The equivalence trial

Didier Concordetd.concordet@envt.fr

NATIONALVETERINARYS 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 animalsSampling

Population of animals

Effect of sampling

Sample of animals

XR = 16.2

Treatment effect

XT = 17.8

A two-steps method

Sample of animals

InferencePopulation of animals

Effect of inference

XR = 16.2

Observed on the samples

XT = 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 samplingMinimize 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 - TNon inferiority

Superiority R + T

Non inferiority

R - Values of TR

R - T

Unacceptable for primary efficacy variable in clinical trialDoes not prove that the treatment T works

Superiority

R + Values of TR

R + T

Primary efficacy variable in clinical trials

Equivalence

Equivalence range

Values of T

R - RR +

Does not prove that the treatment T worksFor secondary efficacy variables in clinical trials

Equivalence

Equivalence range

Values of TR -

RR +

Cli

nica

l eff

ect

Equivalence

Values of TR -

RR +

Cli

nica

l eff

ect

Equivalence

Values of TR -

R R +

Cli

nica

l eff

ect

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 1REFERENCENew TRT

New TRT< RefP<0.001

Clinical trial 2

Cure rate = 90%N = 2000

REFERENCE

Cure rate = 96%N = 1000

New TRT

New TRT < RefP<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 = 39N = 100SD = 1

REFERENCE

X = 37N = 100SD = 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 = 40N = 90SD = 1

REFERENCE

X = 42N = 50SD = 1

New TRT

New TRT< RefP<0.001

Clinical trial 2

X = 30N = 10SD = 1

REFERENCE

X = 32N = 50SD = 1

New TRT

New TRT < RefP<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 dogsRef Test

Mean 15.4SD 2.4

20.02.6

Student t-test

P = 0.23N 3 3

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 dogsRef Test Student t-test

Mean 16.0SD 2.4

18.12.6

N 15 15 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 dogsRef Test Student t-test

Mean 16.0SD 4.9

18.15.1

N 15 15 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 sizeSmall variability

Small sample sizeLarge 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 H0

= risk to declare not equivalent formulations that are equivalent= risk for drug companies

Not important from a regulatory point of viewThe 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 thatT and R are close

T - R bioequivalence

Close in an absolute way

Close in a relative way

bioequivalence 21 R

T

equivalence range (to be discussed)

T - R < or

T - R

bioinequivalence

bioinequivalenceR

T

R

T

21 or

Control the consumer risk

A test controls the risk to wrongly choose the H1 hypothesis

Consumer risk : the risk to wrongly conclude to bioequivalence

BioequivalenceH1

Equivalence range

T - R

R

T

Possible values of

BioinequivalenceH0

BioinequivalenceH0

Hypotheses of a bioequivalence study

H1 : T - R bioequivalence

Additive hypotheses

Multiplicative hypotheses

bioequivalence

equivalence range

H0 :T - R < or T - R bioinequivalence

bioinequivalence

R

T

R

T

21 or H0 :

21 R

T

H1 :