Saturday, 10 May 2014

INR management - the Goldilocks Dose

Since getting a mechanical heart valve (in Nov 2011) I have naturally had to deal with life on a drug called Warfarin. This is known variously by people as its 'corporate product names' like: Marevan or Coumadin. They are essentially the same thing.

I self monitor with a Roche Coaguchek XS (at the time of writing) and am very happy to have the freedom to do so (unlike many in the USA who are slaved to their medical insurance). Self management is becoming as accepted for INR as it already is for diabetics (and can you imagine asking a diabetic now to go to a lab for daily blood samples?).

Jut like anything too much will cause you problems, too little does nothing and so there is a dose which is juuuust right - I call that the Goldilocks Dosage.

Sadly this dose is elusive for many and in reality is a bit of a shifting goal post, but then in reality so too is management of your insulin levels if you happen to be a diabetic.

Quick Summary

I have found a way of using my collected data to make better dose estimations. In short for myself I have found (by examining my data) that I can expect the following INR (on average) ranges as a response to my consistent daily dose of warfarin:

dose mg 7 7.5 8 8.4
MAX INR 3.19 3.14 3.64 3.87
Average INR 2.43 2.60 2.77 2.95
MIN INR 1.82 1.95 2.08 2.21

What is this and what does it mean and how did I determine this? Well the answer is perhaps more complex, so if this is interesting to you then read on ....


One of the great benefits of INR self management is that you can monitor more frequently, this is very helpful in learning about your own metabolic response to warfarin, and indeed not only does it vary from person to person, but varies within a person at various times. Indeed this variance in metabolism and INR responce is what causes problems with gaining the maximum benefits from warfarin and avoiding the dangers.

Basically the INR is the goal and working out the dosing of warfarin is the method of getting yourself to that goal.

In the past the goal INR was given as a range, however a new way of thinking about it is emerging in the literature, which is to simply have a 'target' INR and grasp the idea that consistency of dose is good and values too high increase your problems as do values too low. You can expect your INR to move around, as long as it stays within the window there is nothing to worry about.

To me the new method is wiser because for a start nothing stays in one place (least of all metabolism) and the reality is a continuum not a border. You will not suddenly burst if you go over a threshold (low or high) and so the idea of the range is a little misleading and (in my view) can encourage silly and wrong approaches: IE my Dr said my INR range was 2 ~ 3 so I'm going to sit on 2. This is dangerous because the reality is that you can't sit on 2, you'll dip low and increase your risk of a stroke.

My Data and statistics

Before I go on much more I thought I'd present my INR data from 2013

so from this you can see that my INR varied between 1.9 and 3.3, but the vast majority of the time was between those levels (but as you see always changing). I occasionally read of people complaining of their INR not settling and wonder if they imagine their INR level should somehow be more static, like a line of bricks?

Anyway, in the analysis of this some understanding of stats comes in handy, don't worry its not going to get complex. Basically my average INR was 2.5 (which is exactly the target that the new European Guidelines suggest) with a Standard Deviation of 0.3 (which means that if my INR was away from 2.5 it was mostly within ±0.3 of that; meaning between 2.2 or 2.8). Meaning I'm doing an OK job of managing my INR.

However I always like to understand things more, so I have been doing some data analysis on my data (and I have quite a bit) and have come up with an interesting model which I believe at the very least helps to understand my INR responce better.

Metabolism and Models

I like to model things, and maths (computers) make modeling quite convenient.My experience in modeling is that there are simple models and complex models. The literature on modeling suggests that more complex models may prove more accurate, but if not highly tuned with (accurate) parameters will produce quite unreliable results. Simple models are never going to be as accurate, but as they require far less tuning they are less likely to be wildly inaccurate than a badly tuned complex model. So may actually be more valuable. So I set about to work out a model to allow me to see things other than INR and dose. I call this Metabolism.

Basically my body gets rid of Warfarin as quickly as it can. In the main this is by the cytochrome P450 pathway (but lets not get into that here) in a reasonably consistent manner. The measure of this is its "half life" (which people probably know from radiation physics, but it is equally used in biochemistry too). Of course this half life is probably not going to be consistent from person to person or even perhaps within a person from day to day.  The half life of warfarin in a person varies from between 20 to 60 hours. So I decided for simplicity to pick 48 hours (two days) as a nice easy basis for a start. There will be variations (it is after all a living system).

Further, the level of Warfarin is not an absolute indicator for this, as INR is about the clotting ratio and the manner of action of Warfarin is to inhibit the recycling of Vitamin K in the body (which in turn influences clotting). So its really a push this which shoves that sort of thing and there is some slop in the mechanism (buffering for want of a better word).

 So to try to make things consistent I decided that I would simplify the entire bundle of
  • diet (Vitamin K intake),
  • exersize (effects on metabolism),
  • warfarin intake
  • misc metabolic changes
into one single factor called by me as "Metabolism".

As you may guess its not something which lends itself to being predictable (and that is not my intention for it). My intention is to assist me to grasp things by reducing my variables from many to two - Metabolism and Warfarin dose. As already mentioned simple models are at least less likely to be screamingly wrong and this is a simple model.

The model works by taking the standard half life accumulation over a total of 4 days as its a simple number to work with and the amounts of residual warfarin left from a dose will be quite low by then (and hence of reduced significance overall). Then with a stabilised dose (I choose a week of the same dose as stability) one can apply the "Metabolism" factor (a simple scalar) to this 'standardised warfarin accumulation' to then give the INR which was measured.

That's right, its based on Empirical observation, as I said, it is not predictive in itself.

So with the last two years of data at hand I put this into the model and found that my "Metabolism" varied between 6.15 and 10.78 Now I can plug these numbers into another simple "what if" calculation spread sheet and work out a worst case and best case INR for various stabilised doses.

This is the data from my table at the start of the blog post.

So I can at a glance see that a daily dose of anything from 7 to 8.5mg of warfarin will on average give me an INR between 2.43 and 2.95 ... which would be excellent. However only if my metabolism remains at exactly my median level (which it does not). If I were to pick a dose of (say) 8.5mg then (assuming swings in my metabolsim) my INR could be anywhere between 2.21 and 3.87 - which is only a little over my surgeons initial theraputic range instructions (which were 2.2 ~ 3).

Further, I can now look at my "Metabolism" statistics and see what its MAX MIN and Std Dev are and make reasonably accurate estimations of the likelyhood of being in what range.

As you probably know (hey, a pun) a Std Dev normal bell curve represents likelyhoods for "normally distributed data". So I can apply this now to my Metabolism figures and work out reasonable scenarios.

I've already given my observed MAX and MIN values for Metabolism (10.78 and 6.15) and my Average was 8.08 with a Std Dev of 1.19 ... So from this I can say that within ±1 StdDev of my average Metabolism the doses of 7, 7.5, 8 and 8.5 give:

7mg 7.5mg 8mg 8.5mg
+1 StdDev = 9.27 2.11 2.27 2.42 2.57
-1 StdDev = 6.88 2.85 3.05 3.25 3.46

Which suggests that for "most of the time" my dose could be anywhere in this range and be OK most of the time. Now using this knowledge I can now work out
  • a plain and simple dose which will keep me from going low (and risking clots) but accepting highs (and knowing how high they may be)
  • what (if any) adjustments I wish to make without resorting to guess work (like guessing how by how much I should change my dose by)
  • understanding how long I'm likely to be low for and or high for
which is quite helpful stuff.


This supports the variety of attitudes which exist "out in the wild" of INR management. It supports what many find of "once stabilised don't vary the dose much" while at the same time gives some support to the view that "you should only adjust in small amounts if going out of range". I now use the 2 week moving average on my Metabolism (rather than on the INR which I used previously to developing this, and to be honest I'm still tracking both) to see if my trend is going low or going high.

The astute observer will by now noticed that lower INR is associated with higher Metabolism. This is because my Metabolism is measure of the rate at which the body clears the warfarin (that interferes with Vitamin K recycling). High clearance gives less warfarin in the body and the less warfarin in the system the lower the INR is.

If we go back to my 2013 data set you can actually see that there are definitely trends in my metabolism (best seen in the 2 week moving average). Its possible (if you keep records on a spreadsheet with a graph) to now observe these trends and make them easier to both see and understand.

I think its important to also mention that while cyclic, they do not necessarily (or even is it likely) follow a simple sine wave. Just like looking at some simple regular cycles of different frequency we see an overall effect which is unlike each component. For instance this animated graphic showing the combination of a few frequencies (wave lengths) may make this clearer.

Some parts will be diet, some will be health, some may be other 'cyclic' metabolic trends in the body.

Again I emphasize this is not about prediction of where the INR will be but estimation of where its likely to be within.

The importance of being regular

Lastly just like one's morning movements regularity is good stuff. I disagree with the notions of alternated doses, if for no other reason that they make it unclear exactly what your residual warfarin levels will be at any given time (adding more complexity to analysis at the very least). I know that some people say that a dose change takes a few days to even out, and then use this to justify taking 5 on 3 days per week and 7 on others ... to me that's just setting up even more irregular cycles which you just don't know what will be the result of. For instance changing the dose higher is likely to trigger the mitochondria to deliver a greater enzymatic dose (warfarin is metabolized by cytochromes P450 (CYP1A2 CYP3A4, CYP2C9))  to remove the toxin, and will this then cause the following lower dose to be removed faster. Not a good idea.

Every time I read of some poor bastard having their INR swing all out of control (dangerous stuff) its usually always associated with a bungling clinic varying the doses all over the place.

If you are interested in this process then I encourage you to keep regular records and measure at least weekly. Another myth is that INR does not respond to a dose change for days. Bullshit. I have personally observed (with daily measurement on occasions) the results of going off warfarin (for surgery and oops, missed a dose) and seeing how it changed substantially on a day by day basis.

Data quality is the important thing, there are people who say that you don't need to sample INR more than monthly ... clearly this is a gross misunderstanding looking at my data. Probably daily samples would be ideal for analysis, but in my experience every 3 days is as fine a granularity as really matters (and yes, I've done daily sampling, every 2 days sampling, twice weekly sampling and weekly sampling).

where to next?

Well it is my intention to develop some software to allow people to mange their data in a way that makes it simple : you input your INR readings, the software then preserves that and allows you to look at various analysis of this. I hope this will provide an easy method for people to store and chart their INR and enable them to keep accurate records.

Lets see how my life allows me time for that in the coming year...

Best Wishes

PS: There have been (via different channels) a few requests to contact me about this work. If you would like to email me to discuss this please feel free to me at:


Anonymous said...

I too had a mechanical valve fitted in Nov 11. It's been an interesting few years. I have been keeping records of my INR ever since leaving hospital as I use the coaugucheck meter. The thought of getting tested once every 6 weeks gave me the fear! I dose myself and tell the GP when I visit what has been happening. My cardiologist wasn't too impressed but hey...I"m in charge of me. I just started a low carb high fat/protein diet with no increase in Vit K rich foods. INR dropped like a stone. Dose adjustment time again. More carbs too :-)

Great post and get that software written, I'd buy it !

Anonymous said...

Interesting and in depth analysis. I have had a mechanical valve since 2009 and my surgeon arranged a machine straight away so I could self manage. Early days I checked every couple of weeks, however now just check about every 6 weeks. Pretty easy to get into a routine and get within a range. I like to stick at high end of range as I am more worried about clotting at lower end. Beleive there is far too much bs written about INR checking and Drs have created a whole industry out of it. Only see my GP for Warfarin Prescriptions and he rarely mentions INR as he knows I will make my own decisions.

Unknown said...

Thanks so much for posting--you've been a tremendous encouragement to us. My husband has had a mechanical aortic valve since October 1994 and a home INR monitor since Feb. 2000--first a ProTime and now a Coaguchek XS. We have come to remarkably similar conclusions to yours, although with less math behind them. We're not the least bit afraid of math, though, and would like to learn how to create graphs like yours. He has 16 years of data and he tests every three days so there are plenty of data to work with. We, too, have repeatedly seen a response to dose changes within 24 hours, and the visissitudes of P-450 production with changes in diet (including wine intake), exercise and even temperature/climate. He adjusts his dose in 1 mg increments and never skips a dose unless he's having a medical procedure and needs a window (which is very rare--the last was a dental implant). His "target range" is 2.5-3.5, although we like the idea of a target INR with standard deviations. His dose is currently 11/12 mg per day, although it has varied from 10-15 mg/day over the years. Would you be willing to share your spreadsheet template, or to have some more conversation about your calculations?

obakesan said...

Hey Unknown ... thanks for the kind words and I am indeed glad its providing something of use. I have added an email address for contact to the end of the post

Unknown said...

Great post. I am also working on a model, actually my third model to predict my INR. First one just looked at weekly warfarin and vitamin K intake and used an equation with these two as variables and coefficients chosen to minimize mean squared error.

Second model was much more complicated considering warfarin and vitamin K half lives to predict daily blood concentration levels and then modeling a few other variables like alcohol intake and exercise. It allowed inputs for age, sex, weight to calculate blood volume and then volume of distribution for drug metabolism predictions. It has a food database with automatic look-up of vitamin K content so one can enter intake amounts by food and spreadsheet would add them all in. It got pretty good predictions within 0.2 of my INR mostly. Graphed it with error bars settable from one to three standard deviations.
Three years of collecting data allowed me to come up with another empirical model that is simpler that just took last 46 weekly data points of the INR measured, warfarin and vitamin K intake (moving averages) and with a multi (two) - variable linear regression produced an equation that predicts INR based on those two variables. After experimenting with the input data the equation with highest correlation coefficient (R-squared) was obtained when I used as variables these two: moving average of the last five warfarin doses and moving average of the last three vitamin K doses. I got excited when then next two weekly INRs were predicted exactly and better yet, right on target at 3.0 and 3.0. (I have two mechanicals and one bio-prosthetic valves). Subsequent measurements have been with 0.1 of prediction. Of course it's only as good as the input and there is lots of room for error because you have to either measure or guesstimate the amounts of vitamin-K rich foods that you eat. E.g, that soup had spinach it it bue how much did I eat of spinach? Well ... that was about one tablespoon of cooked spinach, I guess.

We should talk. I also had in mind producing an app that would implement this but have not done it yet mostly because I don't know how. I could write a program in say Python but i don't know how to make phone apps. Maybe we could collaborate. I wrote a spec on what the user input and output screens should look like for a phone app.

obakesan said...

Unknown, sure send me your email address in a comment and I will not publish it and I'll use that to contact you