 per year. Ignoring more detailed retrospective analyses (such as including speed of disease progress and lag time of medical diagnosis), the time-at-risk for having developed primary hyperparathyroidism can roughly be regarded as being the last half-year because a previously developed hypercalcemia would probably have been caught up by the previous blood test. This corresponds to a probability of primary hyperparathyroidism (PH) in the population of: