Friday, January 14, 2011

Why Median Survival Times Aren't (That) Helpful

The median is one of the most common statistical tools used in clinical research reports in oncology. They're also, from the patient's perspective, not as helpful as they seem at first glance. It's very important to be realistic about what statistics mean, especially when our lives are on the line. This doesn't always mean being pessimistic about the data. Rather, it means understanding what the data tells us -- and, equally importantly, what it doesn't tell us.

A median is, briefly, one type of average. There are three types of averages: mean (the most common type outside of clinical research), mode, and median. In short, the median is the point at which 50% of a sample have a particular attribute, or have accomplished some particular task. For instance, a country's median income is a dollar figure which half of the people earn less than, and half of the people earn more than. In cancer trials, median survival means the point at which half the patients recruited into the trial have died. And that's all it means -- it doesn't say when the 50% who died did so, or how long the other 50% are likely to live.

You'll often come across median figures in abstracts. A report on a follicular lymphoma trial of the R-CHOP chemotherapy regimen, for instance, might report that median progression-free survival time was 3 years. This means that, three years after treatment, half of the people have had their disease worsen (or return), and half of the people haven't. In those people the disease is either stable (i.e. hasn't grown), or is in complete remission (i.e. disappeared and hasn't come back).

It's very easy, as a patient, to assume that the median figure is the one that will probably reflect our own experience. In other words, it's easy to look at the above figure (just for example) and say to ourselves, "well, I've probably got about 3 years, give or take, before my cancer returns." In short, we imagine a graph like this, where the large majority of patients progress or die around the five-year mark:

Unfortunately, that's not what the median means -- or at least, it might mean that, but it doesn't have to. Oncologists know this. That's why in the full text of the article (not just the abstract), there's usually a graph or chart. However, the median is still a useful tool for researchers because it represents an objective, commonly accepted point at which you can either stop or at least scale back your efforts. Once your subjects pass the 50% mark, it means that only a minority are still benefiting from treatment.

What we as individual patients really want to know, though, is what is most likely to happen to us, as individuals, and the median point doesn't tell you that. That's because, at the end of the day, the median only tells you what happened to the 50th and 51st out of 100 patients. The rest of us aren't necessarily going to be on the same point on the graph as them. In fact, our experience could end up being almost nothing like theirs.

Just for example, here's another example of a median 5-year survival time. As you can see, there's a vast difference from the above graph. In this case, the same proportion of the original group of patients die every year. This means that while the "average" patient dies at 5 years, actually you're just as likely to die in the first year, or the tenth. That's obviously a very disturbing thing to contemplate, although it's not all that common:

On the other hand, cancer trials often show that a drug doesn't work very well in many patients, but in those patients in which it does work, it works very well. We might end up with the same 5-year median survival time as I showed you in the above graphs, but with a completely different picture of the disease. For example, clinical trials of first-line Bexxar therapy tend to show that only a minority of people have long-term remissions, but that minority tends to be pretty stable. Here's yet another example of a legitimate 5-year median survival graph:

In this case, you're odds of making it to 5 years are the same (50%), but there's two important points. First, a lot of people don't get much benefit at all (almost half make it three years or less). Second, for the minority who do make it 5 years, it looks like their odds of living another 5 years (or more) is very good. When we look at a graph like this, we're tempted to say that at least some patients may well have been completely cured.

All of these graphs are the result of fictional therapies with a 5-year median survival, but obviously if you were taking that treatment you'd be very interested in knowing you fit on Graph 1 (probably living 5 years), Graph 2 (likely to die at any time), or Graph 3 (possibly cured). That's why, from a patient's perspective, knowing a median statistic is just never enough.

1 comment:

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