I’ve been in two minds about whether to post this. On the one hand, I try to keep personal matters out of this blog — though there has been the occasional exception — but on the other hand I have a topic that fits quite nicely with some of what I’ve been writing about recently, since it concerns a fairly important medical decision that I have had to make based on what felt like inadequate information. Since that is quite an interesting situation from a mathematical point of view, and even a philosophical point of view, and since most people have to make similar decisions at some point in their lives, I have opted to write the post.
The background is that over the last fifteen years or so I have had occasional bouts of atrial fibrillation, a condition that causes the heart to beat irregularly and not as strongly as it should. It is quite a common condition: I’ve just read that 2.3% of people over the age of 40 have it, and 5.9% of people over 65. Some people have no symptoms. I myself have mild symptoms — I can feel a slightly strange, and instantly recognisable, feeling in my chest, and I experience a few seconds of dizziness almost every time I stand up from a relaxed seated position — otherwise known as orthostatic hypotension, which I often used to get anyway (as do many people).
I would gladly live with those symptoms, but unfortunately that’s not all there is to it. When a heart is in atrial fibrillation, it is not beating as efficiently as it should, and a little pool of blood can form that doesn’t get pumped away. And if that happens, it can form a clot. And if your heart then goes back into sinus rhythm (that is, it starts to beat normally again), that clot can get pumped out into your bloodstream and wreak havoc: in particular, it can lead to a stroke. I know this all too well, because my father had a severe stroke for exactly that reason in 2001.
Until 2004, my bouts of atrial fibrillation, of which I think there were two, were several years apart and lasted a few hours each. But then in early 2004 I went into atrial fibrillation and didn’t come out anything like so quickly. To decrease the risk of stroke, I had injections of a blood-thinning drug called Heparin (or at least, that’s what it’s called in the UK) into my stomach, once a day. But then I was put on to Warfarin, a drug that is used in rat poison. When a rat eats Warfarin, it goes off and has a haemhorrage and dies, but if you take just the right amount, you can thin your blood to the point where it is not dangerously thin, but atrial fibrillation is less likely to cause clots. The appropriate dose varies widely from person to person, so they have to increase it very gradually, testing your blood several times, until you reach the right INR (international normalized ratio), which roughly speaking means the ratio of the time your blood takes to clot to the time it would take to clot if you didn’t thin it. The recommended INR for people with atrial fibrillation is between 2 and 3.
When my atrial fibrillation ended in 2004, I was at an early stage of the process of getting the dose right. I asked my doctor whether that meant that I had in fact been more or less unprotected at the critical moment, and the answer was yes. So a completely standard procedure — coming off the Heparin before the correct Warfarin dose was established — had a very obvious defect. Fortunately, I didn’t have a stroke. (The probability was quite small, but even so.) That’s nothing compared with my father’s experience: he had his stroke after being advised by his cardiologist to come off Warfarin, a recommendation that other doctors told him later made no sense at all.
Let me try to fast forward to the present day. I have had quite long periods without AF, sometimes as long as two or three years, but I have also had two periods where I went into AF and it became pretty clear that I wasn’t going to come out of it again spontaneously. This, by the way, is very normal — once it starts, it gets gradually worse. Twice I had an electrical cardioversion: you go under a general anaesthetic and are given an electric shock that stops your heart, and when it starts again, if you are lucky it starts in sinus rhythm. When you have an electrical cardioversion, they try three times before giving up. I was lucky both times and went into sinus rhythm after just one shock.
The first cardioversion lasted me three years, apart from one 24-hour bout that ended of its own accord. The second cardioversion was in June, but in early September I went back into atrial fibrillation.
So what is the decision I have recently made? Well, back in 2004, when I first went to visit the person who is now my regular cardiologist, he told me about an operation called a catheter ablation. This is a procedure where the surgeon puts a wire into your leg and up an artery all the way to your heart. The tip of the wire then burns a bit of the surface of your heart, which causes it to form scar tissue that doesn’t conduct some faulty electrical signals that are responsible for the atrial fibrillation. At the time, my cardiologist said that it offered the prospect of a permanent cure for atrial fibrillation, but that it was probably best to wait, since the operation was relatively new and improving all the time.
We occasionally discussed the operation in the intervening years, and then in June he arranged an appointment with somebody who specializes in catheter ablations and performs them at Papworth Hospital, which is near Cambridge and is famous for being where the UK’s first successful heart transplant was carried out. This second specialist told me the following things (some of which I had read on the internet already).
1. I was probably progressing from “paroxysmal AF” (occasional bouts) to “permanent AF” (what it sounds like).
2. Catheter ablation is more effective against paroxysmal AF.
3. Now that more data is available, it has become clear that catheter ablation is not after all a permanent cure, but it might delay the progression of AF by five to ten years or something like that.
4. It is more effective the younger you are when you have it, with the decline in effectiveness quite high at my age, so in his opinion I should have it done sooner rather than later.
5. It has only a 60-70% chance of working at all.
6. It carries risks.
Most of that was pretty negative news, so I left the consultation not entirely sure what to do, though thinking I probably ought to have the operation. But the risks seemed pretty serious — about a 1% risk of a major complication — so I wanted to think a bit harder about them.
The two that bothered me most (and still do) are stroke and death. There are other serious things that can go wrong, but if their effects are temporary, then for me that puts them in a different league from a stroke, which could end my productive life, and death, which would end my life altogether.
The risk of death is put at one in a thousand, and this is where things get interesting. How worried should I be about a 0.1% risk? How do I even think about that question? Perhaps if my life expectancy from now on is around 30 years, I should think of this as an expected loss of 30/1000 years, or about 10 days. That doesn’t sound too bad — about as bad as having a particularly nasty attack of flu. But is it right to think about it in terms of expectations? I feel that the distribution is important: I would rather have a guaranteed loss of ten days than a 1/1000 chance of losing 30 years.
In the end, what convinced me that I shouldn’t worry too much about this risk was looking up what the risk of death is anyway over, say, the next year. I found on this site that the average risk of death in the UK for a man between 45 and 54 is 1/279, much higher than 1/1000. So if I am worried about a 1/1000 mortality rate from an operation, I should be about as worried that I will die from some other cause over the next four months or so. And yet I don’t lose any sleep over that possibility.
But maybe the problem is that I am concentrating four months’ risk into a few hours. Doesn’t that change everything?
Yes it would if I was planning to have lots of catheter ablations, but this is much more of a one-off event (though quite a few people have to have it done two or three times before it works). That makes a significant difference. For example, if aeroplane flights carried a 1/1000 mortality risk, that would be completely unacceptable, since some people take enough flights that all those risks would combine to create a near certainty of dying. So what matters in addition to the risk of the operation is the fact that I will have it at most a very small number of times. Maybe a rough rule of thumb is that I shouldn’t be too concerned, since on average my frequency of having this operation will be significantly less than once every four months.
Another possible counterargument is that for various reasons I am probably less likely than average for my age to die over the next year — by most people’s standards I am well off, I am in generally good health, I don’t smoke, and so on. However, I think that many of those factors also reduce my chances of major complications from a catheter ablation, so I’m inclined to guess that the validity of the rough calculation above is not hugely affected.
What about the risk of stroke? That brings me to something I haven’t yet mentioned. Even if a 1/1000 risk of death isn’t something to get too worked up about, one doesn’t want to take that risk unless there is some benefit from doing so. And because the benefit can be measured in terms of reducing risks, I am in the useful position of being able to compare like with like. In other words, it’s not like being asked whether I want to play Russian roulette for a million pounds, where I would have to weigh up a lot of money against a one in six chance of dying. It’s more like being asked to play Russian roulette (but with much better odds) once in order to avoid having to play it once a year for the next five to ten years, since the additional risk per year of having a stroke if you are in atrial fibrillation is comparable to the risk of having a stroke as a result of catheter ablation, even if one is taking Warfarin. (AF increases your annual stroke risk by a factor of about 5, but Warfarin divides that by about 3, or so I’ve read.) I can’t now find the figures I used. Again, the calculations were complicated by the fact that relative to many AF patients my risks of stroke are quite small, but again I think that applies to the risks as a result of the operation as well. As a precaution, it is standard practice to have weekly blood tests to make sure that one’s INR stays within the right range for a good long time before the operation, which mine has, so I have done what I can to minimize the stroke risk.
One final complication is that Warfarin carries its own risk: because it thins your blood, it increases the chances that you will have a brain haemorrhage, which can have very serious consequences. I think the extra risk may be something like 1% a year. Unfortunately, it isn’t considered safe to stop taking Warfarin after a successful catheter ablation, so this risk isn’t going to go away. But from the point of view of balancing the risks and benefits of the operation, that means that this particular risk doesn’t have to be taken into account, as it will be there either way.
In summary then, I’ve looked online at various statistics, none of which tell me exactly what I want to know — since they refer to populations that are more general than me, and in particular usually somewhat older than me (which is good news, since my risks should therefore be lower than average) — and concluded that probably the risk of having the operation is comparable to the risk associated with not having it. The fact that the last time I went into AF, which I’m in now, was only three months after I had had an electrical cardioversion was what finally persuaded me of that. And if I do have it and it works, then my quality of life will be improved, though not hugely, by my not being in AF. And it seems that when the doctors say that the risks of the operation are low, they are (in this instance) talking sense, since the risks are comparable to the background risk that everyone faces.
The operation is tomorrow. It takes a few hours and is done under a mixture of a local anaesthetic (in your leg where the wires go in) and light sedation. So I’ll be conscious. Assuming all goes well, it should be quite an interesting experience — I’ll report back on that when it’s over.
Two more small things. One is that AF itself is mathematically interesting: it seems that something causes the heart to go from a nice periodic rhythm into a more chaotic one, and it is not well understood why. The other is that I have tried to look things up in the medical literature in order to be able to assess the risks as well as I can. Last night I decided I wanted to look at a paper in the Lancet, that renowned medical journal published by Elsevier. Cambridge subscribes to Science Direct, Elsevier’s huge electronic package of all its science journals, so I in theory I should have been able to read the paper. I won’t go into details, but suffice it to say that even though I was entitled to read it, the system, for some mysterious reason, wouldn’t let me and kept giving annoying error messages. It reminded me why I’m in favour of getting rid of the subscription model for academic journals, and also of why I don’t like being told by Elsevier how much they have invested in Science Direct.
I’ll end by saying that this post is very much not intended to be a plea for sympathy. I know many people who have had much worse decisions (of the same general kind, but with far less favourable probabilities) to face than this one. In fact, it’s supposed to be the opposite of a plea for sympathy: more like an explanation of why a risk of 1/1000, which initially seems quite scary, is in fact not that scary after all. If, very much contrary to expectations, something goes badly wrong tomorrow, that will be the moment for sympathy. But the chances of that are very much smaller even than the chances that Mitt Romney will win the presidential election, something that as an avid Nate Silver reader I find highly encouraging.