Anna Törner: The clinical trial – Periscope to reality
My first encounter with statistics was not exactly love at first sight. We students were bombarded with terms called bell-shaped curves, variance estimates, and statistical tests that for some reason were called "student t-tests," though they had nothing to do with students (the explanation for the name was that someone published a "letter" stating that we could not really calculate the variance properly).
I am a numbers person. But my spontaneous impression was that statistics was too complicated. A normally talented high school student should be able to explain the results of a clinical study. One shouldn’t have to be a mathematics whiz. Patience has never been my forte. So, I dissed the whole course. So, what was it that I didn't understand?
Well, as absurd as it sounds, statistics is not about evaluating how well the patients in the study have done. We can understand that quite easily. Instead, statistics is about using a study, or "sample” (as it’s called in statistical language) to tell us how effective a new treatment really is versus existing treatments. Not just for the patients in the current study, but for an infinite number of patients in Sweden, the world, now and in the future.
With statistics, we can’t get to the absolute truth. The reason is, that we can't possibly gather data from every patient on the planet, now and forever. There will always be a mysterious uncertainty. Since we observe a small sample, that’s as close as we’ll ever get to the truth. For me, getting here is an unforgettable Eureka moment.
With this wildly unshakable feeling, statistics became infinitely beautiful and enchanting to me. Unlike classical mathematics, which (often) offers exact or numerical solutions to problems, statistics is content helping us create a picture of reality. I often think that without statistical methods, we would be forced to believe that more patients recovering in one treatment arm means that there is a real difference in effect between the two treatments. But what if it was just chance fooling us? Can we tell the difference? Yes, this is where the confidence intervals and p-values become our guiding force.
Despite this, we can never know the absolute truth ─ How effective a new drug is (because we can only treat a fraction of the patients). So, the best we can get is an educated guess. This is usually presented in the form of a point estimate. This could be how much a new treatment reduces mortality compared to the established therapy or how much a new treatment reduces a specific symptom, such as pain during a migraine attack.
BUT, here's the crux of the matter: We used a small sample of patients. That’s why we must say how confident we are in our educated guess. We could do this informally by saying that the estimates are uncertain due to few patients and high variability in their responses. But how fun and informative would that be? That’s why we need confidence intervals.
The confidence intervals allow us to give, with good precision (which we often want to be 95%), a range of possible values for the TRUE treatment effect. i.e., what we would observe if we treated all patients who could receive the treatment. Thus, the purpose of the confidence intervals has nothing to do with the current study. On the other hand, it is a prediction ─ How effective the treatment will be, on average, for a future patient population.
Confidence intervals contain the information we need, but often we also use a p-value. The p-value is often interpreted as 'true' or 'false.' In reality, this perception is flawed. The p-value is a measure of randomness (probability). They filter out chance from the truth. That is why they are central to all medical research. So much that they deserve their very own spotlight and a separate column.
And, of course, we don't ignore the actual outcome of the patients in a clinical trial, it was just a cynical interest in getting you to read this column. Though we want to say, as statisticians, we are after something bigger ─ What can a small set of patients tell us about the hundreds of patients that will use this drug in the future?
Lastly, a clinical trial is an opportunity and a lifeline. It gives patients the chance to get new treatments, while simultaneously arming us with vital knowledge to help countless new patients. For those battling devastating diseases like cancer, be their last shot at a cure, after exhausting all existing approved therapies. That's where statistics finds an indispensable place. It is a magical science that helps us evaluate all other sciences and empowers us to make truly informed decisions!
This article has also been published in the newsletter "Statistik är mer än siffror".
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