personalized medicine

S. Senn: Personal perils: are numbers needed to treat misleading us as to the scope for personalised medicine? (Guest Post)

Personal perils: are numbers needed to treat misleading us as to the scope for personalised medicine?

A common misinterpretation of Numbers Needed to Treat is causing confusion about the scope for personalised medicine.

Stephen Senn
Consultant Statistician,


Thirty years ago, Laupacis et al1 proposed an intuitively appealing way that physicians could decide how to prioritise health care interventions: they could consider how many patients would need to be switched from an inferior treatment to a superior one in order for one to have an improved outcome. They called this the number needed to be treated. It is now more usually referred to as the number needed to treat (NNT).

Within fifteen years, NNTs were so well established that the then editor of the British Medical Journal, Richard Smith could write:  ‘Anybody familiar with the notion of “number needed to treat” (NNT) knows that it’s usually necessary to treat many patients in order for one to benefit’2. Fifteen years further on, bringing us up to date,  Wikipedia makes a similar point ‘The NNT is the average number of patients who need to be treated to prevent one additional bad outcome (e.g. the number of patients that need to be treated for one of them to benefit compared with a control in a clinical trial).’3

This common interpretation is false, as I have pointed out previously in two blogs on this site: Responder Despondency and  Painful Dichotomies. Nevertheless, it seems to me the point is worth making again and the thirty-year anniversary of NNTs provides a good excuse.

NNTs based on dichotomies, as opposed to those based on true binary outcomes (which are very rare), do not measure the proportion of patients who benefit from the drug and even when not based on such dichotomies, they say less about differential response than many suppose. Common false interpretations of NNTs are creating confusion about the scope for personalised medicine.

Not necessarily true

To illustrate the problem, consider a 2015  Nature comment piece by Nicholas Schork4 calling for N-of-1 trials to be used more often in personalising medicine. These are trials in which, as a guide to treatment, patients are repeatedly randomised in different episodes to the therapies being compared. 5.

NNTs are commonly used in health economics. Other things being equal, a drug with a larger NNT ought to have a lower cost per patient day than one with a smaller NNT if it is to justify its place in the market. Here however, they were used to make the case for the scope for personalised medicine, and hence the need for N-of-1 trials, a potentially very useful approach to personalising treatment.  Schork claimed, ‘The top ten highest-grossing drugs in the United States help between 1 in 25 and 1 in 4 of the people who take them (p609). This claim may or may not be correct (it is almost certainly wrong) but the argument for it is false.

The figure: Imperfect medicine is based on Schork’s figure Imprecision medicine and shows the NNTs for the ten best selling drugs in the USA at the time of his comment. The NNTs range, for example, from 4 for Humira® in arthritis to 25 for Nexium in heartburn. This is then interpreted as meaning that since, for example, on average 4 patients would have to be treated with Humira rather than placebo in order to get one more response, only one in 4 patients responds to Humira.Imperfect medicine: Numbers Needed to Treat based on a figure in Schork (2015). The total number of dots represents how many patients you would have to switch to the treatment mentioned to get one additional response (blue dot). The red dots are supposed to represent the patients for whom it would make no difference.

Take the example of Nexium. The figure quoted by Schork is taken from a meta-analysis carried out by Gralnek et al6 based on several studies comparing Esomeprazole (Nexium) to other protein pump inhibitors. The calculation of the NNT may be illustrated by taking one of the studies that comprise the meta-analysis, the EXPO study reported by Labenz et al7 in which a clinical trial with more than 3000 patients compared Esomeprazole to Pantoprazole. Patients with erosive oesophagitis were treated with either one or the other treatment and then evaluated at 8 weeks.

Of those treated with Esomeprazole 92.1% were healed. Of those treated with Pantoprazole 87.3% were healed. The difference of 4.8% is the risk difference. Expressed as a proportion this is 0.048 and the reciprocal of this figure is 21, rounded up to the nearest whole number. This figure is the NNT and an interpretation is that on average you would need to treat 21 patients with Esomeprazole rather than with Pantoprazole to have one extra healed case at 8 weeks. For the meta-analysis as a whole, Gralnek et al6 found a risk difference of 4% and this yields an NNT of 25, the figure quoted by Schork. (See Box for further discussion.)

 Two different interpretations of the EXPO oesophageal ulcer data


It is impossible for us to observe the ulcers that were studied in the EXPO trial under both treatments. Each patient, was treated with either Esomeprazole or Pantoprazole. We can imagine what response would have been on either but we can only observe it on one. Table 1 and Table 2 have the same observable marginal probabilities of ulcer healing but different postulated joint ones.

  Not healed Healed Total
Pantoprazole Not healed        7.9        4.8       12.7
Healed        0.0      87.3       87.3
  Total        7.9      92.1     100.0

Table 1 Possible joint distribution of response (percentages) for the EXPO trial. Case where no patient would respond on Pantoprazole who did not on Esomeprazole

In the case of Table 1, no patient that would not have been healed by Esomeprazole could have been healed by Pantoprazole. In consequence the total number of patients who could have been healed are those who were healed with Esomeprazole, that is to say 92.1%. In the case of Table 2, all patients who were not healed with by Esomeprazole, that is to say 7.9%, could have been healed by Pantoprazole. In principle it becomes possible to heal all patients. Of course, intermediate situations are possible but all such tables have the same NNT of 21. The NNT cannot tell us which is true.

  Not healed Healed Total
Pantoprazole Not healed        0.0      12.7       12.7
Healed        7.9      79.4       87.3
  Total        7.9      92.1     100.0

Table 2 Possible joint distribution of response (percentages) for the EXPO trial. Case where all patients did not respond on Esomeprazole would respond on Pantoprazole


A number of points can be made taking this example. First, it is comparator-specific. Proton pump inhibitors as a class are highly effective and one would get quite a different figure if placebo rather than Pantoprazole had been used as the control for Esomeprazole. Second, the figure, of itself, does not tell us the scope for personalising medicine. It is quite compatible with the two extreme positions given in the Box. In the first case, every single patent who was helped by Pantoprazole would have been so by Esomeprazole. If there are no cost or tolerability advantages to the former the optimal policy would be to give all patient the latter. In the second case, every single patient who was not helped by Esomeprazole would have been helped by Pantoprazole. If a suitable means can be found of identifying such patients, all patients can be treated successfully. Third, healing is a process that takes time. The eight-week time-point is partly arbitrary. The careful analysis presented by Labenz et al7 shows healing rates rising with time with the Esomeprazole rate always above that for Pantoprazole. Perhaps with time, either would heal all ulcers, the difference between them being one of speed. Fourth, although it is not directly related to this discussion, it should be appreciated that a given drug can have many NNTs. The NNT will vary both according to the comparator, the outcome chosen, the cut point for any dichotomy or the follow-up8. (The original article proposing NNTs by Laupacis et al1 discusses a number of such caveats.) Indeed, for the EXPO study the risk difference at 4 weeks is 8.7 with an NNT of  rather than 21 for 8 weeks. This shows the importance of not mixing NNTs for different follow-ups in a meta-analysis.

An easy lie or a difficult truth?

There are no shortcuts to finding evidence for variation in response9. Dichotomising continuous measures not only has the capacity to exaggerate unimportant differences it is also inefficient and needlessly increases trial sizes10.

Rather than becoming simpler, ways that clinical trial are reported need to be more nuanced. In a previous blog I showed how a NNT of 10 for headache had been misinterpreted as meaning that only 1 in 10 benefitted from paracetamol. It is, or ought to be obvious, that in order to understand the extent to which patients respond to paracetamol you should study them more than once under treatment and under control. For example, a design could be employed in which each patient was treated for four headaches, twice with placebo and twice with paracetamol. This is an example of the n-of-1 trials than Schork calls for4. We hardly ever run these. Of course for some diseases they are not practical but where we can’t run them, we should not pretend to have identified what we can’t.

The role for n-of-1 trials is indeed there but not necessarily to personalise treatment. More careful analysis of response may simply reveal that this is less variable than supposed11. In some cases such trials may simply deliver the message that we need to do better for everybody12.

In his editorial of 2003 Smith referred to pharmacogenetics as providing ‘hopes that greater understanding of genetics will mean that we will be able to identify with a “simple genetic test” people who will respond to drugs and design drugs for individuals rather than populations.’ and added, ‘We have, however, been hearing this tune for a long time’2.

Smith’s complaint about an old tune is as true today as it was in 2003. However, the message for the pharmaceutical industry may simply be that we need better drugs not better diagnosis.


I am grateful to Andreas Laupacis and Jennifer Deevy for helpfully providing me with a copy of the 1988 paper.


  1. Laupacis A, Sackett DL, Roberts RS. An Assessment of Clinically Useful Measures of the Consequences of Treatment. New England Journal of Medicine 1988;318(26):1728-33.
  2. Smith R. The drugs don’t work. British Medical Journal 2003;327(7428).
  3. Wikipedia. Number needed to treat 2018 [Available from:
  4. Schork NJ. Personalized medicine: Time for one-person trials. Nature 2015;520(7549):609-11.
  5. Araujo A, Julious S, Senn S. Understanding Variation in Sets of N-of-1 Trials. PloS one 2016;11(12):e0167167.
  6. Gralnek IM, Dulai GS, Fennerty MB, et al. Esomeprazole versus other proton pump inhibitors in erosive esophagitis: a meta-analysis of randomized clinical trials. Clin Gastroenterol Hepatol 2006;4(12):1452-8.
  7. Labenz J, Armstrong D, Lauritsen K, et al. A randomized comparative study of esomeprazole 40 mg versus pantoprazole 40 mg for healing erosive oesophagitis: the EXPO study. Alimentary pharmacology & therapeutics 2005;21(6):739-46.
  8. Suissa S. Number needed to treat: enigmatic results for exacerbations in COPD. The European respiratory journal : official journal of the European Society for Clinical Respiratory Physiology 2015;45(4):875-8.
  9. Senn SJ. Mastering variation: variance components and personalised medicine. Statistics in Medicine 2016;35(7):966-77.
  10. Royston P, Altman DG, Sauerbrei W. Dichotomizing continuous predictors in multiple regression: a bad idea. Stat Med 2006;25(1):127-41.
  11. Churchward-Venne TA, Tieland M, Verdijk LB, et al. There are no nonresponders to resistance-type exercise training in older men and women. Journal of the American Medical Directors Association 2015;16(5):400-11.
  12. Senn SJ. Individual response to treatment: is it a valid assumption? BMJ 2004;329(7472):966-68.
Categories: personalized medicine, PhilStat/Med, S. Senn | 7 Comments

S. Senn: Evidence Based or Person-centred? A Statistical debate (Guest Post)


Stephen Senn
Head of  Competence Center
for Methodology and Statistics (CCMS)
Luxembourg Institute of Health
Twitter @stephensenn

Evidence Based or Person-centred? A statistical debate

It was hearing Stephen Mumford and Rani Lill Anjum (RLA) in January 2017 speaking at the Epistemology of Causal Inference in Pharmacology conference in Munich organised by Jürgen Landes, Barbara Osmani and Roland Poellinger, that inspired me to buy their book, Causation A Very Short Introduction[1]. Although I do not agree with all that is said in it and also could not pretend to understand all it says, I can recommend it highly as an interesting introduction to issues in causality, some of which will be familiar to statisticians but some not at all.

Since I have a long-standing interest in researching into ways of delivering personalised medicine, I was interested to see a reference on Twitter to a piece by RLA, Evidence based or person centered? An ontological debate, in which she claims that the choice between evidence based or person-centred medicine is ultimately ontological[2]. I don’t dispute that thinking about health care delivery in ontological terms might be interesting. However, I do dispute that there is any meaningful choice between evidence based medicine (EBM) and person centred healthcare (PCH). To suggest so is to commit a category mistake by suggesting that means are alternatives to ends.

In fact, EBM will be essential to delivering effective PCH, as I shall now explain. Continue reading

Categories: personalized medicine, RCTs, S. Senn | 7 Comments

Your (very own) personalized genomic prediction varies depending on who else was around?


personalized medicine roulette

As if I wasn’t skeptical enough about personalized predictions based on genomic signatures, Jeff Leek recently had a surprising post about a “A surprisingly tricky issue when using genomic signatures for personalized medicine“.  Leek (on his blog Simply Statistics) writes:

My student Prasad Patil has a really nice paper that just came out in Bioinformatics (preprint in case paywalled). The paper is about a surprisingly tricky normalization issue with genomic signatures. Genomic signatures are basically statistical/machine learning functions applied to the measurements for a set of genes to predict how long patients will survive, or how they will respond to therapy. The issue is that usually when building and applying these signatures, people normalize across samples in the training and testing set.

….it turns out that this one simple normalization problem can dramatically change the results of the predictions. In particular, we show that the predictions for the same patient, with the exact same data, can change dramatically if you just change the subpopulations of patients within the testing set.

Here’s an extract from the paper,”Test set bias affects reproducibility of gene signatures“:

Test set bias is a failure of reproducibility of a genomic signature. In other words, the same patient, with the same data and classification algorithm, may be assigned to different clinical groups. A similar failing resulted in the cancellation of clinical trials that used an irreproducible genomic signature to make chemotherapy decisions (Letter (2011)).

This is a reference to the Anil Potti case:

Letter, T. C. (2011). Duke Accepts Potti Resignation; Retraction Process Initiated with Nature Medicine.

But far from the Potti case being some particularly problematic example (see here and here), at least with respect to test set bias, this article makes it appear that test set bias is a threat to be expected much more generally. Going back to the abstract of the paper: Continue reading

Categories: Anil Potti, personalized medicine, Statistics | 10 Comments

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