Monte Carlo simulations and bioequivalence of antimicrobial drugs NATIONAL VETERINARY S C H O O L T O U L O U S E July 2005 Didier 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 : Pathogen A same exposure to an antibiotic does not produce the same effect on different strains of a given pathogen

PK variability Exposure

PD variability

Concentrations µg/mL Time (h) Link between PK and PD (PK/PD indice) Time above MIC MIC T>MIC

Concentrations µg/mL Time (h) Link between PK and PD MIC Cmax Cmax/MIC

Concentrations µg/mL Time (h) Link between PK and PD MIC AUIC (or AUC 24h /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.

Monte-Carlo simulation MIC distribution Exposure distribution Here, percentage of appropriately exposed animals is the percentage of animals with [AUIC≥ 125] Exposures Select 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=AUC 24 /MIC

Bioequivalence Bioequivalence basic assumption : Same effects Same concentrations profile (i.e. AUC, Cmax and Tmax )

Practically Exposure

Average bioequivalence Average (Reference) Exposure Average exposure.

Average Bioequivalence Exposure m Ref. m Test 1.25 m Ref 0.8 m Ref a priori equivalence range

Average BE does not guarantee the same distribution (in addition, here test and ref averages are different ) Exposure m Ref. m Test 1.25 m Ref 0.8 m Ref Equivalence range

Monte Carlo simulation 1 Same distribution for Clearance,volume of distribution and Ka Reference Test Average %F = 90% CV %F = 10% Average %F = 90% CV %F = 30%

Monte Carlo simulation 1 (same averages, different variances) 30% Reference Test

Monte Carlo simulation 2 Same MIC distribution as previously Reference GEN 1 Average %F = 74% CV %F = 10% Average %F =67% CV %F = 20% 35% GEN 2 Average %F =82% CV %F = 20%

Monte Carlo simulation 3 GEN 1 GEN 2 Same MIC distribution as previously GEN 1 GEN 2 Average %F = 90% CV %F = 10% Average %F = 73.0% CV %F = 20% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% auic % of animals with AUIC>auic

ex Vivo effect as a function of the PK/PD surrogate Aliabadi FS, Lees P, AJVR, 62, 12, Log cfu difference after 24 h of incubation vs AUIC

ex vivo effect vs AUIC Link between AUIC and bacterial count (cfu) Curve adapted from Aliabadi FS, Lees P, AJVR, 62, 12, 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 previously Generic 1 Generic 2 Expected %F = 90% CV %F = 10% Expected %F = 73.0% CV %F = 20% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% auic % of animals with AUIC>auic

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Log cfu/ml difference Percentage of animals Bacteriostatic effect Bactericidal effect eradication Efficacy expressed in terms of bacteriological action: the case of two generics GEN 1 GEN 2

Population bioequivalence may avoid these drawbacks Exposure =AUC 24 Select an animal at random in the target population Draw its exposure from the exposure distribution Draw a MIC from the MIC distribution AUC 24 MIC AUIC=AUC 24 /MIC Ref Test

Other bioequivalence definitions could be explored PK /PD bioequivalence 1 : Two formulations R and T are bioequivalent when AUIC(h) Reference Test % less than 5% Less demanding than pop BE

Other bioequivalence definitions could be explored Reference Test Less demanding than pop BE Exposure m Ref. m Test 1.11 m Ref 0.9 m Ref Equivalence range Average BE

Conclusions 1 zClassical 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