SJS Harpenden: Competence and Equivalence 1 Competence and Equivalence Stephen Senn Department of Statistical Science UCL

SJS Harpenden: Competence and Equivalence 2 Outline Why this is important –Practical contexts in which the general problem occurs Particular emphasis on bioequivalence A simple model for competence and equivalence Conclusions

SJS Harpenden: Competence and Equivalence 3 Difference or Equivalence? Much of statistical theory is devoted to methods of proving that putative causes can effect outcomes –streptomycin on course of TB –smoking and lung cancer Sometimes we wish to prove non-effect –MMR does not increase risk of autism –generic is no different from brand-name drug

SJS Harpenden: Competence and Equivalence 4 4 Bioequivalence Studies These are special examples of equivalence studies in which we try to show that two formulations of a drug are equivalent by comparing AUC for the serum concentration over time. Uses: 1) generic versus brand name comparisons 2) development bridging 3) new formulations 4) interaction studies.

SJS Harpenden: Competence and Equivalence 5 When is a drug not a drug? Taylor et al, Lancet 2001 –581 samples, 27 drugs, 35 pharmacies, Lagos and Abuja, Nigeria –48% did not comply with pharmacopoeial limits Newton et al Lancet 2001 –104 samples of anti-malarial artesunate in Burma, Cambodia, Laos, Thailand and Vietnam –39 (38%) had no active ingredient

SJS Harpenden: Competence and Equivalence 6 5 Based on Sheiner (1992) Absorption, Concentration, Effect-Site Concentration Response Dose Equality here implies equality of all response

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8 8 The Basic Position (Testing View) H 0A : (    ) (Exact equality) 0 H 0B : (     H 1   (Diff. allowed for in power calculation) H 1B H 1A H 1 = H 1A  H 1B H 0 = H 0A  H 0B (  ) 

SJS Harpenden: Competence and Equivalence 9 Critical Values for 3 Different Approaches to Bioequivalence  {(k-  )/SE}-  {(-k-  )/SE}

SJS Harpenden: Competence and Equivalence 10 Swatch and Rolex There is more than one quality of a pharmaceutical As soon as you can no longer use serum concentration there is a problem Pharmacodynamics is multi-dimensional Does this not imply that equality has to be proved multi-dimensionally?

SJS Harpenden: Competence and Equivalence 11 How Should Equivalence Trials in Asthma be Designed? The assumption behind the question is that this is possible. I am not convinced that it is. Conventional equivalence trials work like this. Route of absorption 1 Route of absorption 2 Circulation Other sites Equality here implies equality for target and all other sites

SJS Harpenden: Competence and Equivalence 12 Placebo and the 3 doses of the new formulation

SJS Harpenden: Competence and Equivalence 13 With the 3 doses of reference formulation added

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SJS Harpenden: Competence and Equivalence 15 Other Examples Drug interaction issues –no food interaction –no sex interaction Model adequacy issues –no carry-over Safety issues –Breast implants are safe? –Eating beef is safe? –Accidents do not increase risk of MS?

SJS Harpenden: Competence and Equivalence 16 Blinding and Equivalence Running a double blind trial does not protect you against a conclusion of equivalence You do not need to know the treatment code to bias results towards equivalence

SJS Harpenden: Competence and Equivalence 17 The Unscrupulous Pharmacokineticist Take the 12 test tubes for day one for a given volunteer –hour 1,2…12 Take the 12 test tubes for day two for the same volunteer –hour 1,2…12 Mix each pair (by hour) together Divide them into two Et voila –Perfect equivalence without having to unblind

SJS Harpenden: Competence and Equivalence 18 Fanciful? Pharmaceutical companies commonly prosecute cheating doctors Reason –Trial fails to show any effect whereas others do Explanation –The trial never took place –The data have been invented –This will produce a conclusion of equivalence

SJS Harpenden: Competence and Equivalence 19 Fairness and Competence Experiment is fair if treatments are handled equivalently – in all aspects except those that form the essence (definition) of the treatment –cannot be determined by looking at outcomes Competence is the ability to detect differences –can only partly be determined on external grounds –can be established if difference is detected

SJS Harpenden: Competence and Equivalence 20 A Model for Competence

SJS Harpenden: Competence and Equivalence 21 Interpretation of These Parameters  and 1-  reflect the ‘precision’ of our experiments –analogous to type I and II error rates –can be reduced by more and more precise experiments Joint effect of  and  represents factors beyond our control

SJS Harpenden: Competence and Equivalence 22 Notes Under this formulation of the likelihoods it is irrelevant as to whether the trial is competent if the treatments are equivalent. We could require the combination EC as impossible We require  > , but this is a linguistic convention

SJS Harpenden: Competence and Equivalence 23 For those who like formulae

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SJS Harpenden: Competence and Equivalence 26 Consequences Assymetry between concluding equivalance and difference –The former is inherently more problematic Not just a matter of reformulating the problem Conditional on an assumption of competence we can conclude equivalence –However if we have any doubts regarding competence these increase by failing to find a difference

SJS Harpenden: Competence and Equivalence 27 In summary “Equivalence is different”

28 A Koan If not Zen then Senn “The jealous husband fears that his wife is unfaithful and determines to try and set his mind at ease. He hires a private detective to investigate her. Several weeks and large sums of money later the detective issues his report. He has followed the wife for weeks, investigated her phone calls and observed her every movement. In an extensive report he explains that there is no evidence whatsoever that she is having an affair. The husband is much relieved. His prior doubt has been changed into posterior belief. He goes to bed with a light heart for the first time in months. At three o' clock in the morning he wakes with a frightening thought....Suppose his wife is having an affair with the detective?” From Chapter 4 of Dicing with Death, Cambridge University Press 2003 (to appear)