An invisible unicorn has been grazing in my office for a monthâ€¦ Prove me wrong.
Posted on 7th October 2016 by Martin Burton
Yes â€“ itâ€™s true. I have been hosting the beast unwittingly. Donâ€™t believe me? Prove it! Come and prove that the invisible unicorn does not exist. Maybe when you come you wonâ€™t find any evidence that the unicorn has been here. In fact, I suspect you might not.Â Â But â€“ I will counter â€“ you just arenâ€™t looking properly, or carefully enough, or for the right sort of evidence.Â Â It has been described as â€˜a principle of folk logic that one canâ€™t prove a negativeâ€™. Proving something doesnâ€™t exist is difficult: perhaps impossible.
Imagine this trialâ€¦
Imagine a trial to examine the effectiveness of a new drug â€“ weâ€™ll call it unicornal. And letâ€™s imagineÂ that the drug â€“ allegedly â€“ leads to improved vision: an ability to see clearly in a darkened room.Â Â Without the drug only about 5% of normal people (1 in 20) can see in these circumstances.Â Â To see if the drug works, we take 40 people and randomly allocate them to 2 groups with 20 people in each.Â Â One group gets unicornal tablets, the other a dummy, placebo tablet. Nobody knows â€“ neither the people taking the tablets nor the people conducting the experiment â€“ whether or not they are taking unicornal or placebo. We then measure the ability of people to see in the dark. In the group receivingunicornal just one person can do so and similarly in the placebo group one person (as youâ€™d expect).
What can we conclude?
Which of the following is correct?
- This study shows that unicornal does not improve vision in the dark (or to put it another way â€“ there is evidence that there is no effect ofunicornal).
- This study provides no evidence that unicornal is effective in improving vision in the dark (or â€“ there is an absence of evidence thatunicornal is effective).
It can be hard to see the difference between these statements. But one â€“ the first â€“ is about â€œevidence of absenceâ€ and the second is about â€œabsence of evidenceâ€. The first is saying in effect â€œhere is some evidence that allows us to conclude that there is no effect of unicornalâ€. Whilst the second says â€œwe havenâ€™t found any evidence that unicornal works. Maybe it does, maybe it doesnâ€™t â€“ we just donâ€™t knowâ€.
Absence of evidence
There is a key aphorism: the â€œabsence of evidence is not evidence of absenceâ€. This should be taken to heart by everyone interested in understanding evidence. Where does the unicorn come in? Well, there is (you will find when you arrive) an absence of evidence that my unicorn exists. This is not the same as there being evidence that she doesnâ€™t exist. You simply canâ€™t prove that.
In the same way, the evidence from my small study of 40 patients canâ€™t be taken as proving that unicornal does not work (paragraph 1. above). All we can say is that there is no evidence from this study that it does work (paragraph 2).
Letâ€™s dig deeper
But perhaps we should dig a little deeper. Some of you will already be saying â€œthe study was too small, you were never going to show a difference with so few patientsâ€. Well maybe or maybe not. If unicornal had had a very dramatic effect, tripling or quadrupling the number of people who could see in the dark, we may well have seen that even in our small study. In other words when the â€˜effect sizeâ€™ is large or dramatic we may not need a big study.Â Â On the other hand, letâ€™s imagine that the â€œtruthâ€ â€“ if only we could flush it out â€“ is that unicornal does improve the proportion of people who can see in the dark, but only marginally. Â Imagine a group of 10,000 normal people. 5% of them â€“ 500 in all â€“ would be excepted to be able to see in the dark.Â Â If the drug helps another 50 to see (an increase from 5% to 5.5%) the chances of working that out on the basis of a small study of 40 patients is nigh on impossible. We â€œmissed outâ€ on detecting that in our study. There really was a benefit of unicornal and a difference between those taking the drug and those not, but we simply did not find it.
So, when we find no difference between two groups in a trial like this, there are two possibilities;
- The possibility that there is truly no difference between the groups and however big a trial we do we will never find one. Unicornal has absolutely no effect on vision in the dark
- The possibility that there is a difference, but that difference is relatively small and we have â€œmissed itâ€ because our study wasnâ€™t powerfulenough to find it. By saying not â€˜powerfulâ€™ enough we often mean that it didnâ€™t include enough people.
What is important?
There is an important issue here. How big a difference between two groups is important to us? Would it be important to us as a group of researchers or patients, ifunicornal leads to an improvement in vision in the dark in 1 in 50 of the people taking it? Well, that depends on a number of things, not least the â€œdown sideâ€ of taking the drug (its side effects and costs)? Would our answer be the same if it only produces an improvement in 1 person in 10,000 taking it? This discussion is all about â€œminimally important effect sizesâ€ and that is another topic for another day.
Coming back to absences. Whenever you see the statement â€œwe found that the treatment did not workâ€ â€“ beware. The writers are claiming evidence of an absent effect. They are likely to be wrong. On the other hand, applaud those who say â€“ perfectly reasonably â€“ â€œwe did not find any evidence that the treatment workedâ€ and remind yourself that there may be two reasons for this: that the treatment really doesnâ€™t work, or that the study simply wasnâ€™t powerful enough to find a difference.
What can we say with confidence?
Enough of unicorns and the nebulous, allow me to make a very practical final point. Imagine that you have a study with a million people in each group and still there is no difference between the two. Surely in a case like this we can say there is no difference and that this treatment is â€œnot effectiveâ€? Faced with a large body of evidence such as this, we can at least say with confidence that if there is a difference it is very, very small and of no practical significance.Â Â And this is what we do when we have a large body of evidence, large numbers of patients and no detectable difference. We can â€“ having done the appropriate statistical tests â€“ conclude that practically speaking the treatment â€œdoes not workâ€ because any effect size is trivially small and further studies to look at the treatmentâ€™s effectiveness are unnecessary; we are as certain about is as we need or want to be. This is a conclusion that we come to not uncommonly at the conclusion of a large systematic review or RCT.
Alderson P. Absence of evidence is not evidence of absence.Â BMJÂ 2004;328(7438):476-7. Available from:Â https://www.ncbi.nlm.nih.gov/pmc/articles/PMC351831/pdf/bmj32800476.pdf