understanding INR range and variation using statistics

I've been working with managing my INR for some 14 years now (so, not really long), but as well I've helped a few others along the path of being able to self manage. This has been not only helpful for them, but a great learning experience for me too. One of the things I've had to do is teach an understanding of how to use basic statistics to help understand things. Things like the data we have about our INR. Lets look at this set of data, remember, these are daily measurements:

This person was just starting their warfarin therapy and we were working out the optimal dose required for them. We had to make some adjustments but we ended up on 9.5mg daily. You can see from the above that there are some ups and downs;

• for the most part we've been at or above 2
• we've kept times above 3 small (being even as high as 4 isn't really significant)

What we don't really know is "how well we meet the ideal target of 2.5" which was set by the doctors. We could average all those numbers and then know that. In this case the average was 2.57, so that's great! But if we ask "is this variation large" we don't really know. This is where some statistics tools comes in handy.

Statistics is something most of us use but try hard to ignore (probably) because of the trauma of high school maths classes; but we shouldn't because its really helpful. One doesn't need to know how to do the hard work to get the benefits because spread sheets have all this functionality built in; all you have to do is have the data in a column and use a formula to get it all worked out for you; write in =AVERAGE(E20:E130) and there it is.

I'm pretty sure most people are comfortable with average, but alone, average isn't helpful, you need its good mate the Standard Deviation. Lets go with an example: You know that the average height of 16 year old boys is 173.5cm. You have a boy from a class who's 185cm. So the question is "is he very tall or not really unexpectedly so"?

Intuitively we know that the answer is no, because we have experience with children. But if we also find out that the standard deviation is 7.4cm we know that anything between 166.1cm and 180.9cm is a totally expectable result. We know this because that is what Standard Deviation (SD) is designed to measure. Below is a curve which is called a "Normal Distribution", people who have been working in statistics for years know this curve well.

the Normal Curve

It shows us that 68.2% of people (in this case, but its also more generally "of measurements") will fit between -1 SD  and +1 SD (we use the lower case for Greek symbol sigma σ to represent SD which you'll see on the bottom axis of that graph of the Normal Curve).

So just like we know that most boys age 16 are between 166.1cm and 180.9cm we can use the SD to work out how much variation that person has from "the population". The SD for the data in that bar chart above is 0.41, which means that any variation we see where the INR is between 2.16 and 2.98 is entirely normal for this person. Note: we don't know about you because we don't have your data.

Next, looking at this we can see that quite a portion (about a quarter of all measurements) fall within 2 SD either side of the average (or μ) which means INR readings of 1.75 through to 3.39 are to be expected, but just not often. Also 1.34 through to 3.8 may come up (however rarely) and this would be statistically rare, but not impossible.

So how does this help us manage our INR?

It helps to know that if your regularly and reliably taking your regular dose and if you're regularly seeing your INR within 1SD of the average then you shouldn't really make any changes in your dose. Keep your dose consistent and you can then rely on the statistics to understand what is normal for you.

Looking back at the graph of INR we also see something else ... from measurement to measurement we typically don't see that much change. Sure there are a couple where "day to day" we saw substantial on the 1st of August where INR fell from 3.3, through 2.7 (next day) down to 2.3. This was the result of some changes; dose was dropped to 8.5 and it fell fairly quickly but as you see didn't drop below 2.1. The INR then ranged back towards the average within a week.

The approach we should have taken was "keep a steady hand on the tiller" combined with waiting for a few more readings. However ...

As a good (budding) statistician, if you do see a reading which is outside of the 1SD range and you know that nothing has changed (no new foods, no binging on grapefruit, no binging on greens) then you should expect it to gradually change back towards the average. Unless something has changed and you don't know it. If it stays higher then you know "something has changed" and investigation is warranted into what.

So, please do make friends with  both average and SD, incorporate that into your spreadsheet as well as using regular weekly measurements. Occasional mid week samples "just to know" are also often helpful, but as you can see from both the historical experience behind Average and SD, combined with regular dose and weekly readings you can be in INR range in the high 80% of the time.

To get into the 90's you just need a few more strategies ... but that's for another post.

Best Wishes