January, 2009

Schedule 2006

Meeting*

Date

Place

Abstract Deadline

ASCPT

March 8-11, 2006

Baltimore Marriott Waterfront

September 29, 2006 for 2007 meeting

MUFPADA

May 2-3, 2006

Ann Arbor, MI

Contacts: Stephen.olson'pfizer.com Raymond.miller'pfizer.com Brian.corrigan'pfizer.com

International Workshop in Applied Probability

May 15-18, 2006

Storrs, CT

Past (Feb 25, 2006)

ICSA 2006 Applied Statistics Symposium

June 14-17, 2006

Storrs, CT

April 15, 2006

PAGE

June 14-16, 2006

Bruges, Belgium

Sheiner Student Session: March 15, 2006

Regular abstracts:     March 31, 2006

DIA

June 18-22, 2006

Pennsylvania Convention Center, Philadelphia

NA

AAPS/Biotech

June 18-21, 2006

JB Hynes Veterans Memorial Convention Center

Boston, MA

Past (Feb 14, 2006)

ECPAG

July 2006

Rockville, MD

Not Yet Announced

JSM (Joint Statistical Meetings of ASA)

August 5-10, 2006

Seattle, WA

Past (Feb 1, 2006)

2007 Information

ACCP

September 17-19, 2006

Cambridge, MA

May 15, 2006

AAPS

October 29-November 2, 2006

HB Gonzalez Convention Center.  San Antonio, TX

May 9, 2006

Library 2006

Bayesian Data Analysis. A. Gelman, J.B. Carlin, H.S. Stern and D.B. Rubin. 2nd ed. Chapman & Hall/CRC, New York, 2004.
ISBN 1-58488-388-X

Authored by several of the leaders in this field, Bayesian Data Analysis (80) is an essential text for any quantitative pharmacology reference library. The first edition set the tone as a high quality comprehensive text focused on the application of Bayesian data analysis methods to modern data analysis problems. This second edition continues that tradition by providing updated and expanded information on the topic, including many more examples from the authors' recent research. The text begins with a solid introduction to basic concepts of Bayesian inference, probability as a measure of uncertainty, the relationship between Bayesian and frequentist methods, and Bayesian computational methods. The majority of the text is focused on practical application, including examples and descriptions of hierarchical regression models of all types: linear models, general linear models, mixture models, multivariate models, models for missing data, as well as examples of model checking (revised and expanded), models accounting for data collection (revised and expanded), and posterior simulation. The second edition also includes new sections on nonlinear models, Bayesian decision analysis and utility functions, advanced Markov chain simulation, importance sampling, and a discussion of modeling challenges and general advice. Like the first edition, the second edition also includes a useful appendix of common probability distributions and a new appendix describing software tools for Bayesian computation in R using BUGS; (R2WinBUGS package, which can be found at: www.stat.columbia.edu/~gelman/bugsR/).

 

News 2006

Bits and hertz

There’s been a lot of interest lately in run-time performance, particularly as our models to describe pharmacologic systems become more complex and we test them with more rigor, e.g., through bootstrap and sensitivity analyses. Discussions on nmuser’sa regarding multi-core processors, processors with hyper-threading (HT) enabled, and 32-bit versus 64-bit processors have indicated that users can take advantage of multi-core processors either by executing two NONMEM® jobs simultaneously or by executing one job and using the other processor core for word processing, S-PLUS®, R, etc.  However, processors with HT are no better than single core processors (from AMD or Intel) because NONMEM® is unable to take advantage of the HT technology in Intel processors.  It appears that the 32-bit versus 64-bit question still requires additional benchmarking and experience.  There is some consensus that 32-bit compiler+32-bit operating system on a 64-bit CPU may slow the execution of a NONMEM® job, but no benchmarking results were offered.  The effect of a 64-bit compiler+64-bit operating system with a 64-bit CPU on the length of a NONMEM® job is even less understood.  It does seem clear that the current and future direction for NONMEM® job execution will include the use of grids/clusters (larger than those already in use) with multi-core CPU's, rather than stand-alone machines with single-core CPU's.  Other areas that may/will affect the execution time of NONMEM® runs are the choice of compiler (e.g., Intel, GNU G77, Absoft, etc.) and the level of optimization employed during compilation. We’ll continue to follow these topics and other areas relevant to run-time performance in future QPharm UpdateTM issues.

 

NMQual…

Keeping NONMEM® installations up to date with known bug fixes (see “The Official Bug List” @ www.globomax.com/nonmem.htm ) can be challenging due to the nature of the procedure (e.g., manually modifying and compiling code according to bug-fix documents), and the lack of an automated method to update the source files with the bug fixes prior to compilation. NMQual is a tool for automating and documenting the installation of NONMEM®. NMQual updates the NONMEM® source code with all bug fixes at the time of installation, implements any user or site specific changes, installs NONMEM® with minimal user intervention, maintains an electronic trail of all changes made during the installation, and links a NONMEM® run to an installation and any related code changes. It facilitates simultaneous availability of multiple installations with differing install options. NMQual is freely available under license from Metrum Institute (www.metruminstitute.org/downloads/). NONMEM® is available under license from GloboMax™ (Ellicott City, MD).

 

Coding 2006

1. IGNORE=@ in NONMEM® (www.globomax.com/nonmem.htm) When creating an NMTRAN data set, it may be useful to insert rows of text to provide documentation about the data set or header labels for data columns. It is also useful to enable exclusion of certain data records when data are pre-processed by NMTRAN to FDATA. One coding option to allow both of these types of comments is to include IGNORE=@ on the $DATA record of the NMTRAN control stream. IGNORE=@ signifies that any data record having any alphabetic character or “@” as its first non-blank character (not just in column 1) should be ignored.

2. matplot() for R (www.r-project.org) / SPLUS® (www.insightful.com/products/splus/) This tip provides a simple way to superimpose multiple x-y plots on the same axes, as is the case when plotting spaghetti plots of individual data in a population, or summary outcomes from multiple trial replicates from a simulation. One way to do this is to loop over all of the individuals or trial replicates, but a more efficient way is to use the matplot()function. With matplot()a matrix of x-data is plotted vs. a matrix of y-data. The first column of x is plotted against the first column of y, the second column of x against the second column of y, etc. If one matrix has fewer columns, plotting will cycle back through the columns again. Points involving missing values are not plotted. The following example illustrates the use of QQ Plotsmatplot() to display a series of super-imposed quantile-quantile (q-q) plots from a predictive check simulation (100 replicates). Each column of the matrix test.y contains the quantile-sorted values of Cmax from a single simulated trial replicate, while test.x is a matrix of columns of the corresponding quantile-sorted observed Cmax data. Lines for each set of q-q plots are plotted with a reference line. matplot(test.y, test.x, type="l",lty=4,lwd=1,xlab="Observed Cmax (ng/mL)",ylab="Simulated Cmax(ng/mL)", col=c(rep(13,100))) abline(0,1, lty=1,lwd=3,col=1) title(main="Q-Q Comparison of Cmax Distributions")

 

Publications 2006

Modeling and Simulation Methods Research

 

...  A New Approach to Modeling Covariate Effects and Individualization in Population Pharmacokinetics-Pharmacodynamics (33).  A 'hybrid' approach is described for approximating the maximum likelihood, where a more 'standard' first order (FO) approximation is used when sufficient data are available for an individual and Monte Carlo (MC) integration is used to estimate the likelihood for subjects with sparse data.  This hybrid approach for likelihood approximation attempts to thwart the weaknesses of each method as it stands alone; FO approximation is most prone to error with sparse sampling, whereas impractical computational times are required for MC integration with too much data.  The authors also present alternative approaches to covariate analyses; one method involves regression splines, the other neural networks.  Precision and bias measures are used to compare these methods to the more standard method using linear regression.

 

... Propagation of Population PK and PD Information Using a Bayesian Approach: Dealing with Non-Exchangeability (34).  As differences between the prior and test populations become greater, the degree of non-exchangeability becomes greater.  This non-exchangeability with the priors can lead to biased results, and so needs to be considered during a Bayesian analysis.  When the prior and test population differences are systematic, the differences can be reconciled through covariates that model the association.  However, when the differences are random, an alternative approach is necessary.  Dokoumetzidis and Aarons have proposed an extra hierarchical level to account for inter-study variability.  Here, this fourth level does not apply directly to individual parameters, but does indirectly influence their estimation, and so provides for a more diffuse (or conservative) prior (34).  The authors demonstrate that the 4-level model was unbiased, although with expectedly more uncertainty, compared with the more typical 3-level model.  Therefore, this four-level approach may offer protection against bias for misspecified and/or overly informative (strong) priors.

 

... Inherent Correlation between Dose and Clearance in Therapeutic Drug Monitoring Settings: Possible Misinterpretation in Population Pharmacokinetic Analyses (35).  Dose titration initiated by therapeutic drug monitoring will often be based on a subject's failure to achieve a target drug plasma concentration, where too low of an exposure will lead to an increase in dose and vice versa.  As these exposures are inherently linked to clearance, subjects with lower clearance will likely be titrated to lower doses, and higher clearance subjects would receive a higher dose.  Thus, TDM may impose a correlation between individual clearance and the individualized dose.  Be cautious of routine clinical PK data collected from such a design.  Ahn et al. show how this correlation may lead to the false positive inclusion of dose as a covariate for clearance.  The authors simulated a TDM scenario for carbamazepine to illustrate how such a correlation can arise and lead to misleading interpretations regarding dose-dependent clearance.

 

... Mapping the Dose-Effect Relationship of Orbofiban from Sparse Data with an Artificial Neural Network (36).  A neural network (NN) offers an attractive approach for quantifying clinical pharmacological systems, in that it does not require a structural model. To compare the utility of this approach to more traditional population PK-PD modeling,  the predictive performance of a neural network PD model was compared to a population PK-PD model (36).  A back-propagation NN was designed to predict pre- and post-drug treatment effect from a Phase II dose-finding study for orbofiban.  The population PD model was a direct-effect sigmoidal inhibition model.  Relative bias was comparable between the two methods, but the population model showed greater precision.  Despite this result, the authors conclude the NN result would provide a useful approach for individualizing pharmacotherapy if drug concentrations were either poorly predictable or unavailable.

 

... Prediction Discrepancies for the Evaluation of Nonlinear Mixed-Effects Models (37).  The predictive performance of models has been undergoing greater and greater scrutiny.  This is rightfully so, as simulations from these models are often used to guide therapeutic development decisions, and so it is imperative that precision and bias are well understood.  Prediction errors, or standardized prediction errors, have been at the forefront of this evaluation since their seminal introduction by Beal and Sheiner in 1981 (38). A new method is being proposed to use the predictive distribution to calculate a 'predictive discrepancy' for which a Kolmogorov-Smirnov (KS) test can be used to test model adequacy (37).  The predictive distribution is described for each observation and is based on the random effect estimates.  In the example provided, parameter uncertainty is ignored.  The predictive distribution is estimated using stochastic Monte Carlo integration, and so does not require linearization of the structural model.  Model evaluation diagnostics are provided, and an improvement in both Type I and II error is demonstrated relative to evaluations through standardized prediction errors.

 

Modeling and Simulation in Specific Therapeutic Areas

 

HIV/AIDS ... innovative applications of quantitative modeling and simulation continue to evolve from HIV research.  The concept of model-based drug development was exemplified through a recent report of Phase IIa dose selection for the novel (CCR5-receptor antagonism) anti-HIV drug maraviroc (UK-427,857).  Modeling included a short-term disease progression model and viral load pharmacodynamic data combined into a PK-PD model, which ultimately accelerated the drug's development and assisted the design of clinical studies (39).   Other notable applications included:

 

...population PK analysis for enfuvirtide (ENF), which summarized that ENF serum concentrations were lower and more variable than expected, and so many patients may achieve insufficient concentrations (40).

 

... PK modeling of indinavir (IDV) along with MDR1 genotype data was used to show there was no support for an association between MDR1 genetic polymorphisms and modeled IDV clearance (41).

 

...population PK model developed for efavirenz promises to be a useful tool for optimization of efavirenz-containing antiretroviral therapy, e.g., by the use of Bayesian estimation of individual pharmacokinetic parameters.  Of interest, this efavirenz PK model included a chain of three transition compartments to model oral absorption (42).

 

...model validation through simulation (a predictive check) was used to evaluate modeling to describe changes in cholesterol level in HIV subjects under alternative antiretroviral regimes.  Five models which differed in their assumptions were compared on treatment variability and pattern of effect over time, to determine the most appropriate model based on specific validation criteria.  The authors conclude that this approach to model validation through simulation offers possible extension to other purposes, such as the assessment of efficacy, safety, and equivalence of treatments in clinical trials (43).

 

Pediatrics... it's not surprising to see so many publications reporting the use of pharmacokinetic (PK) and pharmacodynamic (PD) modeling and simulation in pediatric studies.  Pediatric studies require special attention, given the ethical limitations for collecting data, as well as the scientific and ethical drive to gain the most information from the data.  Population modeling is a sensible match for such studies, where the maximum information can be gained through sparse sampling.

 

Quantitative methods have been used to support the design aspects for optimal data collection (44) and also for analyses to develop appropriate dosage regimens.  Many studies report using PK and/or PK-PD modeling to equate dose to exposures and treatment goals across pediatric populations.  Recent examples include evaluations of chemotherapy (topotecan) (45) and antibiotics meropenum (46), vancomycin (44), amikacin (47), and amphotericin B (48).  Other therapeutic applications were for the anesthetic propofol (49), low molecular weight heparin (50), and the anticonvulsant oxcarbazepine (51).   Bottom line: applications of quantitative pharmacology are helping a wide range of pediatric patients.

 

Developmental differences in pediatrics are often captured through age and weight relationships.  Allometric scaling based on body weight is one such method.  This method was recently compared to an in silico calculation of CYP-mediated metabolism (52).  The author concluded that allometric scaling was inappropriate for use in neonates and infants, where this method does not account for lower drug-metabolizing capacity of the liver at birth.  It was found that the in silico prediction provided initial estimates of drug clearance, but was still no substitute for an actual clinical investigation.

 

... That being said, a sensible application of in silico predictions is for toxin exposures.  Using a physiologic-based PK (PBPK) model and scaling based on capacity of CYP-mediated metabolism, researchers have used Monte Carlo simulation of toluene exposure to demonstrate how inter-individual variability and population characteristics can assess exposure risks of volatile organics (53).

 

Oncology... the benefits of quantitative pharmacology continue to be shown for oncology therapy.  PK and PK-PD modeling are used to develop individualized or other standardized regimens.  Examples include a combination fluorouracil-epirubicin-cyclophosphamide regimen in breast cancer patients (54), topotecan in children with medulloblastoma (45), busulfan in hematopoietic stem cell transplantation patients (55), capecitabine in metastatic cancer patients (56), rituximab in heterogeneous clinical settings (57), and cyclophosphamide in a high-dose combination with thiotepa and carboplatin (58).

 

Mechanistic PK-PD models are adding to our understanding of chemotherapeutics effects.  Cell life span models are useful for describing hematological effects, but these models can be difficult to implement due to their need for delay differential equations.  But now a description and discussion of these models along with example NONMEM coding is available (59).  ... An application of a cell life span model has recently been published, where it was used to describe the time-course of reticulocyte, red blood cell count, and hemoglobin changes following single and multiple subcutaneous administration of recombinant human erythropoietin (60).

 

A similar approach was used to describe the time-course of neutropenia following treatment with pemetrexed.  Using a semi-mechanistic PK-PD model, investigators were able to explore the impact of dose, exposure, and/or patient characteristics on neutropenic response (61;62).  Continuation of this work, using population PK modeling with combined data from 10 Phase 2 trials, led to a suggestion that dose adjustments for pemetrexed be based on renal function, rather than body surface area (63).

Clinical Toxicology... physiologic-based PK models are being used more and more to predict exposure risks.  An application in pediatrics regarding exposure to toluene was described above (53). In addition, PBPK was recently used to evaluate the cancer risk in mice to dichloromethane exposure (64).  Another PBPK model quantified possible ranges of human exposure to xylenes based on the degree of inter-individual variability (65).

 

Hypnotics, sedatives and anesthetics... A PK-PD model using a categorical PD endpoint for sedation provided a comparison of lorazepam and midazolam following long-term infusion in critically ill patients.  Results revealed similar intra- and inter-individual PD variability for each agent (66).

 

... PK-PD effects of general anesthetics may now be quantified using spectral entropy, a new electroencephalogram (EEG)-derived parameter.  A PK-PD analysis for sevoflurane has used this new marker (67).

 

... PET imaging and radiolabeled [C-11] flumazenil were used to evaluate changes in GABA(A)-receptor density and affinity play in a preclinical application of quantitative pharmacology.  This work involved development of a population PK model to describe the plasma concentration-time course and distributions to body, brain, as well as binding specifically within the brain (68).

 

... tracer plasma concentrations of radiolabeled [C-11] flumazenil were also used in clinical study to develop a population PK model and assess the effects of patient-related covariates.  The data were obtained from 51 patients with either depression or epilepsy, and model results were used to develop an optimal sampling strategy (69).  For more on optimal trial design, please check out the SPOTLIGHT above.

 

 

Other Therapeutics ... PK and PK-PD modeling of anti-infectives continues to provide therapeutic guidance.  The utility of simulation to predict the likelihood of achieving the desired exposure in humans for antibiotic treatment was demonstrated for agents targeting extended spectrum beta-lactamase (ESBL)-producing organisms (70). Other applications... PK analyses of gentamycin and vancomycin in patients with unstable renal function following cardiothoracic surgery (71), cefipime in plasma and cerebrospinal fluid of hospitalized patients with external ventriculostomies (72), fosfomycin in pus to evaluate antibiotic abscess penetration (73), rifapentine in South African tuberculosis patients (74), and a novel lipoglycopeptide dalbavancin (75) were all recently reported.

 

An evaluation of metformin population PK in pregnant women with either gestational or Type II diabetes revealed that PK were similar to those in non-pregnant patients, and so no dosage adjustment was warranted (76).  Such information is right in line with the draft FDA guidance Pharmacokinetics in Pregnancy, and so may provide useful prescribing guidance.  The draft guidance discusses the clinical utility of PK information in cases where a medication is known to be prescribed in or used by pregnant women.  According to the American Diabetes Association, gestational diabetes is estimated to affect about 4% of all pregnant women, equating to approximately 135,000 cases each year in the United States alone.  Metformin study authors caution that despite the similarity in PK, metformin readily crosses the placenta, exposing the fetus to concentrations approaching those in the maternal circulation. The sequelae to such exposure, e.g., effects on neonatal obesity and insulin resistance, remain unknown (76).

 

More on semi-mechanistic PK-PD models ... using salivary concentrations of the antimalarial artemisinin and parasite count data from Vietnamese malaria patients, a semi-mechanistic PK-PD model was developed to reflect the parasite life-cycle (77).  The model described both the salivary PK time course after repeated dosing and the number of parasites.  The study included two different dosage regimens, which in consideration with the PK-PD model, may lead to support of appropriate therapeutic regimens.

 

A population PK-PD analysis of a class IC antiarrhythmic, pilsicainide, in patients with cardiac arrhythmias concluded that sex and creatinine clearance were covariates of weight-normalized systemic clearance, where clearance was 50% lower in women than in men.   Therefore, these covariate effects may be associated with augmented ECG responses to pilsicainide (78).

 

Transplant patients often require monitored adjustments to their pharmacotherapy.  To help guide these adjustments, a recent characterization of tacrolimus population PK in Asian liver transplant patients has identified and quantified sources of interindividual PK variability (79).  This information may be useful for clinicians to individualize therapy through Bayesian forecasting.  Similarly, the development of a time-dependent PK model for cyclosporine in de novo renal transplantation patients may also provide information on individualized dose titration, either through development of nomograms or Bayesian forecasting.

 

References

(33)                   Lai TL, Shih MC, Wong SP. A New Approach to Modeling Covariate Effects and Individualization in Population Pharmacokinetics-Pharmacodynamics. J Pharmacokinet Pharmacodyn 2006;1-26.

(34)                   Dokoumetzidis A, Aarons L. Propagation of Population Pharmacokinetic Information Using a Bayesian Approach: Comparison with Meta-Analysis. J Pharmacokinet Pharmacodyn 2005;(Online First).

(35)                   Ahn JE, Birnbaum AK, Brundage RC. Inherent correlation between dose and clearance in therapeutic drug monitoring settings: possible misinterpretation in population pharmacokinetic analyses. J Pharmacokinet Pharmacodyn 2005; 32(5-6):703-18.

(36)                   Mager DE, Shirey JD, Cox D, Fitzgerald DJ, Abernethy DR. Mapping the dose-effect relationship of orbofiban from sparse data with an artificial neural network. J Pharm Sci 2005; 94(11):2475-86.

(37)                   Mentre F, Escolano S. Prediction Discrepancies for the Evaluation of Nonlinear Mixed-Effects Models. J Pharmacokinet Pharmacodyn 2005;(Online First).

(38)                   Sheiner LB, Beal SL. Some suggestions for measuring predictive performance. J Pharmacokinet Biopharm 1981; 9(4):503-12.

(39)                   Rosario MC, Jacqmin P, Dorr P, van der RE, Hitchcock C. A pharmacokinetic-pharmacodynamic disease model to predict in vivo antiviral activity of maraviroc. Clin Pharmacol Ther 2005; 78(5):508-19.

(40)                   Stocker H, Kloft C, Plock N, Breske A, Kruse G, Herzmann C et al. Pharmacokinetics of enfuvirtide in patients treated in typical routine clinical settings. Antimicrob Agents Chemother 2006; 50(2):667-73.

(41)                   Verstuyft C, Marcellin F, Morand-Joubert L, Launay O, Brendel K, Mentre F et al. Absence of association between MDR1 genetic polymorphisms, indinavir pharmacokinetics and response to highly active antiretroviral therapy. AIDS 2005; 19(18):2127-31.

(42)                   Kappelhoff BS, Huitema AD, Yalvac Z, Prins JM, Mulder JW, Meenhorst PL et al. Population pharmacokinetics of efavirenz in an unselected cohort of HIV-1-infected individuals. Clin Pharmacokinet 2005; 44(8):849-61.

(43)                   Abbas I, Rovira J, Casanovas J. Validation by simulation of a clinical trial model using the standardized mean and variance criteria. J Biomed Inform 2006.

(44)                   Ohnishi A, Yano Y, Ishibashi T, Katsube T, Oguma T. Evaluation of Bayesian predictability of vancomycin concentration using population pharmacokinetic parameters in pediatric patients. Drug Metab Pharmacokinet 2005; 20(6):415-22.

(45)                   Stewart CF, Iacono LC, Panetta JC, Gajjar A, Freeman Iii BB. Using plasma topotecan pharmacokinetics to estimate topotecan exposure in cerebrospinal fluid of children with medulloblastoma. Neuro -oncol 2006.

(46)                   Du X, Li C, Kuti JL, Nightingale CH, Nicolau DP. Population pharmacokinetics and pharmacodynamics of meropenem in pediatric patients. J Clin Pharmacol 2006; 46(1):69-75.

(47)                   Allegaert K, Anderson BJ, Cossey V, Holford NH. Limited predictability of amikacin clearance in extreme premature neonates at birth. Br J Clin Pharmacol 2006; 61(1):39-48.

(48)                   Wurthwein G, Groll AH, Hempel G, dler-Shohet FC, Lieberman JM, Walsh TJ. Population pharmacokinetics of amphotericin B lipid complex in neonates. Antimicrob Agents Chemother 2005; 49(12):5092-8.

(49)                   Shangguan WN, Lian Q, Aarons L, Matthews I, Wang Z, Chen X et al. Pharmacokinetics of a Single Bolus of Propofol in Chinese Children of Different Ages. Anesthesiology 2006; 104(1):27-32.

(50)                   Kuhle S, Massicotte P, Dinyari M, Vegh P, Mitchell D, Marzinotto V et al. Dose-finding and pharmacokinetics of therapeutic doses of tinzaparin in pediatric patients with thromboembolic events. Thromb Haemost 2005; 94(6):1164-71.

(51)                   Northam RS, Hernandez AW, Litzinger MJ, Minecan DN, Glauser TA, Mangat S et al. Oxcarbazepine in infants and young children with partial seizures. Pediatr Neurol 2005; 33(5):337-44.

(52)                   Bjorkman S. Prediction of cytochrome p450-mediated hepatic drug clearance in neonates, infants and children : how accurate are available scaling methods? Clin Pharmacokinet 2006; 45(1):1-11.

(53)                   Nong A, McCarver DG, Hines RN, Krishnan K. Modeling interchild differences in pharmacokinetics on the basis of subject-specific data on physiology and hepatic CYP2E1 levels: A case study with toluene. Toxicol Appl Pharmacol 2006.

(54)                   Sandstrom M, Lindman H, Nygren P, Johansson M, Bergh J, Karlsson MO. Population analysis of the pharmacokinetics and the haematological toxicity of the fluorouracil-epirubicin-cyclophosphamide regimen in breast cancer patients. Cancer Chemother Pharmacol 2006;1-14.

(55)                   Takama H, Tanaka H, Nakashima D, Ueda R, Takaue Y. Population pharmacokinetics of intravenous busulfan in patients undergoing hematopoietic stem cell transplantation. Bone Marrow Transplant 2006; 37(4):345-51.

(56)                   Urien S, Rezai K, Lokiec F. Pharmacokinetic modelling of 5-fu production from capecitabine-a population study in 40 adult patients with metastatic cancer. J Pharmacokinet Pharmacodyn 2005; 32(5-6):817-33.

(57)                   Regazzi MB, Iacona I, Avanzini MA, Arcaini L, Merlini G, Perfetti V et al. Pharmacokinetic behavior of rituximab: a study of different schedules of administration for heterogeneous clinical settings. Ther Drug Monit 2005; 27(6):785-92.

(58)                   de Jonge ME, Huitema AD, van Dam SM, Rodenhuis S, Beijnen JH. Population pharmacokinetics of cyclophosphamide and its metabolites 4-hydroxycyclophosphamide, 2-dechloroethylcyclophosphamide, and phosphoramide mustard in a high-dose combination with Thiotepa and Carboplatin. Ther Drug Monit 2005; 27(6):756-65.

(59)                   Perez-Ruixo J, Kimko H, Chow A, Piotrovsky V, Krzyzanski W, Jusko W. Population Cell Life Span Models for Effects of Drugs Following Indirect Mechanisms of Action. J Pharmacokinet Pharmacodyn 2005;(Online First).

(60)                   Krzyzanski W, Jusko WJ, Wacholtz MC, Minton N, Cheung WK. Pharmacokinetic and pharmacodynamic modeling of recombinant human erythropoietin after multiple subcutaneous doses in healthy subjects. Eur J Pharm Sci 2005; 26(3-4):295-306.

(61)                   Latz JE, Karlsson MO, Rusthoven JJ, Ghosh A, Johnson RD. A semimechanistic-physiologic population pharmacokinetic/pharmacodynamic model for neutropenia following pemetrexed therapy. Cancer Chemother Pharmacol 2006; 57(4):412-26.

(62)                   Latz JE, Rusthoven JJ, Karlsson MO, Ghosh A, Johnson RD. Clinical application of a semimechanistic-physiologic population PK/PD model for neutropenia following pemetrexed therapy. Cancer Chemother Pharmacol 2006; 57(4):427-35.

(63)                   Latz JE, Chaudhary A, Ghosh A, Johnson RD. Population pharmacokinetic analysis of ten phase II clinical trials of pemetrexed in cancer patients. Cancer Chemother Pharmacol 2006; 57(4):401-11.

(64)                   Marino DJ, Clewell HJ, Gentry PR, Covington TR, Hack CE, David RM et al. Revised assessment of cancer risk to dichloromethane: Part I Bayesian PBPK and dose-response modeling in mice. Regul Toxicol Pharmacol 2006.

(65)                   Adams JC, Dills RL, Morgan MS, Kalman DA, Pierce CH. A physiologically based toxicokinetic model of inhalation exposure to xylenes in Caucasian men. Regul Toxicol Pharmacol 2005; 43(2):203-14.

(66)                   Swart EL, Zuideveld KP, de JJ, Danhof M, Thijs LG, Strack van Schijndel RM. Population pharmacodynamic modelling of lorazepam- and midazolam-induced sedation upon long-term continuous infusion in critically ill patients. Eur J Clin Pharmacol 2006;1-10.

(67)                   McKay ID, Voss LJ, Sleigh JW, Barnard JP, Johannsen EK. Pharmacokinetic-pharmacodynamic modeling the hypnotic effect of sevoflurane using the spectral entropy of the electroencephalogram. Anesth Analg 2006; 102(1):91-7.

(68)                   Liefaard LC, Ploeger BA, Molthoff CF, Boellaard R, Lammertsma AA, Danhof M et al. Population Pharmacokinetic Analysis for Simultaneous Determination of B (max) and K (D) In Vivo by Positron Emission Tomography. Mol Imaging Biol 2005;1-11.

(69)                   van Rij CM, Huitema AD, Swart EL, Greuter HN, Lammertsma AA, van Loenen AC et al. Population plasma pharmacokinetics of 11C-flumazenil at tracer concentrations. Br J Clin Pharmacol 2005; 60(5):477-85.

(70)                   Andes D, Craig WA. Treatment of infections with ESBL-producing organisms: pharmacokinetic and pharmacodynamic considerations. Clin Microbiol Infect 2005; 11 Suppl 6:10-7.

(71)                   Staatz CE, Byrne C, Thomson AH. Population pharmacokinetic modelling of gentamicin and vancomycin in patients with unstable renal function following cardiothoracic surgery. Br J Clin Pharmacol 2006; 61(2):164-76.

(72)                   Lodise TP, Jr., Rhoney DH, Tam VH, McKinnon PS, Drusano GL. Pharmacodynamic profiling of cefepime in plasma and cerebrospinal fluid of hospitalized patients with external ventriculostomies. Diagn Microbiol Infect Dis 2006.

(73)                   Sauermann R, Karch R, Langenberger H, Kettenbach J, Mayer-Helm B, Petsch M et al. Antibiotic abscess penetration: fosfomycin levels measured in pus and simulated concentration-time profiles. Antimicrob Agents Chemother 2005; 49(11):4448-54.

(74)                   Langdon G, Wilkins J, McFadyen L, McIlleron H, Smith P, Simonsson US. Population pharmacokinetics of rifapentine and its primary desacetyl metabolite in South African tuberculosis patients. Antimicrob Agents Chemother 2005; 49(11):4429-36.

(75)                   Buckwalter M, Dowell JA. Population pharmacokinetic analysis of dalbavancin, a novel lipoglycopeptide. J Clin Pharmacol 2005; 45(11):1279-87.

(76)                   Charles B, Norris R, Xiao X, Hague W. Population Pharmacokinetics of Metformin in Late Pregnancy. Ther Drug Monit 2006; 28(1):67-72.

(77)                   Gordi T, Xie R, Jusko WJ. Semi-mechanistic pharmacokinetic/pharmacodynamic modelling of the antimalarial effect of artemisinin. Br J Clin Pharmacol 2005; 60(6):594-604.

(78)                   Ogawa R, Kishi R, Mihara K, Takahashi H, Takagi A, Matsumoto N et al. Population Pharmacokinetic and Pharmacodynamic Analysis of a Class IC Antiarrhythmic, Pilsicainide, in Patients With Cardiac Arrhythmias. J Clin Pharmacol 2006; 46(1):59-68.

(79)                   Sam WJ, Tham LS, Holmes MJ, Aw M, Quak SH, Lee KH et al. Population pharmacokinetics of tacrolimus in whole blood and plasma in asian liver transplant patients. Clin Pharmacokinet 2006; 45(1):59-75.

 

Spotlight 2006

 

Trial Design Optimization Approaches

 

Informed trial design using collective information about the therapeutic agent, comparator agents, disease dynamics and trial logistics has continued to evolve with the advocacy of multi-disciplinary teams, progression of in silico capabilities, and advancement of methodologies.  The key design considerations often include the number of patients, elementary (study structure) design features; and, to evaluate clinical measurements, the number of measurements (or samples) and the time(s) at which it is best to collect them.  Two areas of methodological research for optimizing these design considerations are information theory based optimization and Monte Carlo simulation.

 

Information theory

Information theory has developed from the Rao-Cramer inequality, which states that the inverse (-1) of the Fisher Information Matrix (FIM) is the lower bound of the variance-covariance matrix of the (unbiased) parameter estimates. In D-optimality, the FIM-1 provides an estimate of precision; where for design comparisons, a 'smaller' FIM-1 (or larger FIM) indicates a more precise design.  The determinant of FIM [det(FIM)] is often calculated as a scalar quantity for comparisons of variance-covariance matrices (i.e., from separate design options).   For comparisons of designs with different numbers of parameters (P), an efficiency term may be calculated.  For example, the ratio of det(FIM)1/P provides a dimensionless average of the difference in error variance.  Of interest, an analytical solution for FIM does not exist for nonlinear mixed effects models, and so approximations have been calculated using either a first order Taylor Series expansion or Monte Carlo integration (1).

 

Rather than manually comparing the multitude of possible designs that derive, for example, from N possible number of patients, K number of samples, and T collection times; algorithms have been employed to search for the optimal combination of design variables across the population det(FIM) 'response surface.'  These algorithms include simplex, simulated annealing, adaptive random search, Fedorov-Wynn, and Fedorov exchange.  Of cautionary note, some search methods (e.g., simplex) are prone to settling into local minima, and so various starting conditions (initial values) should be tested.

 

Duffull et al. compared four optimization algorithms (simplex, non-adaptive random search, non-adaptive random search followed by simplex and simulated annealing (SA)) for various scenarios (2).  In each case, SA performed better than the other methods, particularly with more complex designs.  However, SA did require considerably greater computation time.  For more information on search algorithms, a brief summary has been provided in the "Introduction and background" of Ogungbenro et al. (3).  These authors present an additional search method, a modified Fedorov exchange algorithm (MFEA), which is demonstrated to perform better than SA.  Similar to the comparative findings discussed above for SA, the benefits of MFEA were most evident as design complexity increased; but this algorithm also required the most computational time.

 

Despite the relative increase in computational time for some search algorithms, D-optimality remains a fairly fast and efficient method for design development.  However, an issue to consider when using D-optimality is its reliance on point estimates of model parameters as the true, unbiased value.  In other words, levels of parameter uncertainty are sometimes not considered, depending on the methodology employed.  This may be an invalid assumption when designing studies for future development stages, if population differences impart varied model parameter effects.  For example, drug clearance, and/or its inter-individual variance, may differ considerably between Phase I healthy subjects used to generate the existing PK model versus Phase II or III subjects to be studied in a population PK design.  Thus, reliance on fixed priors from the healthy population may impose a bias leading to an inappropriate design for the patient population.

 

Optimality Software Examples

 

Individual or Mean Model Parameters:

 

Population Model Parameters (PMP):

 

PMP with Parameter Uncertainty:

www.uq.edu.au/pharmacy/sduffull/POPT.htm

 

 

Extensions to D-optimality exist that allow for incorporation of parameter uncertainty.  These include ED-, EID-, and API-optimality, which evaluate the expectations of det(FIM),  1/det(FIM), and log(det(FIM)), respectively (7),  (8).  Dodds et al. compared ED-optimality with D-optimality under conditions of misspecified priors (9).  Studies were designed using the misspecified values, but simulated using the hypothetically 'true' values.  Parameter bias and precision were markedly better for the ED-optimality compared to the D-optimality designed studies, indicating that inclusion of parameter uncertainty allowed for the 'recovery' of appropriate estimates from the ED-optimality designs.

 

In addition to consideration of parameter uncertainty for D-optimality applications, it is also important to understand that the output from this approach relies on only one measure of predictive performance, namely, precision; but does not provide any measure of bias.  As shown through the simulation evaluation of D- and ED-optimality described above (9), designs determined through optimality approaches may provide optimal precision; but the degree of bias, which may be considerable, remains completely unknown if using this methodology alone.

 

A final consideration for optimality is that the search algorithms generally 'look' for the design that minimizes the variability (increases precision) across all model parameters.  In doing so, the design may be heavily influenced by highly variable parameters, regardless of their relative clinical importance.  For example, variable oral absorption, described through a parameter ka and associated inter-individual variance in a population PK model, may result in a concentration of sample collections during the absorption phase, at the expense of collections at later times that possibly would be more informative for clinical measures of total exposure (e.g., clearance parameter estimation).  Thus, the user of D-optimality should be cognizant of trade-offs being made between the most variable parameter relative to parameters of most interest.  Adjustments to relative variances may be considered to balance these interests.

 

Further examples of population FIM application include Mentre et al. (10), Retout et al. [(11),  (12)], Green et al. (13) and Chenel et al. (14).

 

Monte Carlo Simulation

A second method for trial design optimization involves Monte Carlo simulation, where outcome (e.g., PK, PD, safety or efficacy) data based on a particular set of design variables are simulated using random number generation, and parameters are subsequently re-estimated to evaluate the predictive performance of the given design.  Although more time intensive than information theory approaches, simulation/estimation evaluations provide estimates of both precision and bias that may be compared for given designs.

 

A brief summary of the advantages and limitations of trial simulation is provided below.  For an in depth review of simulation methods, suggested textbooks are Simulation Modeling and Analysis (15), and, for specifics on clinical trial simulation, Simulation for Designing Clinical Trials (16).  A review article on clinical trial simulation is also available (17).

 

A direct application for evaluating a population PK design has been reported by Kowalski and Hutmacher using a simulation case study (18).  In addition to evaluation of precision and bias through simulation and parameter re-estimation, these authors describe a method for determining the power of the study design to detect model effects (e.g., covariates).  This portion of the simulation study was conducted to estimate the number of subjects that would be needed to estimate a 40% reduction in CL, given a subpopulation prevalence of 5 or 10%, at a desired power of at least 90%.  This involved replicated simulation of PK datasets (N=300), including the covariate effect, for each of two sample sizes (n=150 and 225) and each subpopulation prevalence.  A null and covariate model were re-estimated from the simulated datasets, and the likelihood ratio test was used to determine the percentage of the 300 trials for which a 'statistically significant' (α=0.05) difference in CL was observed.  This percentage was used as a measure of the power of the study design (18).  Similar applications should consider the limits of the likelihood ratio test [(19), (20), (21) and (22)], as well as the potential for selection bias among small sample sizes (23).

 

Overall, design optimization through simulation provides an opportunity to evaluate many intricacies of the trial; including the traditional design aspects, i.e., number of subjects, number of samples and their collection times, and basic structure (e.g., cohort designs, cross-over vs. parallel).  Simulations also provide an opportunity to evaluate the design pertaining to multiple outcomes, which may include PK, PD, safety and/or efficacy measurements.  Therefore, trade-offs between endpoints (e.g., establishment of a therapeutic index) can be considered and designs adjusted as needed.

 

By evaluating multiple endpoints, the most appropriate (informative) clinical endpoints can be prioritized enabling an a priori determination of the most appropriate statistics for the analysis plan.  Thus, those endpoints of most clinical relevance can be the focus of trial optimization, rather than a generalized approach to minimize variance across all parameters.

 

Perhaps the most beneficial utility, though, is the use of simulation to explore additional scenarios that may greatly impact trial outcomes.  For example, simulations may include models for medication compliance, drop-out, or other sources of missing data; such as those described by Girard et al. (24), and Hu and Sale (25).  Various assumptions for compliance or dropout can be simulated, their impact evaluated, and, if necessary, proactively managed through alterations in study design and/or conduct (e.g., incorporate programs to improve compliance or patient retention).

 

Along this line, an important consideration in interpreting simulation results is the sensitivity of these results to underlying assumptions or uncertainty about the simulation model and parameters. Trial simulation outputs should be viewed relative to their sensitivity to model parameter uncertainty using a sensitivity analysis.

 

Simulation Software Examples

Simulation and Estimation:

  • NONMEM®
  • S-PLUS®
  • SAS®

 

Simulation Only:

  • Pharsight® Trial SimulatorTM

 

A global sensitivity analysis is based on simulations conditioned on uncertainty distributions across all parameters.   Monte Carlo methods are used to simulate from the uncertainty distributions at the inter-trial level.  The sensitivity of simulation outcome(s) to simulation parameter uncertainty (assumptions) is viewed over a continuous range of parameter uncertainty.  Oftentimes, this information can be used to determine if enough information is available to move forward with a given trial design.  For example, consider the following scenario: an EC50 parameter is estimated to have a typical value of 50 ng/mL with an uncertainty range (i.e., 90% CI) of 35 to 75 ng/mL.  Simulations across this range of possible EC50 values indicate markedly different results if the 'actual' EC50 is at either extreme of this range.  It, therefore, would be warranted to either: 1) research (or conduct experiments to generate) additional data to improve the precision of this parameter, or 2) if possible, develop a more robust trial design that would be less sensitive to this probable range for the model.  Examples of simulation with uncertainty are available for physiologically-based PK models [(26), (27)] and clinical trial simulations [(28), (29)].

 

Further examples of trial optimization through simulation include Nakade et al. (30), Hashimoto and Sheiner (31), and Hashimoto et al. (32).

 

In summary, simulation enables one to evaluate and optimize many facets of trial design.  However, unlike the search algorithms with D-optimality, simulations (and estimations) must be performed for each considered design.  Consequently, the actual number of designs that can be evaluated is limited by practicality.  Perhaps a best approach would be a combination of both methods, where information theory would be used to limit the range of possible designs, and simulation would provide a thorough characterization of this range of inputs and outputs to refine the final design.  We look forward to continued evolution of these methods along with consistent application; the incentive will be better informed study designs with more focused outcomes, accompanied by lower costs and more efficient use of time.

 

Issue 1

Issue for 2006:

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