8.4 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Differential diagnosis | 4/6 | https://en.wikipedia.org/wiki/Differential_diagnosis | reference | science, encyclopedia | 2026-05-05T07:27:56.437702+00:00 | kb-cron |
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
%
{\displaystyle {\begin{aligned}&\Pr({\text{hypercalcemia is present despite no disease in individual}})\\=&{\frac {\Pr({\text{hypercalcemia WHOIFPI by no disease}})}{\Pr({\text{hypercalcemia WHOIFPI}})}}\\=&{\frac {0.0014}{0.00335}}=0.418=41.8\%\end{aligned}}}
For clarification, these calculations are given as the table in the method description:
Thus, this method estimates that the probability that the hypercalcemia is caused by primary hyperparathyroidism, cancer, other conditions or no disease at all are 37.3%, 6.0%, 14.9%, and 41.8%, respectively, which may be used in estimating further test indications. This case is continued in the example of the method described in the next section.
=== Likelihood ratio-based method === The procedure of differential diagnosis can become extremely complex when fully taking additional tests and treatments into consideration. One method that is somewhat a tradeoff between being clinically perfect and being relatively simple to calculate is one that uses likelihood ratios to derive subsequent post-test likelihoods.
==== Theory ==== The initial likelihoods for each candidate condition can be estimated by various methods, such as:
By epidemiology as described in the previous section. By clinic-specific pattern recognition, such as statistically knowing that patients coming into a particular clinic with a particular complaint statistically has a particular likelihood of each candidate condition. One method of estimating likelihoods even after further tests uses likelihood ratios (which is derived from sensitivities and specificities) as a multiplication factor after each test or procedure. In an ideal world, sensitivities and specificities would be established for all tests for all possible pathological conditions. In reality, however, these parameters may only be established for one of the candidate conditions. Multiplying with likelihood ratios necessitates conversion of likelihoods from probabilities to odds in favor (hereafter simply termed "odds") by:
odds
=
probability
1
−
probability
{\displaystyle {\text{odds}}={\frac {\text{probability}}{1-{\text{probability}}}}}
However, only the candidate conditions with known likelihood ratio need this conversion. After multiplication, conversion back to probability is calculated by:
probability
=
odds
odds
+
1
{\displaystyle {\text{probability}}={\frac {\text{odds}}{{\text{odds}}+1}}}
The rest of the candidate conditions (for which there is no established likelihood ratio for the test at hand) can, for simplicity, be adjusted by subsequently multiplying all candidate conditions with a common factor to again yield a sum of 100%. The resulting probabilities are used for estimating the indications for further medical tests, treatments or other actions. If there is an indication for an additional test, and it returns with a result, then the procedure is repeated using the likelihood ratio of the additional test. With updated probabilities for each of the candidate conditions, the indications for further tests, treatments, or other actions change as well, and so the procedure can be repeated until an endpoint where there no longer is any indication for currently performing further actions. Such an endpoint mainly occurs when one candidate condition becomes so certain that no test can be found that is powerful enough to change the relative probability profile enough to motivate any change in further actions. Tactics for reaching such an endpoint with as few tests as possible includes making tests with high specificity for conditions of already outstandingly high-profile-relative probability, because the high likelihood ratio positive for such tests is very high, bringing all less likely conditions to relatively lower probabilities. Alternatively, tests with high sensitivity for competing candidate conditions have a high likelihood ratio negative, potentially bringing the probabilities for competing candidate conditions to negligible levels. If such negligible probabilities are achieved, the clinician can rule out these conditions, and continue the differential diagnostic procedure with only the remaining candidate conditions.
==== Example ==== This example continues for the same patient as in the example for the epidemiology-based method. As with the previous example of epidemiology-based method, this example case is made to demonstrate how this method is applied but does not represent a guideline for handling similar real-world cases. Also, the example uses relatively specified numbers, while in reality, there are often just rough estimations. In this example, the probabilities for each candidate condition were established by an epidemiology-based method to be as follows:
These percentages could also have been established by experience at the particular clinic by knowing that these are the percentages for final diagnosis for people presenting to the clinic with hypercalcemia and having a family history of primary hyperparathyroidism. The condition of highest profile-relative probability (except "no disease") is primary hyperparathyroidism (PH), but cancer is still of major concern, because if it is the actual causative condition for the hypercalcemia, then the choice of whether to treat or not likely means life or death for the patient, in effect potentially putting the indication at a similar level for further tests for both of these conditions. Here, let's say that the clinician considers the profile-relative probabilities of being of enough concern to indicate sending the patient a call for a clinician visit, with an additional visit to the medical laboratory for an additional blood test complemented with further analyses, including parathyroid hormone for the suspicion of primary hyperparathyroidism. For simplicity, let's say that the clinician first receives the blood test (in formulas abbreviated as "BT") result for the parathyroid hormone analysis and that it showed a parathyroid hormone level that is elevated relative to what would be expected by the calcium level. Such a constellation can be estimated to have a sensitivity of approximately 70% and a specificity of approximately 90% for primary hyperparathyroidism. This confers a likelihood ratio positive of 7 for primary hyperparathyroidism. The probability of primary hyperparathyroidism is now termed Pre-BTPH because it corresponds to before the blood test (Latin preposition prae means before). It was estimated at 37.3%, corresponding to an odds of 0.595. With the likelihood ratio positive of 7 for the blood test, the post-test odds is calculated as: