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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

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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

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

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

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

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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

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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

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Tree kinds of study T - R Equivalence study R - T Non inferiority Superiority R + T

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

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Superiority R + Values of T RR R + T Primary efficacy variable in clinical trials

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

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Equivalence Equivalence range Values of T R - RR R + Clinical effect

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Equivalence Values of T R - RR R + Clinical effect

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Equivalence Values of T R - RR R + Clinical effect

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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)

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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

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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)

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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

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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”

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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

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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

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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

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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

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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

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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

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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

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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

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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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