8.5 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Differential diagnosis | 5/6 | https://en.wikipedia.org/wiki/Differential_diagnosis | reference | science, encyclopedia | 2026-05-05T07:27:56.437702+00:00 | kb-cron |
Odds
(
PostBT
P
H
)
=
Odds
(
PreBT
P
H
)
⋅
L
H
(
B
T
)
=
0.595
⋅
7
=
4.16
,
{\displaystyle \operatorname {Odds} ({\text{PostBT}}_{PH})=\operatorname {Odds} ({\text{PreBT}}_{PH})\cdot LH(BT)=0.595\cdot 7=4.16,}
where:
Odds(PostBTPH) is the odds for primary hyperparathyroidism after the blood test for parathyroid hormone Odds(PreBTPH is the odds in favor of primary hyperparathyroidism before the blood test for parathyroid hormone LH(BT) is the likelihood ratio positive for the blood test for parathyroid hormone An Odds(PostBTPH) of 4.16 is again converted to the corresponding probability by:
Pr
(
PostBT
P
H
)
=
Odds
(
PostBT
P
H
)
Odds
(
PostBT
P
H
)
+
1
=
4.16
4.16
+
1
=
0.806
=
80.6
%
{\displaystyle \Pr({\text{PostBT}}_{PH})={\frac {\operatorname {Odds} ({\text{PostBT}}_{PH})}{\operatorname {Odds} ({\text{PostBT}}_{PH})+1}}={\frac {4.16}{4.16+1}}=0.806=80.6\%}
The sum of the probabilities for the rest of the candidate conditions should therefore be:
Pr
(
PostBT
r
e
s
t
)
=
100
%
−
80.6
%
=
19.4
%
{\displaystyle \Pr({\text{PostBT}}_{rest})=100\%-80.6\%=19.4\%}
Before the blood test for parathyroid hormone, the sum of their probabilities were:
Pr
(
PreBT
rest
)
=
6.0
%
+
14.9
%
+
41.8
%
=
62.7
%
{\displaystyle \Pr({\text{PreBT}}_{\text{rest}})=6.0\%+14.9\%+41.8\%=62.7\%}
Therefore, to conform to a sum of 100% for all candidate conditions, each of the other candidates must be multiplied by a correcting factor:
Correcting factor
=
Pr
(
PostBT
rest
)
Pr
(
PreBT
rest
)
=
19.4
62.7
=
0.309
{\displaystyle {\text{Correcting factor}}={\frac {\Pr({\text{PostBT}}_{\text{rest}})}{\Pr({\text{PreBT}}_{\text{rest}})}}={\frac {19.4}{62.7}}=0.309}
For example, the probability of cancer after the test is calculated as:
Pr
(
PostBT
cancer
)
=
Pr
(
PreBT
cancer
)
⋅
Correcting factor
=
6.0
%
⋅
0.309
=
1.9
%
{\displaystyle \Pr({\text{PostBT}}_{\text{cancer}})=\Pr({\text{PreBT}}_{\text{cancer}})\cdot {\text{Correcting factor}}=6.0\%\cdot 0.309=1.9\%}
The probabilities for each candidate conditions before and after the blood test are given in following table:
These "new" percentages, including a profile-relative probability of 80% for primary hyperparathyroidism, underlie any indications for further tests, treatments, or other actions. In this case, let's say that the clinician continues the plan for the patient to attend a clinician visit for a further checkup, especially focused on primary hyperparathyroidism. A clinician visit can, theoretically, be regarded as a series of tests, including both questions in a medical history, as well as components of a physical examination, where the post-test probability of a previous test, can be used as the pre-test probability of the next. The indications for choosing the next test are dynamically influenced by the results of previous tests. Let's say that the patient in this example is revealed to have at least some of the symptoms and signs of depression, bone pain, joint pain or constipation of more severity than what would be expected by the hypercalcemia itself, supporting the suspicion of primary hyperparathyroidism, and let's say that the likelihood ratios for the tests, when multiplied together, roughly results in a product of 6 for primary hyperparathyroidism. The presence of unspecific pathologic symptoms and signs in the history and examination are often concurrently indicative of cancer as well, and let's say that the tests gave an overall likelihood ratio estimated at 1.5 for cancer. For other conditions, as well as the instance of not having any disease at all, let's say that it is unknown how they are affected by the tests at hand, as often happens in reality. This gives the following results for the history and physical examination (abbreviated as P&E):
These probabilities after the history and examination may make the physician confident enough to plan the patient for surgery for a parathyroidectomy to resect the affected tissue. At this point, the probability of "other conditions" is so low that the physician cannot think of any test for them that could make a difference that would be substantial enough to form an indication for such a test, and the physician thereby practically regards "other conditions" as ruled out, in this case not primarily by any specific test for such other conditions that were negative, but rather by the absence of positive tests so far. For "cancer", the cutoff at which to confidently regard it as ruled out maybe more stringent because of severe consequences of missing it, so the physician may consider that at least a histopathologic examination of the resected tissue is indicated. This case is continued in the example of Combinations in the corresponding section below.
== Coverage of candidate conditions == The validity of both the initial estimation of probabilities by epidemiology and further workup by likelihood ratios are dependent on the inclusion of candidate conditions that are responsible for a large part as possible of the probability of having developed the condition, and it is clinically important to include those where relatively fast initiation of therapy is most likely to result in the greatest benefit. If an important candidate condition is missed, no method of differential diagnosis will supply the correct conclusion. The need to find more candidate conditions for inclusion increases with the increasing 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, then it may be acceptable to stop finding more candidate conditions, but this would much more likely be unacceptable if the presentation would have been severe pain.