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1 Exercise 14 Dose titration and selection of a therapeutic dose for a new quinolone in pigs

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2 Objectives of the exercise 1.To y understand the limits of the classical dose titration to select a dose. 2.To understand how to determine a dose for an antibiotics using PK/PD concepts 3.To analyse qualitative clinical results using a logistic model to compute a probability of cure (POC) 4.From a dose titration trial, to be able to establish a breakpoint value for the selected PK/PD index that guarantee a POC of 90% in pigs. 5.To understand the concept of Target Attainement Rate ( TAR) 6.To select a dosage regimen to achieve a TAR of 90% for the established PK/PD index value in the pigs population 7.To perform a sensitivity analysis to identify the most critical factors of variability (PK or PD) influencing the TAR.

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3 Designs for dose titration and the determination of an effective dose

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4 The simple parallel design

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5 The parallel design The null hypothesis –placebo = D1 = D2 = D3 The statistical linear model –Yj = wj + j Conclusion –D3 = D2 > D1 > Placebo Placebo Dose Response 123 * * NS Selected dose

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6 The parallel design or Dose (log) Response Dose (log) Response Average population Dose (log) Response

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7 An alternative to the classical dose titration for the selection of a rational dosage regimens for an antibiotic is the so-called PK/PD approach

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8 Three PK/PD indices are used to predict clinical and bacteriological outcomes For quinolone, – AUC/MIC is the appropriate index –Its numerical values (or breakpoint value) that is predictive of a good clinical efficacy is typically of 125h; it is equivalent to say that the goal is to find a dose achieving an avrage plasma concentration over 24h that is 5 times higher than the targeted MIC.

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9 The first task of the project we are developing a new antibiotic for metaphylaxis (control) in pigs, The first task will be to establish, experimentaly, the breakpoint value of AUC/MIC that is predictive of a probability of cure rate (POC) of 90% in pig.

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10 Step 1: Establishing the breakpoint value of AUC/MIC for the new antibiotic that is predictive of a probability of cure rate (POC) of 90% in pig

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11 Design of the trial A classical parallel design with 4 dose levels (Dose0, Dose1, Dose 2 & Dose3) An infectious challenge with a pathogen having a given MIC blood samples should be collected to establish individual AUCs Clinical endpoint : cure or not cure

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12 Data analysis Possibility to establish a conventional dose titration Model the relationship between the measured AUCs scaled by the MIC of the pathogen actually used for the infectious challenge and the porobability of cure (POC); – i.e to consider AUC/MIC as generic explicative variable and the POC as the dependent variable;

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13 Individual results obtained in 40 pigs during a dose-titration trial.

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14 Logistic regression When an all-or-none effect is observed due to the selected binary endpoint (cured or not cured for antibiotics), the concentration-response curve is described by a quantal dose-response curve

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15 Logistic regression This logistic model represents the probability at which a concentration (or AUC/MIC) of a drug produces the all-or-none effect

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16 Logistic vs. Emax model Despite the fact that the graph of a S- shaped model looks like the one of an Emax model, a quantal dose-response curve differs of the Emax model because it does not relate dose to intensity of effect but to the probability an effect.

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17 A logistic model where POC is the probability of cure (from 0 to 1) θ1 is a parameter for baseline (here a placebo effect) θ2 is an index of sensitivity (a slope). X is the independent variable i.e. AUC/MIC ratio any other quantitative index predicting drug efficacy can be used as X

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18 A logistic model If θ2 equal 0, the response is independent of X and the POC correspond to the placebo effect

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19 A logistic model For a logistiv curve, the equivalent of the EC50 (or ED50) is named EL50; –The EL50 can be estimated by the ratio –θ1/θ2, it is now the median effective level of the independent variable (e.g. dose, AUC/MIC..) for which 50% of the subjects are cure, The slope of the curve now represents the dispersion (variance) of the threshold in a population.

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20 Fit data with the following equation the placebo effect is given by 1/(1+e a ), the POC 50% by an AUC/MIC ratio equal to a/b the POC 90% by a AUC/MIC ratio equal to (a+2.1972)/b.

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21 Enter your data and code it

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22 Build a user model of the logistic model MODEL remark ****************************************************** remark Developer:PL Toutain remark Model Date:04-01-2011 remark Model Version:1.0 remark ****************************************************** remark remark - define model-specific commands COMMANDS NFUNCTIONS 1 NPARAMETERS 2 PNAMES 'a', 'b' NSECONDARY 3 SNAMES 'Placebo', 'POC50', 'POC90' END remark - define temporary variables TEMPORARY index=x END remark - define algebraic functions FUNCTION 1 F= 1/(1+exp(a-b*x)) END remark - define any secondary parameters SECONDARY Placebo=1/(1+exp(a)) POC50=a/b POC90=(a+2.1972)/b END remark - end of model EOM

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23 The command block COMMANDS NFUNCTIONS 1 NPARAMETERS 2 PNAMES 'a', 'b' NSECONDARY 3 SNAMES 'Placebo', 'POC50', 'POC90' END

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24 The TEMPORARY block TEMPORARY index=x END

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25 The FUNCTION block FUNCTION 1 F= 1/(1+exp(a-b*x)) END

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26 The SECONDARY block SECONDARY Placebo=1/(1+exp(a)) POC50=a/b POC90=(a+2.1972)/b END

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27 Run the model

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28 Estimated parameters

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29 Conclusion of the first step The placebo effect was estimated to 30% and the POC90% (our breakpoint value) to 109.77 rounded to 110h It should be stressed that what is determined at this step is not a dose for pivotal clinical trials but a target value for a PK/PD surrogate that can be used for predicting clinical efficacy

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30 Step 2: determination of a dose to achieved a Target Attainement Rate of 90% for the breakpoint value of the PK/PD index

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31 The selection of a dosage regimen The selection of a final dosage regimen intended for use across a population of animals needs to account for interanimal variability. We expect to find a dosage regimen able to achieve a TAR of 90% for the breakpoint value of the PK/PD index as determined at the preceeding step (110h) – i.e. to find the dose for which the breakpoint value of the PK/PD index is actually achieved in at least 90% of the pigs in a population. –For that we have to take into account the different factors of variabilty able to influence final dose

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32 Equation giving the daily dose Dose(per day) = the daily maintenance dose at steady state; CL = the plasma clearance (in mL/hour); –It is because the AUC/MIC target is expressed in hours per 24h that the clearance should be expressed per hour and not per day to compute a daily dose with this equation (see attached reprint by Toutain et al explaining why) (AUC/MIC)target = the AUC/MIC breakpoint value to achieve (110 h in our example) MIC= a given MIC as MIC90 or any other MIC. fu = is the free fraction = the fraction of unbound drug in the plasma or serum (where values range from 0 to 1). For the sake of simplicity fu has been set at a constant value of 1 in this tutorial F = the absolute bioavailability (where values range from 0 to 1). Equation given the dose for a given AUC/MIC breakpoint ; here AUC/MIC was established in vivo and no correction is required but if you pick up the BP value of the PKPD indice from the litterature, you have to consider fu.

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33 Solve the equation With point estimates With distribution using MCS

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34 Stochastic determination of a dose to achieve a TAR of 90% for the PK/PD index ;

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35 Build the excel sheet

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36 Numerical values to use for simulation CL values was assumed to be log-normally distributed with a geometric mean of 60 ml/kg/h and a GSD of 1.1, Bioavailability (F ) was assumed to conform to a uniform distribution i.e. all values had the same occurrence probability in the range of 0.3 to 0.7. MIC distribution had 5 classes (0.1µg/mL with P=0.1; 0.2µg/m with P=0.2; 0.5µg/mL with P=0.3; 1µg/ml with P=0.3 and 2µg/ml with P=0.2)

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37 Results

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38 The MCS and the sensitivity analysis A major advantage of the PK/PD framework is that it permits the separate evaluation of the principal sources of PK and PD variability. PK variability reflects interanimal differences for plasma clearance, bioavailability… while PD variability is mainly associated to differences in microbial susceptibility ( MICs of the pathogen).

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39 Our questionment For the dosage regimen previously calculated, it may be of interest to identify the impact of the various model factors on the final dose. Why the dose is so high? – is it due to the clearance variability (and I can do nothing) or the erratic bioavailability (I can improve my formulation) or to the MICs (and I can recommend or not susceptibility testing)

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40 The MCS and the sensitivity analysis Sensitivity analysis is the study of how the variability in the model output (the computed dose) can be apportioned, quantitatively, to different sources of variation of the model input (here CL, F and MIC distribution).

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41 Sensitivity chart

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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.

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.

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