THE ODDS OF BENEFIT VERSUS NON-BENEFIT OF THERAPY ASSOCIATED WITH THE NUMBER NEEDED TO TREAT
Author(s)
Kamae I1, Aino H1, Yanagisawa S1, Nishimura K2, 1Kobe University, Kobe, Japan; 2Harvard University, Boston, MA, USA
OBJECTIVE: To investigate one of the most common misunderstandings on the number needed to treat (NNT) that implies 'certainly', not statistically, one adverse event can be prevented if the patients of the NNT size are treated with the new therapy: to correct the wrong interpretation, we developed the odds method for the NNT to describe the benefit vs. non-benefit of therapy. METHOD: The binomial distribution, B(n,p), was used to model and simulate the probabilistic outcomes of therapy with the NNT and the absolute risk reduction (ARR) assigned to the trial size n and the event probability p, respectively. In this model, r out of n patients can prevent the adverse event with the probability P(x=r) defined by B(n,p). We calculated the values of the P(x=r) according to any case for r=0, 1, 2,..., NNT as the size of NNT increases from one to larger numbers. Moreover, we developed the formula, as a function of NNT, to represent the odds of benefit vs. non-benefit of therapy, i.e., P(x=1)/P(x=0). RESULTS: The probabilities of non-benefit, i.e., P(x=0), were between .25 and .40 for any size of NNT. It suggested the likelihood of non-benefit of therapy cannot be negligible even if the NNTs of small size seem to be 'beneficial'. The numerical evaluation of the odds formula showed that the larger the sizes of NNT became, the smaller did the values of the odds. The progression over the NNTs of more than 5 was lower than 2.0, asymptotically converging to e-1 (i.e., about 1.7) as the size of NNT increases to infinity. CONCLUSIONS: Although the NNT is a quite useful benchmark of the benefit of therapy, we must interpret it as carefully as possible with the odds which indicates the 'relative' benefit associated with the non-benefit of therapy.
Conference/Value in Health Info
2002-05, ISPOR 2002, Arlington, VA, USA
Value in Health, Vol. 5, No. 3 (May/June 2002)
Code
PMI23
Topic
Methodological & Statistical Research
Topic Subcategory
Modeling and simulation
Disease
Multiple Diseases