Number Needed to Torment…

There is a lot about math that gets in the way of Evidence-based Medicine.  Arguably the most useful methods to express some of the results of clinical research data – the Number Needed to Treat and the Likelihood Ratio – are somehow seen as arcane and complex mathematical problems for many medical learners.  I'm told (usually by my wife, but also by others) that I have lost perspective from having taught this material for so long, but I think it is a bigger problem.  In his article "Physician numeracy as the basis for an evidence-based medicine curriculum," Rao also notes this problem – there are a set of medical learners that are just not very good with numbers.  And it's not just the weirder aspects of probability that confound learners…when we're calculating NNT and LR, we're only talking about algebra.  But more than the calculations, I don't think we spend enough time talking about what we are using the numbers for.  There's such an emphasis on just knowing the formulas for the test, we don't spend time on the "proofs" – the arguments for why these numbers are used.  The students don't (or can't) spend time trying to understand them, and the faculty eventually give up trying to teach them. 

However, I have also encountered examples of the opposite problem.  One of the more frequent arguments I get as a course director is about rounding of these numbers – usually as a result of an incorrect answer on an assessment.  Math majors can circumvent some of the sensitivity/specificity/predictive value calculation problems I give them using estimation techniques that were certainly not part of my math education.  I once had a resident publically evince his frustration with the Bayesian approach to diagnostic testing using likelihood ratios and applying them to estimates of pre-test probability.  We were discussing methods of determining a patient's pretest probability ranging from population prevalence to probability developed by a clinical decision rule to "clinical impression" (categorized as likely (80-90% pre-test probability), unlikely (10-20% pretest probability, and intermediate (50% pretest probability).  The idea that we would calculate a likelihood ratio to even 1 significant figure and then apply it to a "clinical impression" guesstimate using a completely different order of magnitude of pre-test probability was too much for this computer-science-and-mathematics-trained family medicine resident.  

I believe there is a middle ground here, but as with most middle grounds, it's not well defined and can feel a little too much like compromise.  To use evidence-based medicine best, we require a deeper understanding of the meaning and derivation of the numbers combined with some common sense about the application of the numbers.  We need a comfort with numbers (both algebraic and statistical) so that we can speak the language of the science that is an essential part of our discipline.  We should recognize when the details of the numbers "don't add up" and the circumstances in which those details are improtant.  We should also recognize when the numbers are being used simply for illustration to aid in decision making.  Math is a primary tool in evidence-based medicine, but the focus is to make better decisions for our patients.  Sometimes the details distract us from this goal.