An article in this week’s New York Times called Will This Treatment Help Me? There’s a Statistic for that highlights the disconnect between the risks (and risk reductions) that epidemiologists, researchers, guideline writers, the pharmaceutical industry, and policy wonks think are significant and the risks (and risk reductions) patients intuitively think are significant enough to warrant treatment.
The authors, bloggers at The Incidental Economist, begin the article with a sobering look at the number needed to treat (NNT). For the primary prevention of myocardial infarction (MI), if 2000 people with a 10% or higher risk of MI in the next 10 years take aspirin for 2 years, one MI will be prevented. 1999 people will have gotten no benefit from aspirin, and four will have an MI in spite of taking aspirin. Aspirin, a very good drug on all accounts, is far from a panacea, and this from a man (me) who takes it in spite of falling far below the risk threshold at which it is recommended.
One problem with NNT is that for patients it is a gratuitous numerical transformation of a simple number that anybody could understand (the absolute risk reduction – “your risk of stroke is reduced 3% by taking coumadin“), into a more abstract one (the NNT – “if we treat 33 people with coumadin, we prevent one stroke among them”) that requires retransformation into examples that people can understand, as shown in pictograms in the NYT article. A person trying to understand stroke prevention with coumadin could care less about the other 32 people his doctor is treating with coumadin, he is interested in himself. And his risk is reduced 3%. So why do we even use the NNT, why not just use ARR?
I cannot answer that question, because the NNT is a gratuitous transformation for physicians too. Referencing the article that introduced NNT as a concept in 1980, we find scant justification for transforming the ARR to its reciprocal. The authors state that “because the expression of the absolute risk reduction as a decimal fraction may not seem sensible to practicing physicians, this measure may be difficult for them to remember and incorporate into clinical practice,” and in their conclusion that “[the ARR’s] reciprocal, the number needed to be treated, expresses the absolute risk reduction in a manner that is easily understood by clinicians.”
Thirty-five years later, I find these statements to be both condescending and false. What justification is there to say that physicians cannot understand and remember decimals and subtract them? To the contrary, many physicians do not remember how to calculate the NNT or to retransform it back to the ARR. I am going to posit that the NNT took on a life of its own because it was published in the NEJM, and it became academically vogue to prattle on about it without really thinking about whether it added anything to a basic understanding of simple math.
Back to patients and their making decisions on the basis of data. Suppose a patient is discussing taking aspirin as primary prevention with his physician who presents him with the ARR for MI of 0.05% (1/NNT) over two years. A patient considering this (or any small number or its NNT transformation with associated analogies and diagrams) may elect to “take their chances” because “0.05% ain’t much, Doc.” Is this person rational? One way to judge this is to evaluate the patient’s decision to defer aspirin for congruence with other behaviors that demonstrate his revealed preferences. Does this person smoke, does he exercise, drive the speed limit, wear his seatbelt, own a firearm, drink excessively, etc? Is he a person who takes chances on a daily basis (and has during his lifetime) that are on par with the chances he takes by foregoing aspirin for primary prevention? If so, not taking aspirin (or another therapy) may be a congruent, rational decision for this individual.
(We demonstrated in an article in Medical Decision Making that physicians, too, have an intuition that smaller ARRs (yet much larger than 0.05% are not worthy of their endorsement. When evaluating a trials with identical characteristics except ARR (which was manipulated as the independent variable in a randomized case vignette study) willingness to adopt a new therapy with a ARR of 3% was 20-35% less than willingness to adopt the same therapy if the ARR was 10%. And in our study the outcome of the ARR was short-term mortality and the treatment had no opportunity costs and minimal/no side effects.)
But researchers, public health types, and policy activists are less concerned with the nuances and abstractions of individual decisions than they are with decisions that affect entire populations. At thepopulation level, thousands of heart attacks will be prevented each year, (THOUSANDS!) if several million people at risk take aspirin, or many other treatments with smallish ARRs. What one may deem negligible at the individual level is not negligible at the population level.
Suppose the above patient’s physician convinces him to take aspirin for primary prevention of coronary disease. I will call this situation the Therapeutic Paradox, borrowing from the Voter’s Paradox, which is the observation that, since the likelihood that any individual’s vote will influence the outcome of an election is small, and since it is costly in terms of time and effort to vote, it is paradoxical that anybody votes. (The paradox of voting is related to the Tragedy of the Commons.) In the Therapeutic Paradox, a patient is taking a drug or other therapy that benefits the population but that may not benefit him either because he is not one of the patients who gets the benefit, the risk reduction is not congruent with his other behaviors, or because his value system makes the side effects or costs unacceptable to him, even though the epidemiologist thinks the population as a whole would be better off if he (and everybody else) were to take the treatment. (Perhaps the biggest Therapeutic Paradox is the use of INH prophylaxis for positive PPDs [tuberculin tests], which have may net negative benefit for the individual but positive benefit for the population, but I digress.)
This patient’s risk of dying in a motor vehicle accident this year, assuming he will drive 12,000 miles, is 0.014%. It is small, but certainly not negligible on the individual level, and on the population level it is magnified to on the order of 40,000 deaths per year in the United States. Yet this patient does not awaken and think “I should drive fewer miles today to reduce my risk of death in a car crash.” (Nor does he think of the other negative externalities of driving 12,000 miles a year, and maybe he should be more mindful of both.) If he does not, it is not irrational for him to forego aspirin for primary prevention of cardiovascular disease, and perhaps many other therapies that may be offered to him if he knew the actual ARRs associated with those therapies. Thus, I think that candid discussion of risk and its reduction may have unanticipated paradoxical effects that are the opposite of those that are intended.
So how do we get patients to take the therapies that we (physicians and public health types) believe are good for them and for the population? One way is to nudge the pendulum away from the autonomy model of decision making back towards the paternalistic model – the doctor (or Mr. Bloomberg) simply says “I think you should take aspirin” – and the patient does it because the doctor knows best, just like he always votes because grandpa always said you should exercise your right to vote. Thus, the physician serves a dual role as a public health practitioner. It is abundantly clear that “shared decision making” is a utopia that few doctors or their patients have the luxury of, or even want to have the luxury of. Many and perhaps most patients don’t want to split hairs about taking an aspirin, or consider the small numbers and all their transformations and the analogies necessary for a proper understanding of risk and its reduction – they just want their doctor to tell them what is best, and if she says “take an aspirin a day” they are more than happy to oblige, whatever their Framingham score or their appraisal of the raw numbers and how negligible they may seem. On the other hand, some patients are aversive to medications with much larger ARRs than aspirin and there is little that can be done to convince them otherwise. Indeed, exploration of patients’ perceptions of risk may do little more than expose the Therapeutic Paradox and allow them to realize that many of the medications they are taking have what they would consider to be negligible benefits.
One thing is clear: the NNT is not any kind of magical transformation that makes the concept of risk and its reduction more accessible to patients (or physicians). Quite the contrary.
Scott Aberegg, MD is a physician based in Salt Lake City, Utah. He blogs regularly at The Medical Evidence Blog, where this blog post first appeared.