To continue the first post we take the results from our first example and see if there is any way we can determine whether there is a clinically significant difference in our patient. As a reminder, these results are for demonstration purposes only, calculations are not shown, it for conceptual understanding first.
We left our last case with a sample referred to our hospital, and a result that we obtained.
Are the results analytically different?
We determined that the results are analytically different as the second result of 14.6 seconds was >0.9 seconds different from the original result at Hospital A. Again, methods to determine this will be discussed in later posts.
Are the results abnormal?
We quoted a reference range of 10.2- 13.4 seconds for the PT at both Hospitals. At first sight the results obtains at both centres appear to be abnormal. But are they really?
- Hospital A – 13.6 seconds (10.2 – 13.4 seconds)
- Hospital B 14.6 seconds (10.2 – 13.4 seconds)
We must first consider how a reference range is calculated. Or indeed the many ways that they may be applied to assays. In the cases of both Hospital A and Hospital B both ranges were determined by the central 95% of 30 “normal volunteers” – as a sample to represent the population. It is important that we know that before making any conclusions.
By definition, statistically, 2.5% of the normal population will be below the reference range and 2.5% will be above. This is with the assumption that our measurand is normally distributed amongst the population – not always the case.
So this begs the question again – are either, or both, of these results abnormal?
Our ranges are from 10.2 to 13.4 seconds. That is a range of 2 standard deviations and therefore covering the central 95% of our normal sample. Therefore one standard deviation is equal to half of the range = 1.6 seconds.
If we extend the range to cover 3 standard deviations we will include 99.7% of our “normal population”, thats pretty close to 100% but not quite. Therefore to be able to say that a result is out with our normal range (and therefore “abnormal” the result would need to be <8.8 or >15 seconds.
From this we can say that neither of our results are actually abnormal as they are both within this 3 SD range.
At hospital B the patient is retested
This time a result of 16.8 seconds +/- 1 second is reported (with 95% confidence)
What does this tell us now?
a. The result has increased from 14.6 to 16.8, a change of 2.2 seconds
Is the result analytically different?
Yes, as there is a difference greater than the 0.9 seconds defined earlier
Is the result abnormal?
Yes, it is above the reference range (even the wider range defined using 3 standard deviations, and taking into account 99.7% of our representative sample)
Is the change in results clinically significant?
Hmmmm, we can’t answer this yet. What else do we need to know?
Does the measurand vary in an individual over time? Yes of course it does
Can we quantify this? Yes, to a certain extent, using the biological database hosted on Westgard QC.com
BUT, and it is a BIG BUT
The intra individual biological variations quoted are not from “abnormal” patients. Is it unreasonable to assume that biological variability will differ in different disease states? No it is not.
Do we know any more clinical information? At the moment, No.
Without our clinical information we are still reliant on our interpretation of the results based on what we do know.
By combining the imprecision component of our assay along with the intra biological variation of our measurand from WestgardQC.com we can calculate that we require a 13% change in results to be analytically and biologically different. This equates to a change of 1.9 seconds.
Our change of 2.2 seconds is obviously greater than 1.9 seconds so we can say that they’re is a clinically significant change in our patient.
This was a very brief walk through to attempt to put measurement uncertainty into context for how we can use it. I have intentionally spared the mathematical details, we will work through that in the upcoming posts. For the time being it is worth noting that we do much of this assessment in our working lives as it is. What MU determination provides us is a means to quantify and monitor these factors precisely.