Diagnosis
There are multiple lobar and segmental ventilation / perfusion mismatches
with a normal chest X-ray. The lung scan is very positive;
the posterior probability of pulmonary embolism is high.
Dilemma
Bayes' Theorem
In this case, nuclear medicine physicians have a natural understanding
of the probability of pulmonary embolism before and after the lung scan.
However, a dilemma arises in explaining the probabilities using Bayes'
Theorem. Bayes' Theorem relates prior probability of disease, the
test result which can be given as a likelihood ratio, and the posterior
probability of disease (see for example: Parker JA: Java Calculators for
Radiology Applications: Absorbed Dose and Bayes' Theorem. http://ej.rsna.org/EJ_0_96/0054-97.fin/converters.html).
Usually, the posterior probability is calculated from the prior probability
and the likelihood ratio, but we can use the same Theorem to calculate
the likelihood ratio from the prior and posterior probabilities of disease.
Likelihood Ratio from the PIOPED Study
Determining the likelihood ratio for a positive lung scan from the PIOPED
data (JAMA 263:2753, 1990) is complicated by the patients in whom pulmonary
angiography was not performed and the patients in whom the results of the
pulmonary angiography was uncertain; however, no matter which way it is
calculated, the high category had a likelihood ratio less than 20.
Calculate Your Estimate for the Likelihood Ratio from Your Prior and Posterior
Probabilities of Pulmonary Embolism
Following are some prior probability, test result likelihood ratios and
posterior probability combinations:
Prior Probability of
Pulmonary Embolism |
Likelihood Ratio
for Test Result |
Posterior Probability of
Pulmonary Embolism |
| 2% |
20 |
30% |
| 2% |
200 |
80% |
| 5% |
20 |
51% |
| 5% |
200 |
91% |
| 20% |
20 |
83% |
| 20% |
200 |
98% |
You can enter your own prior and posterior probabilities of disease
and calculate the test likelihood ratio for the combination using the Bayes'
calculator in Parker JA: Java Calculators for Radiology Applications: Absorbed
Dose and Bayes' Theorem. http://ej.rsna.org/EJ_0_96/0054-97.fin/converters.html.
Most nuclear medicine physicians will enter a very low prior probability
of pulmonary embolism and a high posterior probability of pulmonary embolism
resulting in a likelihood ratio for the test which is much larger than
20 - much larger than the data from the PIOPED study would suggest.
Possible Explanations for the Dilemma
-
If your estimates for the prior and posterior probabilities of disease
resulted in a reasonable likelihood ratio, then there is no dilemma for
you.
-
The likelihood ratio in this case is much higher than the average positive
V/Q scan. There are different degrees of positivity for a V/Q scan.
This very positive test probably has a much higher likelihood ratio than
the average high likelihood ratio scan.
-
Bayes' Theorem assumes that there is no interaction between the patient
history and a test outcome. A young, previously healthy patient is
unlikely to have other pulmonary disease, so a positive test is more likely
to indicate pulmonary embolism, e.g. "What else could it be?"
-
The gold standard in the PIOPED study (pulmonary arteriography) is not
perfect. A non perfect gold standard will reduce the apparent accuracy
of the study being tested; however, the likelihood ratio, 20, which we
have been using for discussion is higher than that calculated form the
data, and may compensate for this effect.
-
In follow up it turns out that the patient did have a family history of
pulmonary embolism (see Follow Up). Since she denied a family history of
clotting problems at the time of evaluation, this piece of information
cannot be used in assessment of prior probability.
Explanation 2 may be the most important, but explanation 3 is probably
also important.
Follow Up
The patient was asked about a family history of clotting disorder at the
time of initial evaluation, and she did not know of any history.
During hospitalization, it was discovered that there was a history of a
grandfather and a great grandfather who both suffered from massive pulmonary
embolism, ultimately leading to both their deaths.
The patient did well on treatment with heparin. There was marked improvement
on a lung scan performed one week later.
Initial
Perfusion Scintigraphy |
 |
Perfusion Scintigraphy
Seven Days Later |
 |
Follow up perfusion scan seven days after presentation shows good resolution
of pulmonary embolism. The right lower lobe has less activity compared
to the right upper lobe on follow up; however, the right lower lobe was
abnormal initially, and this change may represent apparent worsening do
to a drop in pulmonary artery resistance as opposed to recurrent embolism
(Moser KM, Am J Med 55:434, 1972).
Click here to go to Joint
Program in Nuclear Medicine home page and Copyright notice.
J. Anthony Parker, MD PhD, Tony_Parker@bidmc.harvard.edu
