Are the results of this study important?
Let's begin by drawing a 2x2 table, using the results from the study that we identified:
|Target Disorder (iron deficiency anaemia)||Totals|
test result (serum ferritin)
|Test Positive (≤ 45 mmol/l)||
a + b
|Test Negative (>45 mmol/l)||
c + d
a + c
b + d
Our patient's serum ferritin comes back at 40 mmol/l and looking at the Table, we can see that she fits in somewhere in the top row (either cell 'a' or cell 'b'). From the Table we can also see that 82% (70/85) of people who have iron deficiency anaemia have a serum ferritin in the same range as our patient - this is called the sensitivity of a test. And, 10% (15/150) of people without this diagnosis have a serum ferritin in the same range as our patient - this is the complement of the specificity (1-specificity). The specificity is the proportion of people without iron deficiency anemia who have a negative or normal test result. We're interested in how likely a serum ferritin of 40 mmol/l is in a patient with iron deficiency anaemia as compared to someone without this target disorder. Our patient's serum ferritin is 8 (82%/10%) times as likely to occur in a patient with iron deficiency than in someone without iron deficiency anaemia - this is called the likelihood ratio for a positive test. We can now use this likelihood ratio to calculate our patient's posttest probability of having iron deficiency anaemia.
Our patient's posttest probability of having iron deficiency anaemia is obtained by calculating:
posttest odds/(posttest odds + 1)
posttest odds = pretest odds x likelihood ratio
The pretest odds are calculated as pretest probability/1-pretest probability. We judge our patient's pretest probability of having iron deficiency anaemia as being similar to that of the patients in this study
pretest odds = (0.36/(1-0.36)
pretest odds = 0.56
Using this we can calculate
posttest odds = 0.56 x 8
posttest odds = 4.5
posttest probability = 4.5/5.5
posttest probability = 82%
For an even easier method to determine the posttest probability, try the stats calculator and graph the posttest probability!
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With this information, we can conclude that based on our patient's serum ferritin, it is very likely that she has iron deficiency anaemia (posttest probability > 80%) and that our posttest probability is sufficiently high that we would want to work our patient up for causes of this target disorder.
Instead of doing all of the above calculations, we could simply use the likelihood ratio nomogram. Considering that our patient's pretest probability of iron deficiency anaemia was 36%, and that the likelihood ratio for a serum ferritin of 40 mmol/l was 8, we can see that her posttest probability of iron deficiency anaemia is just over 80%.
In the paper we found, the serum ferritin results are divided into 3 levels: =45 mmol/l, 46-100 mmol/l and >100 mmol/l. We can see that more information about the diagnostic test is available when results are presented in multilevels:
|Diagnostic test result||Target Disorder (iron deficiency anaemia)||Likelihood ratio|
|≤ 45 mmol/l||70/85||15/150||8|
|> 45 ≤ 100 mmol/l||7/85||27/150||0.4|
|> 100 mmol/l||8/85||108/150||0.1|
If our patient's serum ferritin was 110 mmol/l (and using her pretest probability of 36% and the likelihood ratio of 0.1), her posttest probability of iron deficiency anaemia would be less than 3%, virtually ruling out the possibility of this diagnosis. However, if her serum ferritin came back at 65, her posttest probability would be 10% and we'd have to decide if this was sufficiently low to stop testing or if we needed to do further investigations.