# The equivalence trial Didier Concordet NATIONAL VETERINARY S C H O O L T O U L O U S E.

## Presentation on theme: "The equivalence trial Didier Concordet NATIONAL VETERINARY S C H O O L T O U L O U S E."— Presentation transcript:

The equivalence trial Didier Concordet d.concordet@envt.fr NATIONAL VETERINARY S C H O O L T O U L O U S E

Comparison of two treatments Population of animals  R = 17.8 Treatment effect  T = 16.8 Aim of all trials : to compare treatments on the population of individuals Impossible in practice

A two-steps method Sample of animals Sampling Population of animals

Effect of sampling Sample of animals X R = 16.2 Treatment effect X T = 17.8

A two-steps method Sample of animals Inference Population of animals

Effect of inference X R = 16.2 Observed on the samples X T = 17.8 Truth in the population  R = 17.8  T = 16.8 New Treatment T > Ref Ref > New Treatment T Lead to a wrong conclusion

A good trial Minimize the risk of bias in sampling Minimize the risk of a wrong conclusion in inference - All Randomised Study Animals - Per Protocol Set of Study Animals - Response Variable - Experimental (study) design - Consumer Risk - Producer Risk - Relevant difference

Tree kinds of study     T -  R    Equivalence study  R -     T Non inferiority Superiority  R +     T

Non inferiority  R -   Values of  T RR  R -     T Unacceptable for primary efficacy variable in clinical trial Does not prove that the treatment T works

Superiority  R +   Values of  T RR  R +     T Primary efficacy variable in clinical trials

Equivalence Equivalence range Values of  T  R -   RR  R +   Does not prove that the treatment T works For secondary efficacy variables in clinical trials

Equivalence Equivalence range Values of  T  R -   RR  R +   Clinical effect

Equivalence Values of  T  R -   RR  R +   Clinical effect

Equivalence Values of  T  R -   RR  R +   Clinical effect

Even with a good question, a poor design leads to poor conclusions Superiority clinical trials Cure rate = 83% N = 2400 REFERENCE Cure rate = 79% N = 2100 New TRT Reference < New TRT ( P<0.001)

Even with a good question, a poor design leads to poor conclusions Clinical trial 1 REFERENCE New TRT New TRT< Ref P<0.001 Clinical trial 2 Cure rate = 90% N = 2000 REFERENCE Cure rate = 96% N = 1000 New TRT New TRT < Ref P<0.001 Conclusion : Reference > New TRT Superiority trials Cure rate = 50% N = 400 Cure rate = 63% N = 1100

Even with a good question, a poor design leads to poor conclusions Superiority clinical trials X = 39 N = 100 SD = 1 REFERENCE X = 37 N = 100 SD = 1 New TRT Reference < New TRT ( P<0.001)

Even with a good question, a poor design leads to poor conclusions Clinical trial 1 X = 40 N = 90 SD = 1 REFERENCE X = 42 N = 50 SD = 1 New TRT New TRT< Ref P<0.001 Clinical trial 2 X = 30 N = 10 SD = 1 REFERENCE X = 32 N = 50 SD = 1 New TRT New TRT < Ref P<0.001 Conclusion : Reference > New TRT Superiority trials

Usual statistical tests are not intended to answer to useful questions Efficacy variable on two groups of dogs Ref Test Mean 15.4 SD 2.4 20.0 2.6 Student t-test P = 0.23 N33 In the population  R = 14.5 ;  T = 19.7 this difference is clinically important Conclusion : “EQUIVALENCE”

Comparison of two treatments Efficacy variable on two groups of dogs Ref Test Student t-test Mean 16.0 SD 2.4 18.1 2.6 N15 P = 0.03 In the population  R = 16.8 ;  T = 17.8 This difference is not clinically important Conclusion : NO EQUIVALENCE Study 1

Comparison of two formulations Efficacy variable on two groups of dogs Ref Test Student t-test Mean 16.0 SD 4.9 18.1 5.1 N15 P = 0.26 This difference is not clinically important Conclusion : EQUIVALENCE Study 2 In the population  R = 16.8 ;  T = 17.8

Consequences Large samples size Small variability Small sample size Large variability "Equivalence" Penalty for companies to show equivalence An ill-posed problem that encourages poor trials A bad answer to a wrong question

A wrong question ? H 0 :  T =  R Classical hypotheses for student t-test H 1 :  T   R Treatments are equivalent  T = population mean for test treatment  R = population mean for reference treatment Too restrictive and not relevant  T and  R are close Treatments are not equivalent

A bad answer ? H 0 :  T =  R Classical test of null hypothesis (student t-test) H 1 :  T   R The controlled risk  = risk to wrongly reject H 0 = risk to declare not equivalent formulations that are equivalent = risk for drug companies Not important from a regulatory point of view The consumer risk is uncontrolled Treatments are equivalent Treatments are not equivalent

Bioequivalence : objectives Check that  T and  R are close Control the consumer risk risk to declare equivalent treatments that are not with regard to clinical relevance

Check that  T and  R are close     T -  R    bioequivalence Close in an absolute way Close in a relative way bioequivalence      equivalence range (to be discussed)  T -  R <   or    T -  R bioinequivalence

Control the consumer risk A test controls the risk to wrongly choose the H 1 hypothesis Consumer risk : the risk to wrongly conclude to bioequivalence Bioequivalence H 1   Equivalence range  T -  R Possible values of Bioinequivalence H 0 Bioinequivalence H 0

Hypotheses of a bioequivalence study H 1 :     T -  R    bioequivalence Additive hypotheses Multiplicative hypotheses bioequivalence      equivalence range H 0 :  T -  R <   or    T -  R bioinequivalence H 0 : H 1 :

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