Thursday, January 29, 2015

The Therapeutic Paradox: What's Right for the Population May Not Be Right for the Patient

Bad for the population, good for me
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 the population 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.  One man's trash is another man's treasure.

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.  A similarly apropos concept is the St. Petersburg Paradox, which I address in a comment at the end of the blog.) )  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.


  1. I would be happy to take my cardiologist's advice on medicines except when you tap his knee with a reflex hammer, he writes a script for whatever AstraZenca has to offer in that category. I've looked at the studies for Brilinta and Crestor and do not find benefit equal to the difference in cost of Plavix or simvastatin. As someone with no medical training, I KNOW he is in a better position to evaluate the studies I struggle to understand, but when I see that his evaluation is being skewed by the AZ rep, I'm hard pressed to take his advice.

    How do you solve that problem? Crestor is 71 times more expensive than simvastatin and while it appears that Crestor may be marginally better in preventing adverse outcomes, it is not 71 times better.

    1. There is certainly no substitute for a physician you can trust, and I have no doubt that they are hard to find. And it is hard to trust a physician who is a pawn of the pharmaceutical industry.

      The rosuvastatin (Crestor) versus simvastatin (Zocor) or atorvastatin (Lipitor) question can easily be answered: take generic and save your money. These drugs clearly have a class effect and despite some small differences, they're basically interchangeable. In one of the original trials for primary prevention with a statin (pravastatin - see: the absolute annual risk reduction was 0.48% per year in death and MI. In the recent rosuvastatin trial with the CRP testing (on which the primary author, Paul Ridker has a patent: the annual ARR in terms of a similar combined primary endpoint was 0.59%. I'm going to just say that this is an equivalent benefit, that the confidence intervals overlap and the differences are statistical noise. So, it is my belief that a person can take statins interchangeably. Personally my "favorite" statins are atorva and simva - those are the ones would take, and if they were similar in cost I would take atorvastatin. Even if simvastatin were the only generic, I would take it over any other branded statin just because it was generic.

      The Brilinta quesion is a bit more difficult. As I blogged about the ticagrelor study, it was a very good study in my opinion because it went head to head with the competitor. And ticagrelor was superior to plavix by about 2.0%, yeah that's right 2 full percentage points.

      I did a simple google search and it appears that Brilinta costs about $150/month and Plavix maybe as low as $15/month. So the annual cost differential is $1620. I'm not the guy to do a formal cost-effectiveness analysis, and I don't believe in super complicated analyses anyway, they're too opaque for me, I prefer back of the envelope, order of magnitude type analyses. If you multiply the $1620 cost differential by 1/0.02 (the reciprocal of the risk reduction) you get about $81,000. So, if you pay the differential for Brilinta, you are in essence saying that if you had the choice between having a heart attack and/or dying or paying $81,000, you would pay the $81,000.

      If I were in the position of having to decide whether to pay an additional $1620 per year for a 2% reduction in the risk of death or MI, I would first assess my finances. If they were good, I would just pay and be done with it.

      If this were a strain on my finances, I would look at it this way. How many years am I going to live, based on life tables. If the answer is 5, I would say, well, 2% x 5 years = 10%, it's unlikely that I"m going to benefit from the extra advantage of Brilinta, and 5 years of it is going to cost $8100 more than plavix, and I can use that money for something else. If the time horizon were longer, I could make the same argument,saying well, in 5-6 more years Brilinta will be generic and I'll save the money between now and then and start taking Brilinta when it goes generic. I would also look at other things I may be able to do to confer that same 2% we're talking about - free stuff like exercise and weight loss. I would look at other ways to save money too, like cancelling netflix, seeing if I can get my car insurance cheaper, etc.

      I admit it is a difficult choice with that Brilinta. Very difficult. Because I think the PLATO study showed it's clearly better, and it's not like it's priced in the stratosphere.

      I'm considering making some posts like my response here on the Status Iatrogenicus blog. If you have some more interesting analyses that I could make a whole post on, email me and I may devote a post to them, if they are interesting and of general interest.

  2. Thanks for this post; I agree with your take on ARR versus NNT. As a teacher of this stuff, I always considered NNT to be a neat twist - another perspective, but when I talk to patients, I give them the two risks and subtract them because it is so easy for them to digest that information. You made me realise that I never use NNT when I talk to patients.

  3. As a physician I am a health consultant to my patients, not their father.
    My job is to evaluate, diagnosis and offer treatment options and help each individual patient achieve the options he/she chose.

    NNT is one discussion I have with each patient.

    It is their choice in treatment, and mine to help them obtain it, as long as we agree.

    First do no harm!

  4. In a perfect world, yes we would spend hours discussing risk and its reduction and all the options with patients. In the real world, there are several barriers to this, first among them time, as well as limited understanding of patients of many of these concepts, and their limited interest in the nitty gritty. The patient who commented above is obviously very informed, and it still took me over an hour to do the relevant research and fact checking to answer his/her question confidently. Who has that kind of time? Being a paternalistic doctor is not the same as being a father.

  5. Interesting- utilitarianism (NNT) vs autonomy (ARR)

  6. There has been some discussion about whether a continuous population risk can be translated to the individual where outcomes are binary (you either stroke or you don't). Here is my explanation, taken from comments on this blog post which was shared on

    I just had an argument with a cardiologist friend who was in my MPH class over the weekend about whether the 3% ARR for stroke with warfarin is a population risk reduction or an individual risk reduction. That argument could go on ad infinitum, but that would not be practical. The practical thing is for patients to think that warfarin reduces THEIR risk of stroke by 3%. And it does.
    Warfarin is a ticket for entry into the treatment group where strokes occur at a rate of 2% per year from the placebo group where it occurs at a rate of 5% per year. When you switch groups you switch risks.
    Think of it another way. Suppose I have a 3% chance of crashing my motorcycle each time I take it to the track (experience suggests that it is actually higher than that – ask me how I know). I take it to the track 10 times per year. Since, like annual stroke risk, the risk is cumulative, my annual risk of crashing on the track is 30%. Each time I elect to “sit out” during one of the 10 annual track days, I reduce my annual track crash risk by 3% because I have removed myself from the “track” group (3% risk) and put myself in the “spectator” group (0% risk).
    We get too caught up in these abstractions about stroke being a binary event for the person, and the population risk and whatnot. I think they’re the same thing. Even if they are not, I don’t think there is a superior way of communicating them, in terms of accuracy or understandability.

    1. Nitpick: The risk of crashing doesnt add like that. You get a binomial distribution. With 3% risk of crashing per time you go, the chance of crashing at least one time is 26% over 10 times. If you go 9 times, the chance is 24%

    2. Not sure I agree for several reasons, though I do recognize that you qualified this as a nitpick. Firstly, with enough "trials" the binomial distribution will approximate the normal distribution. Thus, secondly, your binomial distribution with 10 trials already closely approximates my additive estimate of 30%. Thirdly, the binomial distribution assumes you know the risk of each crash with a day at the track or the risk of a stroke with each passing year, like you can know the probability of a heads or tails coin flip. But we don't get the probabilities of a stroke or a crash from probability theory or the logic of randomness, we get them from empiric observation. We can then fit the empirically observed probabilities to any model we wish, making assumptions with each model. The "daily" risk of crashing is not a discrete event, it is a series of laps. It could be reduced ad infinitum to a "risk per meter" of track, like stroke can be reduced to daily risk. In any case, the point is taken, and the results with 10 trials are close enough to being additive as to obviate use of a binomial calculator, thus simplifying understanding for the majority of people.

  7. NNH: the number needed to harm. This is an essential part of the mix. I'm surprised it's been neglected here.

    In the circumstance where one in 2,000 is helped by aspirin, one in 3,333 is harmed with a major bleed. This NNH is less bad than the NNT is good by about 1.5 times. It puts a slightly different light on the situation. Nonetheless, I still take my aspirin.

    Look at NNT for statins. One in 104 is helped to avoid a heart attack in 5 years. But... one in 10 is harmed with muscle damage. We need our muscles to exercise - perhaps the single most beneficial aspect of "lifestyle" we can engage in. And... One in 50 is harmed by developing diabetes. Of course we all know that diabetes is a prime risk factor for... what? Heart disease! Another different light. I've not been prescribed a statin. Yet. It would entail a detailed discussion before I would "comply" with that.

    Look more closely at stains. Pravastatin is not as effective as others for risk reduction, but looked at in that other light, it's least harmful in terms of muscle damage and diabetes risk.
    Wouldn't you like to see some research evidence that combines all these factors?

    THEN we could have that statin discussion.

  8. I just realized that the Therapeutic Paradox has things in common not only with the Voter's Paradox, but also with the St. Petersburg Paradox, which is an example of an apparent failure of expected utility theory to provide a correct normative model for human behavior. In the SPP, a gamble has infinite expected utility, but few people would pay more than a few dollars to play it, because the probability of a large payout is infinitesimally small even though the expected value is infinite. This too is like the Therapeutic Paradox, where an economic analysis predicts adoption/use of many of these therapies, but people do not adopt, because they consider the risk so small as to be negligible.



Note: Only a member of this blog may post a comment.