Development and evaluation of optimal designs for population pharmacokinetic and pharmacokinetic-pharmacodynamic studies of anti-malarial drugs

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1 Development optimal designs for -pharmacodynamic of Development of SSAI Victorian branch meeting Centre for Molecular, Environmental, Genetic Analytic Epidemiology, Melbourne School of Population Health, The University of Melbourne 26 June PD Conclusions

2 PhD submission Development of -PD Conclusions

3 What is malaria? Malaria is a parasitic infection transmitted to humans by the bite of an infected female Anopheles mosquito Development of Four species of Plasmodium malaria parasites infect humans P. falciparum causes almost all severe diseases deaths of human malaria -PD Conclusions

4 Where malaria occurs Development of -PD Conclusions

5 Current treatment The World Health Organization recommends artemisinin-based combination therapy (ACT) as first line treatment for uncomplicated falciparum malaria in all malaria endemic areas [12]. ACT consists of: an artemisinin-derivative (short-lived, highly effective) a partner drug (less potent, longer-lived) Drugs of focus: artemisinin-derivative: oral artesunate partner drugs: mefloquine (given with artesunate), lumefantrine (artemether), piperaquine (dihydroartemisinin) amodiaquine (artesunate) Development of -PD Conclusions

6 Population PK PK-PD Effective treatment of malaria requires drug concentrations over time (the or PK profile) to be sufficient to kill all of the parasites (pharmacodynamic or PD profile) Population PK aim to characterise the processes of drug absorption, distribution elimination for an intended target, how much these processes vary across patients in that (via nonlinear mixed-effects models). Population PK-PD go a step further by relating the drug concentration to the drug effect (again via nonlinear mixed-effects models). Development of -PD Conclusions

7 Population s Concentration (ng/ml) Population PK model example Development of -PD Conclusions Time (h)

8 Population s Concentration (ng/ml) Population PK model example Development of -PD Conclusions Time (h)

9 Population s Concentration (ng/ml) Population PK model example Development of -PD Conclusions Time (h)

10 Population s Concentration (ng/ml) Population PK model example Development of -PD Conclusions Time (h)

11 Population s Concentration (ng/ml) Population PK model example Development of -PD Conclusions Time (h)

12 Population s-pharmacodynamics Development of Kill rate Parasites increase No change Drug Concentration Parasites decrease log10 parasite count log10 parasite count 12 DHA concentration MQ concentration 10 Detection limit of parasites day Concentration (ng/ml) -PD Conclusions

13 Nonlinear mixed-effects models y i = f (θ i, t i ) + ε i θ i = θ exp(η i ) η i N(0, Ω) ε i N(0, σ 2 ) Development of L i (θ, Ω, σ 2 ) = p(y i θ, Ω, σ 2 ) = N L(θ, Ω, σ 2 ) = L i (θ, Ω, σ 2 ) i=1 p(y i θ, η i, σ 2 )p(η i Ω)dη -PD Conclusions f (θ + η i, ξ) f (θ, ξ) + f (θ, ξ) θ θ η i, θ = log(θ)

14 The role of PK-PD Results from these can be used to optimise dosing regimens identify causes of treatment failure determine risk of toxicity identify patient-specific characteristics that help optimise the dose for each person However... The parameter estimates need to be precise, which leads back to study design... Development of -PD Conclusions

15 Design of The following three factors of design will determine the precision of the parameter estimates: the number of patients, the number of blood samples per patient, when the blood samples are taken. Determining these factors requires the consideration of: the structural form of the PK or PK-PD models, logistical constraints (e.g. clinical workload), ethical constraints (e.g. taking blood from children). Development of -PD Conclusions

16 Population PK PK-PD of Currently, PK-PD of anti-malarial drugs are primarily based on: logistics - outpatient cohorts, clinical workload, etc ethical issues - invasiveness of taking blood passing knowledge of the PK or PK-PD profiles How the structural model(s) is fit to the data is not considered formally, which could lead to insufficient designs (imprecise estimates, difficulty estimating parameters, etc). Development of -PD Conclusions

17 Optimal design Over the past two decades, optimal design methodology has been developed for PK-PD [7, 9]. The idea: Determines a design (analytically) that will yield precise estimates of model parameters from within the practical constraints of sampling patients. Development of -PD Conclusions

18 Optimal design This is the design that maximises the determinant of the Fisher information matrix. So for some design (sampling schedule) ξ for individual i, the Fisher information matrix (FIM) is M F (Ψ, ξ i ) = ( f (θ,ξ) θ the FIM is M F (Ψ, Ξ) = θv 1 f (θ,ξ) 1 0 θ θ 0 2 tr ( V N M F (Ψ, ξ i ), i=1 1 V λ ) V 1 V λ ) Development of -PD Conclusions

19 Optimal design User specifies: Structural PK model(s) parameter values Initial sampling scheme any restrictions on the sampling schedule Development of Optimization algorithm: Output: Searches for a design within the specified restrictions on the sampling schedule that will yield the smallest stard errors of the model parameters Final design with expected stard errrors of the model parameters -PD Conclusions

20 The aims of this work were to: 1. Use optimal design methods to determine evaluate sets of designs for of oral artesunate (AS) the partner drugs that are used in the most widely used ACTs. 2. Use optimal design methodology to determine evaluate designs for -PD of oral artesunate. Development of -PD Conclusions

21 Research conducted To achieve the aims of this research, three major projects were undertaken: 1. The development of oral AS. 2. The development of the partner drugs co-administered with artemisinin derivatives (MQ, LF, PQ AQ). 3. The development -PD of AS. Development of -PD Conclusions

22 Methods: of AS 1. Appropriate models parameter values were determinied by data analyses (non-pregnant adults, children) or from the literature (pregnant women). 2. Sampling constraints: 4 samples for adults, 3 samples for children; at least 15 minutes between consecutive samples; 60 patients (determined from a questionnare administered to active malaria researchers). 3. Optimal designs were determined in POPT [3] based on the models constraints from 1 2 above. 4. The derived designs were evaluated via a simulation-estimation procedure that was automated in NONMEM [2]. 5. For all optimal sampling times, sampling windows (time intervals that include the optimal time) were derived in POPT. Development of -PD Conclusions

23 Results: of AS [5] Development of -PD Conclusions

24 Methods: for the partner drugs 1. Appropriate models parameter values were determined from the literature. 2. Sampling constraints: 5 samples per patient (two sampling schedules were specified), one sample fixed on the seventh day of treatment [11], 100 patients 3. Optimal designs were determined in POPT [3] based on the models constraints from 1 2 above. 4. The derived designs were evaluated via a simulation-estimation procedure that was automated in NONMEM [2]. 5. For all optimal sampling times, sampling windows were derived in POPT. Development of -PD Conclusions

25 Results: of the partner drugs [6] Concentration (ng/ml) Mefloquine 8.3 mg/kg at 0, 24, 48 h (first three days) Group 1 Group Time (h) Concentration (ng/ml) Mefloquine 8.3 mg/kg at 0, 24, 48 h (entire follow up) Non pregnant adults, Ashley et al. Non pregnant adults (SR), Svensson et al. Non pregnant adults (RS), Svensson et al. Pregnant women, Nabangchang et al. Children (split dose), Simpson et al. Children (single dose), Simpson et al Time (h) Development of Concentration (ng/ml) Mefloquine 15 mg/kg at 24 h, 10 mg/kg at 48 h (first three days) Group 1 Group 2 Concentration (ng/ml) Mefloquine 15 mg/kg at 24 h, 10 mg/kg at 48 h (entire follow up) Non pregnant adults, Ashley et al. Non pregnant adults (SR), Svensson et al. Non pregnant adults (RS), Svensson et al. Pregnant women, Nabangchang et al. Children (split dose), Simpson et al. Children (single dose), Simpson et al. -PD Conclusions Time (h) Time (h)

26 Results: of the partner drugs [6] Concentration (ng/ml) Concentration (ng/ml) Group 1 Group 2 Lumefantrine (first three days) Group 1 Group 2 Time (h) Piperaquine (first three days) Concentration (ng/ml) Concentration (ng/ml) Lumefantrine (entire follow up) Time (h) Piperaquine (entire follow up) Non pregnant adults, Ezzet et al. Pregnant women, Tarning et al. Children, Hietala et al. Non pregnant adults, Tarning et al. Non pregnant adults, Hung et al. Pregnant women, based on Tarning et al. Children, Hung et al. Development of -PD Time (h) Desethylamodiaquine (first three days) Time (h) Desethylamodiaquine (entire follow up) Conclusions Concentration (ng/ml) Group 1 Group 2 Concentration (ng/ml) Children, Stepniewska et al. Children, Hietala et al. Non pregnant adults, based on Jullien et al. Pregnant post partum women, Tarning et al. (unpublished) Pregnant post partum women, Tarning et al. (unpublished) Time (h) Time (h)

27 Methods: -PD of AS The following designs were derived evaluated: (i) a robust T-optimal design for that aim to employ the parasite clearance estimator [4], which is based on the log parasitema-time course for an individual (PD only), (ii) a composite design for a -PD study of AS in non-pregnant adults using a mechanistic discrete-time PK-PD model proposed by Saralamba et al. [10]. Development of -PD Conclusions

28 Methods (i): designs for the parasite clearance estimator The parasite clearance estimator (PCE) is a recently established tool that calculates the slope of the log (base e) parasitaemia-time relationship for an individual patient, accounting for any initial delay (or lag) in anti-malarial effect [4]. Development of -PD Conclusions

29 Methods (i): designs for the parasite clearance estimator Design: requires blood sampling that is frequent enough to characterise individual parasite-time profiles adequately (e.g. detect lag) but also provides means for model discrimination (e.g. between quadratic cubic profiles). A robust T-optimal design was derived, which determines a sampling schedule that provides means for model discrimination, has the additional benefit of not assuming a true parasite-time profile. Constraints: 6 samples over the first 48 hours of treatment (suggested minimum for exploration of different profiles, e.g. linear, quadratic, cubic). Also, the designs were based on quadratic cubic profiles. Development of -PD Conclusions

30 Results: T-optimal design for the PCE Lag phase* Tail* Development of Log parasitemia *As defined in Flegg et al. -PD Conclusions Time (h)

31 Results: T-optimal design for the PCE Table: Evaluation of the T-optimal design for estimation of the parasite clearance estimator Percentage of runs where the appropriate method to calculate K was selected True model Linear 97 Quadratic 98 Cubic 100 Development of -PD Conclusions

32 Methods results (ii): design for a PK-PD study of AS in non-pregnant adults The model: Development of P i (t + 1, a + 1) = P i (t, a) exp ( β i,j (t)) for a = 1, 2,..., 47 P i (t + 1, 1) = PMF P i (t, 48) exp ( β i,j (t)) β i,j (t) = ( ) 100 α i ln 100 E i,j (C i (t)) E i,j (C i (t)) = E maxi,j C i (t) γ i,j C i (t) γ i,j + C50 i,j γ i,j. -PD Conclusions

33 Methods results (ii): design for a PK-PD study of AS in non-pregnant adults A composite design, based on: (i) the T-optimal design derived for the PCE, (ii) the D-optimal sampling times derived previously for of AS. This design was evaluated by a simulation-estimation procedure via Stata (data managment) NONMEM (simulation analysis) R (used as a platform to run the entire procedure). Development of -PD Conclusions

34 Methods results (ii): design for a PK-PD study of AS in non-pregnant adults Development of Empirical %RSEs from the simulation-estimation procedure: Rings Trophozoites Schizonts E max C 50 γ E max C 50 γ E max C 50 γ Fixed to Ω Emax Ω C50 Ω γ σ prop σ add 9.8e07 4.1e05 1.6e PD Conclusions

35 Conclusions The designs proposed in this work: utilise current knowledge of the PK-PD profiles of ACTs accommodate practical constraints of sampling patients are robust efficient should be considered for future where intensive sampling is not possible can be considered prototypes for an iterative open access support tool The designs will be provided by the Clinical Pharmacology module of the Worldwide Anti-malarial Resistance Network (WWARN) [1]. Development of -PD Conclusions

36 Future work Development of Use recent optimal design methods [8] to determine the sample size required to detect clinically important differences in the PK parameters across the key target s of non-pregnant adults, pregnant women children. -PD Conclusions

37 Acknowledgements Supervisors: A/Prof Julie Simpson, Prof Steve Duffull, A/Prof Lyle Gurrin Colleagues at the Mahidol-Oxford Tropical Medicine Research Unit (Bangkok): Dr Joel Tarning, A/Prof Niklas Lindegardh ( ), Prof Nick White, Dr Lisa White, Dr Sompob Saralamba Prof Ric Price, Menzies School of Health Research (Darwin) Local colleagues: Dr Sophie Zaloumis, Prof Carl Kirkpatrick, Dr Kashyap Patel, Ms Katherine Smith Funding: NHMRC Public Health Scholarship, Special Postgraduate Studentship (NHMRC Project Grant ) Development of -PD Conclusions

38 Acknowledgements Development of -PD Conclusions

39 References I K I Barnes, N Lindegardh, O Ogundahunsi, P Olliaro, C V Plowe, M Rrianarivelojosia, G O Gbotosho, W M Watkins, C H Sibley, N J White. World antimalarial resistance network (warn) iv: clinical pharmacology. Malar J, 6:122, S L Beal, L B Sheiner, A J Boeckmann. NONMEM Users Guides. Icon Development Solutions, Ellicott City, Maryl, USA, S B Duffull. Popt - installation user guide. ver 3.0, Jennifer A Flegg, Philippe J Guerin, Nicholas J White, Kasia Stepniewska. Stardizing the measurement of parasite clearance in falciparum malaria: the parasite clearance estimator. Malar J, 10:339, K M Jamsen, S B Duffull, J Tarning, N Lindegardh, N J White, J A Simpson. Optimal designs for of oral artesunate in patients with uncomplicated falciparum malaria. Malar J, 10:181, K M Jamsen, S B Duffull, J Tarning, N Lindegardh, N J White, J A Simpson. Optimal designs for of the partner drugs co-administered with artemisinin derivatives in patients with uncomplicated falciparum malaria. Malar J, 11:143, F Mentre, A Mallet, D Baccar. Optimal design in rom-effects regression models. Biometrika, 84: , Development of -PD Conclusions

40 References II K Ogungbenro L Aarons. How many subjects are necessary for experiments? confidence interval approach. Eur J Clin Pharmacol, 64:705 13, K Ogungbenro I Gueorguieva et al. Optimal design for multiresponse -pharmacodynamic models - dealing with unbalanced designs. Journal of Pharmacokinetics Pharmacodynamics, 34(3): , Sompob Saralamba, Wirichada Pan-Nguma, Richard J. Maudea, Sue J. Lee, Joel Tarning, Niklas Lindegardh, Kesinee Chotivanicha, Francois Nosten, Nicholas P. J. Day, Duong Socheatd, Nicholas J. White, Arjen M. Dondorp, Lisa J. White. Intrahost modeling of artemisinin resistance in plasmodium falciparum. PNAS, 108:397402, NJ White, K Stepniewska, K Barnes, RN Price, J Simpson. Simplified antimalarial therapeutic monitoring: using the day-7 drug level? Trends Parasitol, 24: , World Health Organization. Guidelines for the treatment of malaria, second edition. Geneva, Switzerl. ISBN , Development of -PD Conclusions

Biometrics by the Harbour Dr. Sophie G Zaloumis 1, A/Prof. Julie A Simpson 1 and PKPD IV-ARS Study Group

Biometrics by the Harbour Dr. Sophie G Zaloumis 1, A/Prof. Julie A Simpson 1 and PKPD IV-ARS Study Group Application of a Bayesian Markov chain Monte Carlo approach for modelling the dynamics of Plasmodium falciparum parasitaemia in severe malaria patients Dr. Sophie G Zaloumis 1, A/Prof. Julie A Simpson