Monte Carlo simulations and bioequivalence of antimicrobial drugs

NATIONALVETERINARYS C H O O L

T O U L O U S E

July 2005Didier Concordet

Why to revisit bioequivalence criteria for antibiotic products ?

At the 44th ICAAC, it was reported that BE does not predict therapeutic equivalence (neutropenic murine thigh infection model) for several different antibiotics and that current criteria for BE deserve attention

(abstracts A-1877,1878,1879)

Two main sources of variability

A given dose administered (or offered )to different animals does not lead to the same exposure in every animals

PK : Antibiotic exposure

PD : PathogenA same exposure to an antibiotic does not produce the same effect on different strains of a given pathogen

PK variability

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PD variability

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MIC

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Time (h)

Link between PK and PD (PK/PD indice)

Time above MIC

MIC

T>MIC

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Link between PK and PD

MIC

Cmax

Cmax/MIC

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Link between PK and PD

MIC

AUIC (or AUC24h/MIC)

AUIC ≈ AUC/MIC

Schentag J and Tillotson, GS (1997). Chest. 112(6 suppl) :314S-319S

PK/PD indices

For a given MIC, an animal is assumed to be appropriately exposed as soon as:

AUIC≥ 60 to 125 h[T>CMI] ≥ 40 to 80%[Cmax/MIC] ≥ 10

These cut-off values are only indicative and should be selected based upon clinical considerations(bacteriological /clinical cure), to minimize the

likelihood of resistance etc.

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MIC%

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Monte-Carlo simulation

MIC distribution Exposure distribution

Here, percentage of appropriately exposed animals is the percentage of animals with [AUIC≥ 125]

ExposuresSelect randomly an animal in the target population i.e. draw its exposure from the exposure distribution

Draw randomly the MIC from the MIC distribution

AUIC=AUC24/MIC

Bioequivalence

Bioequivalence basic assumption :

Same effects

Same concentrations profile (i.e. AUC, Cmax and Tmax)

Practically

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Exposure

Average bioequivalence

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Average (Reference)

ExposureAverage exposure.

Average Bioequivalence

ExposuremRef. mTestmTest

1.25 mRef0.8 mRef

a priori equivalence range

Average BE does not guarantee the same distribution (in addition, here test and ref averages are different )

ExposuremRef.mTest

1.25 mRef0.8 mRef

Equivalence range

Monte Carlo simulation 1

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MIC

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Same distribution for Clearance,volume of distribution and KaReference Test

Average %F = 90%CV %F = 10%

Average %F = 90%CV %F = 30%

Monte Carlo simulation 1 (same averages, different variances)

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Test

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REF

GEN2

GEN1

Monte Carlo simulation 2Same MIC distribution as previouslyReference GEN 1

Average %F = 74%CV %F = 10%

Average %F =67%CV %F = 20%

35%

GEN 2Average %F =82%CV %F = 20%

Monte Carlo simulation 3

GEN 1

GEN 2

Same MIC distribution as previouslyGEN 1 GEN 2

Average %F = 90%CV %F = 10%

Average %F = 73.0%CV %F = 20%

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ex Vivo effect as a function of the PK/PD surrogate

Aliabadi FS, Lees P, AJVR, 62, 12, 2001.

Log cfu difference after 24 h of incubation vs AUIC

ex vivo effect vs AUIC

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Link between AUIC and bacterial count (cfu)

Curve adapted from Aliabadi FS, Lees P, AJVR, 62, 12, 2001.

Hypothesis: same relationship between AUIC and cfu count in ex vivo and in vivo conditions

Monte Carlo simulation 3

GEN 1

GEN 2

Same MIC distribution as previouslyGeneric 1 Generic 2

Expected %F = 90%CV %F = 10%

Expected %F = 73.0%CV %F = 20%

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-6 -5 -4 -3 -2 -1 0 1Log cfu/ml difference

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Bacteriostatic effect

Bactericidal effect

eradication

Efficacy expressed in terms of bacteriological action: the case of two generics

GEN 1GEN 2

Population bioequivalence may avoid these drawbacks

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MIC

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Exposure =AUC24Select an animal at random in the target populationDraw its exposure from the exposure distribution

Draw a MIC from the MIC distribution

AUC24MIC

AUIC=AUC24/MIC

RefTest

Other bioequivalence definitions could be explored

%10RT AUICAUICP

PK /PD bioequivalence 1 : Two formulations R and T are bioequivalent when

AUIC(h)

Reference

Test

0.05

10%

%10RAUIC

less than 5%

Less demanding than pop BE

Other bioequivalence definitions could be explored

Reference

Test

Less demanding than pop BE

ExposuremRef.mTest

1.11 mRef0.9 mRef

Equivalence range

Average BE

Conclusions 1

Classical average BE (PK criteria) does not guarantee that a pioneer and a generic products are able to cover the same percentage of subjects as shown by PK/PD simulations

Conclusions 2

• Pop BE that guarantee that the PK exposure distributions of the pioneer a generic products do not differ more than an a priori selected value

Such bioequivalence depends on the current MIC distribution and should be re-evaluated with regard to MIC distribution drift

Several solutions to be explored

• PK/PD BE using actually a PK/PD criteria consisting to guarantee that

• the percentage of patients with an exposure less than the quantile 10% of the exposure of the pioneer is less than a selected percentage • a selected quantile (e.g. 10%) does not differs by more than an a priori value having a therapeutic meaning