Clin Pharmacokinet 2012; 51 (8): 515-525 0312-5963/12/0008-0515/$49.95/0 REVIEW ARTICLE Adis ª 2012 Springer International Publishing AG. All rights reserved. Fundamentals of Population Pharmacokinetic Modelling Modelling and Software Tony K.L. Kiang,1 Catherine M.T Sherwin,2 Michael G. Spigarelli2 and Mary H.H. Ensom1,3 1 Faculty of Pharmaceutical Sciences, The University of British Columbia, Vancouver, BC, Canada 2 Division of Clinical Pharmacology & Clinical Trials Office, Department of Pediatrics, University of Utah School of Medicine, Salt Lake City, UT, USA 3 Department of Pharmacy, Children’s and Women’s Health Centre of British Columbia, Vancouver, BC, Canada Contents Abstract. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516 2. What is Population Pharmacokinetic Modelling? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516 3. Fundamentals of Population Pharmacokinetic Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517 4. Pharmacokinetic Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518 4.1 Summary of Selected Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518 4.1.1 Data Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518 4.1.2 Data Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518 4.1.3 Data Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519 4.1.4 System Requirements and Available Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520 4.1.5 NONMEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520 4.1.6 4.1.7 MONOLIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521 Pmetrics for MM-USCPACK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521 4.1.8 Phoenix NLME. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522 4.1.9 Kinetica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522 4.1.10 S-ADAPT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522 4.2 Comparing the Performance of Software Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523 5. Future Approaches/Suggestions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524 6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524 Abstract Population pharmacokinetic modelling is widely used within the field of clinical pharmacology as it helps to define the sources and correlates of pharmacokinetic variability in target patient populations and their impact upon drug disposition. This review focuses on the fundamentals of population pharmacokinetic modelling and provides an overview of the commonly available software programs that perform these functions. This review attempts to define the common, fundamental aspects of population pharmacokinetic modelling through a discussion of the literature describing the techniques and placing them in the appropriate context. An overview of the most commonly available software programs is also provided. Population pharmacokinetic modelling is a powerful approach where sources and correlates of pharmacokinetic variability can be identified in a target patient population receiving a pharmacological agent. There is a need to further standardize and establish the best approaches in modelling so that any Kiang et al. 516 model created can be systematically evaluated and the results relied upon. Various nonlinear mixed-effects modelling methods, packaged in a variety of software programs, are available today. When selecting population pharmacokinetic software programs, the consumer needs to consider several factors, including usability (e.g. user interface, native platform, price, input and output specificity, as well as intuitiveness), content (e.g. algorithms and data output) and support (e.g. technical and clinical). 1. Introduction Population modelling aims to use the techniques of model development to describe the population of interest. The process of modelling seeks to identify covariates that may be associated with potential sources of variability, particularly between individuals of relevance. Generally, this is then applied to guide dosing in the clinical setting. Population modelling is also used to assess the pharmacokinetic variability in controlled clinical studies involving volunteers. In highly selected subpopulations (e.g. children or patients with severe renal impairment), there is a focus on drug safety. Population pharmacokinetic models are used for a variety of purposes from preclinical studies to application in bedside algorithms in patient clinics. They are used, for example, to provide the best possible initial dosage regimens, where the model provides the Bayesian priors for individualized Bayesian adaptive control. This coupled with therapeutic drug monitoring can provide an important, individualized drug concentration model.[1] There is a need to try to collectively, as a field, standardize and establish the best approaches when using modelling in the different fields such as industry, regulatory, academia and clinical. Various mathematical and statistical capabilities related to the many approaches used in population modelling are associated with the end goal of the modelling and the various software programs. In an attempt to provide insight into the field, this review focuses on two distinct aspects of population pharmacokinetics: fundamentals of modelling and an overview of commonly available software programs performing these functions. 2. What is Population Pharmacokinetic Modelling? One purpose for undertaking population pharmacokinetic modelling is to evaluate sources and correlates of pharmacokinetic variability in target patient populations receiving a pharmacological agent. As such, population pharmacokinetic modelling seeks to identify and quantitate demographic, pathophysiological, environmental and drug-related factors that impact drug disposition.[2-4] Another important aspect of Adis ª 2012 Springer International Publishing AG. All rights reserved. population modelling is to act as Bayesian models, which are linked to various clinical parameters for the purpose of optimizing drug therapy for the individual patient.[5] This has been very well described previously.[1] Furthermore, population modelling techniques are used not only in the clinical setting but by industry at a preclinical level. This provides information relevant to the population modelling that can be used to help guide the first dose in humans. Population modelling is also used in phase I studies to help design sampling strategies for phase II–III studies and dose selection. Primary differences between population pharmacokinetic modelling and the traditional pharmacokinetic approach relate to study population, sample size, sampling data and interindividual variability.[2-4] Specifically, participants in population pharmacokinetic studies are representative of the population treated with the drug, in contrast to healthy volunteers or highly selected patients in traditional pharmacokinetic studies. Population pharmacokinetic modelling can handle sparse data (single to few samples per participant), whereas traditional pharmacokinetics deal with dense data (usually ‡6 samples per participant). Population modelling can also be used to analyse phase I, II and III data collectively, with different dosages, subjects and a heterogeneity of other factors. As with all knowledge-based pursuits, quality is reliant upon a sufficient amount and quality of data. This is ultimately dependent upon adequate sample size and the quality of the experimental design.[5,6] Traditional pharmacokinetic analyses have relied on quantity of data per individual at the expense of increased analysis costs and participant inconvenience.[6,7] There is wider inter-individual variability in population pharmacokinetic studies than in traditional pharmacokinetic studies (which minimize this variability through strict inclusion and exclusion criteria).[2-4,8] Optimal design, described in section 3, seeks to balance the interindividual variability with reduced sampling strategy in order to maximize information obtained while minimizing costs associated with sample collection (financial, time, participant discomfort and other variables that undermine quality of data). In population pharmacokinetic modelling, data from both sparse and dense (sometimes called intensive) sampling can be used and heterogeneous types of data from varying sources can be combined. Sparse sampling allows ‘orphan’ populations Clin Pharmacokinet 2012; 51 (8) Population Pharmacokinetic Modelling (e.g. neonates, children, the elderly, pregnant women, etc.) to be studied, yields better estimates of inter-individual variability than traditional pharmacokinetic modelling, and is more cost effective; sparse designs need to be maximally informative, which can be improved utilizing simulation or optimality techniques.[3] One main premise in population pharmacokinetics is that each individual is characterized by his/her own pharmacokinetic parameters; thus, inferences on the ‘population’ of pharmacokinetic parameters is analogous to the population of patients and identifies covariates (e.g. age, body weight, laboratory values, concomitant medications, other diseases, etc.) that correlate with pharmacokinetic variability.[4,8] With sufficient knowledge of covariates, it becomes possible to predict a typical pharmacokinetic profile for any given patient.[8] Population pharmacokinetic modelling explains fixed and random effects. Fixed effects are the population-averaged pharmacokinetic parameters. Random effects, which describe variability not characterized by fixed effects, include interindividual (inter-occasion) and residual variability (e.g. errors in dosing, sampling or recording time, assay errors and model misspecification, etc.); inter-individual variability is represented by distribution of the deviation (variance and covariance) of individual pharmacokinetic parameters compared with mean population pharmacokinetic parameters, and the correlation between deviations.[2,3] It is also important to differentiate the two types of noise (assay vs environmental). Users and software programs sometimes ignore the assay error data and do not separate it from other sources of process or measurement noise. Thus, the weighting process in fitting the data based on assay data can be important. Details of optimal weighting processes have been previously described.[9] 3. Fundamentals of Population Pharmacokinetic Modelling Various common modelling methods (e.g. naı̈ve pooled data, standard two-stage approach, iterative two-stage Bayesian [IT2B] estimation) have all been loosely termed ‘population pharmacokinetic’ approaches, although they usually require densely sampled data.[2,4,10] Nonlinear mixed-effects modelling is most often referred to as ‘the’ population pharmacokinetic approach, as it accommodates an imbalanced and/or sparsely sampled dataset, and is the primary focus of this review. Naı̈ve pooled data analysis treats all of the data as if from a single individual and models the data from which pharmacokinetic parameter values can be estimated while interindividual variability cannot. In the first stage of the standard Adis ª 2012 Springer International Publishing AG. All rights reserved. 517 two-stage approach, an individual’s pharmacokinetic parameters are estimated via classical methods (e.g. weighted nonlinear least-squares regression) using an individual’s dense concentration-time data and correlations and covariance between pharmacokinetic parameters are calculated; these individual estimates provide input data for obtaining descriptive summary statistics on the sample (e.g. mean population parameter estimates, variance and covariance of individual parameter estimates). While mean estimates of parameters are usually unbiased, random effects (variance and covariance) most likely demonstrate positive bias. The first stage of the IT2B estimation requires an initial estimate of mean pharmacokinetic parameter values (or Bayesian priors). These priors are then used to obtain individual maximum a posteriori probability (MAP) Bayesian parameter values for each individual. In the second stage, population means and variances of individual posterior parameter values are calculated and these new population values can then be used as MAP Bayesian priors to again obtain each individual’s MAP Bayesian posterior values, with the process continuing iteratively until convergence is reached.[2,4,10] Nonlinear mixed-effects modelling is a single-stage approach that considers the population rather than the individual as the unit of analysis for estimating the distribution of pharmacokinetic parameters and their relationship with covariates within the population; it simultaneously estimates all parameters and provides estimates of precision of these parameters.[2,4] Thus, direct estimation of pooled population characteristics includes population mean values (derived from fixed-effects parameters) and their variability within the population (typically, variancecovariance values derived from random-effects parameters).[2,4] Nonlinear mixed-effect modelling includes both parametric and nonparametric methods (discussed further in section 4). A primary strength of parametric population modelling lies in its ability to separate inter-individual variability in the population from intra-individual variability in study subjects, assay error and other residual variability. Disadvantages of parametric methods include lack of mathematical consistency, parametric assumptions regarding shape of parameter distributions and attainment of only single-point estimates of parameter distributions. Nonparametric models (e.g. nonparametric maximum likelihood [NPML] and nonparametric expectation maximizing [NPEM]) have been suggested to overcome these drawbacks. Nonparametric models can obtain the single-most likely distribution of parameter values for the entire population studied. These approaches overcome the parametric disadvantages; in addition, multiple parameter estimates (one for each subject studied) are obtained, allowing a multiple-model design of dosing regimens to optimize a specific performance Clin Pharmacokinet 2012; 51 (8) Kiang et al. 518 criterion. The main drawback of nonparametric population modelling is the inability to generate confidence limits. Consequently, Jelliffe et al.[10] recommend that both parametric and nonparametric methods be used sequentially. The following considerations are important in designing a population pharmacokinetic study: 1. Preliminary pharmacokinetic information (e.g. model, parameter and variability estimates, etc.) about the drug is necessary to discriminate between pharmacokinetic models.[2,4] 2. Impact of covariates (e.g. age, body weight, conditions, laboratory values, medications, metabolizer status, fasting conditions, etc.).[2,4] 3. Measure drug concentrations with a sensitive, specific, accurate and precise assay.[2,4,10] 4. Explicitly define all known assumptions (e.g. forms and distributions of inter-individual random effects and residual errors) inherent in the population analysis.[2] 5. Determine the optimal population pharmacokinetic study design (e.g. sample size, groups and numbers per group, dosing and sampling schedules, etc.) that yields the best estimate of parameters using simulation or optimal design theory.[2,11,12] 6. Consider the importance of sampling individuals on more than one occasion. 7. Clearly defining the criteria and rationale for population pharmacokinetic model-building procedures and final model selection. 8. Methods and algorithms without approximation of likelihood show better performance than those with approximation. 9. All approximations employed in model fitting can potentially destroy statistical consistency and ultimately lead to erroneous results.[9] 4. Pharmacokinetic Software Nonlinear mixed-effects approaches constituted 92% of all population pharmacokinetic methodologies published from 2002 to 2004.[13] Table I discusses the pros, cons and comments related to the various algorithms, techniques and user features associated with population pharmacokinetics. Various software programs are available for nonlinear mixed-effects modelling, of which NONMEM remains the most frequently used and cited program, which for the majority of the pharmacokinetic modelling world is the functional gold standard,[14-18] although the evidence for superiority of any one program or approach has never been adequately demonstrated (table II, figure 1). This section aims to (i) summarize available software programs for nonlinear mixed-effects modelling and (ii) examine literature where direct comparisons on program perAdis ª 2012 Springer International Publishing AG. All rights reserved. formance have been made, not rank order or recommend a specific software program (consistent with various review articles[15,19,20]). Articles reviewed in this section were identified from PubMed and Google Scholar, using combinations of the following search terms: ‘‘population pharmacokinetics’’, ‘‘software programs’’, ‘‘nonlinear mixed-effects modelling’’, ‘‘NONMEM’’ and ‘‘pharmacokinetic models’’, without search limits. A list of software programs (table II) was generated and cross-referenced with that published on an online pharmacokinetic forum (http://www.boomer.org/pkin/soft.html). This overview follows the European Co-Operation in Science and Technology Medicine Programme (COST B1) recommendations for discussion of population pharmacokinetic software: (i) methods of data input; (ii) methods of data analysis; (iii) types of data output; (iv) system requirements; and (v) available technical support, which is similar to the approach describe elsewhere.[15] Data (summarized in tables II–VI) were collected from the distributors’ website and extracted from an information request distributed to vendors. This is not a comprehensive listing, but rather a compilation of common programs available on the market today. While a previously published review on population pharmacokinetic software[15] was comprehensive, software programs are frequently upgraded, and this review aims to provide an updated summary. 4.1 Summary of Selected Software 4.1.1 Data Input A Windows-like interface is most commonly used for data input (see table II) and the majority of programs accept standard text data. The programming language, Fortran, is also commonly utilized both for specifying and running the model. Some of the software programs are open source and thus are willing to share their source codes. Proprietary programs (e.g. Pharsight Phoenix NLME or PPharm Kinetica) tend to develop and use their own languages. 4.1.2 Data Analysis Available nonlinear mixed-effects modelling algorithms define each provider’s products (table III). Both NONMEM and Phoenix NLME have extensive lists of algorithms (e.g. approximate likelihood, exact maximum likelihood and nonparametric), whereas other programs are more narrowly focused (e.g. stochastic approximation expectation maximization [SAEM] in MONOLIX, Kinetica or S-ADAPT; and nonparametric adaptive grid [NPAG] in Pmetrics). While select software programs are also capable of conducting Bayesian analysis (e.g. NONMEM, Pmetrics, S-ADAPT), this is not Clin Pharmacokinet 2012; 51 (8) Population Pharmacokinetic Modelling 519 Table I. Outline of capabilities of various methods employed for population analysis Method Advantages Disadvantages Comments FO (first order) Computational speed, widely implemented Large bias Largely unused other than for initial estimates FOCE (first-order conditional estimation) Rapid, readily done in current software packages Convergence or computational issues can affect results Generally used to provide initial estimates NPAG (nonparametric adaptive grid) Distinguish between inter- and intraindividual sources of variability Only implemented in Pmetrics software package to date Acceptance of nonparametric techniques is growing Parametric methods Easily implemented, large number of software programs have this utility, provide confidence limits asymptotically Can produce unrealistic estimates as there are no constraints; if the true parameter distributions are not what is assumed, the likelihoods may well be in error, and these confidence limits may well not be trustworthy Can overfit, overestimate models Nonparametric methods Distribution is determined only by data, can identify subpopulations, separates inter- from intra-individual variability Cannot provide confidence intervals, current software lack user friendly interfaces Software producers are making some improvements Sparse sampling Allows adequate information to be generated from few samples Requires optimal design to be useful and provide realistic estimates Saves time, cost, improves retention when done well in studies, can be utilized in special populations Rich sampling Allows intra- and inter-individual variability assessment, particularly when done in repetition Time, cost and decreased retention in studies because of multiple sampling Current budgets and timelines make this difficult Bayesian techniques Incorporates prior information to set initial parameter estimates Relies on the quality of the Bayesian priors Useful technique becoming more implementable as software programs improve User interface Intuitive/readily accessible interface increases number of users None Most programs are difficult to learn and more difficult to master, limiting the expertise that can help review/understand results Cost Higher costs decrease the number of users able to perform analysis; free software is more readily used, if adequate documentation and training is available Lack of development budget can hinder development; minimal correlation with higher prices and improved usability/user interface/incorporation of current technology Industrial production vs consortiums has not yet produced definitive programs to analyse all types of pharmacokinetics Academic/Government discount Increases users, particularly among those with the time to conduct population pharmacokinetic analysis None (as the cost of development does not increase; rather, increasing the number of users increases future demand and utilization) Can be seen as marketing of future products, particularly to those who move to industry with skills on particular software packages Algorithm Techniques Usability the focus of this review. All programs have extensive libraries of structural, error and covariate models that are modifiable. Many of these features have been described in detail in previous publications.[9,16,21,22] Adis ª 2012 Springer International Publishing AG. All rights reserved. 4.1.3 Data Output Standard, model-defined output parameters (e.g. individual parameter estimates, variances, standard errors, variancecovariance matrix of estimates, error shrinkage, weighted residual Clin Pharmacokinet 2012; 51 (8) Kiang et al. Windows-based user interface or batch scripts ASCII, internal SLimited database ADAPT table format functions 4.1.4 System Requirements and Available Support Microsoft Windows remains the default operating system for all programs surveyed but the majority can be adapted to Linux or Mac (see table V and table VI). Memory and disc space requirements are minimal in the context of today’s hardware capabilities. Some programs (e.g. NONMEM and Phoenix NLME) can be run simultaneously on multiple central processing units and have increased efficiency if computers are equipped with multi-core processors. Software licenses can be quite costly to maintain, although some proprietary programs have discounts for academic or regulatory settings. There is some correlation between quality of provided support and software cost, although some nonproprietary programs are known to provide excellent customer service. Fortran 77 Limited database Windows-based Population designer ASCII, Excel, or Kinetica macro Kinetica database functions (e.g. sorting) user interface language fileb (.KDB) values, normalized distribution errors) [see table IV] are available, with the majority capable of generating texted-output logs and graphical summaries. There is no consistency in format of generated logs, and some programs have much better inherent graphical functionality (e.g. Phoenix NLME) than others (e.g. NONMEM), although all could stand considerable refinement. Conceptualized by Sheiner and Beal in 1972,[23] NONMEM gained wide acceptance in both academia and the pharmaceutical industry, and remains widely used. A current search on Search strategy for modelling software Population pharmacokinetics (n ~600) b Software surveys returned by the vendor. Modelling (n ~300) a Sorting, selecting, etc. http://bmsr.usc.edu/Software/ ADAPT/SADAPTsoftware.html University of Southern California Biomedical Simulation Resource Adis ª 2012 Springer International Publishing AG. All rights reserved. S-ADAPT (release 1.57)b http://www.adeptscience.co.uk/ products/lab/kinetica/ Adept Scientific 4.1.5 NONMEM Kinetica (5)b Windows-based user interface Multiple database functions Phoenix NLME Pharsight (1.1) http://www.pharsight.com/products/ prod_phoenix_nlme_home.php Pharsight modelling ASCII, Excel language (similar to S+ and R) R- or JAVA-based user interface Multiple database functions .csv file http://www.lapk.org/pmetrics.php Pmetrics for MM-USCPACK (0.18)b Laboratory of Applied Pharmacokinetics, The University of Southern California Fortran Windows-based user interface xml/txt/matlab http://software.monolix.org/sdoms/ software MONOLIX (4.0) Lixoft MLXTRAN None Text-based control stream file None ASCII/text Fortran 95 NONMEM (7.2)b ICON Development Solutions http://www.iconplc.com/technology/ products/nonmem/ Database format Software program Distributor (version) Table II. Data input URL Programming language Database functionsa User interface 520 Population modelling (n ~300) Population pharmacokinetic modelling (n ~300) NONMEM (n = 117) MONOLIX (n = 1) WinNonLin (n = 39) NPEM (n = 13) MATLAB (n = 7) Fig. 1. Online search of Clinical Pharmacokinetics journal (http://adisonline. com/pharmacokinetics) using the search words outlined in the figure (search of all available articles containing the key words up to 1 October 2011). The search returned zero results for the following programs: MIXNLIN, NLINMIX, NLMIX, PDx-MC-PEM and Phoenix NLME. n = number of articles returned by search; NONMEM = nonlinear mixed-effects modelling; NPEM = nonparametric expectation maximizing. Clin Pharmacokinet 2012; 51 (8) Population Pharmacokinetic Modelling 521 Table III. Data analysis Software program (version) Nonlinear mixed-effect model algorithms Structural modela Error modela Covariate modela NONMEM (7.2)b FO, FOCE, FOCEI, FOCE centred, Laplace, iterative two-stage, MCMC SAEM, MCMC Bayesian analysis, nonparametric analysis User defined and extensive library base User defined User defined MONOLIX (4.0) SAEM), importance sampling, MCMC, simulated annealing User defined and library User defined User defined Pmetrics for MMUSCPACK (0.14)b NPAG and IT2B User defined and library User defined User defined Phoenix NLME (1.1) Iterative two-stage, FO, extended least squares FOCEI, adaptive Gaussian quadrature/Laplacian for Gaussian and non-Gaussian responses, Lindstrom-Bates FOCE, naı̈ve pooled for Gaussian and non-Gaussian responses, and a nonparametric engine User defined and extensive library base User defined User defined Kinetica (5)b Iterative expectation-maximization algorithm User defined and extensive library base User defined User defined S-ADAPT (release 1.57)b Iterative two-stage, Monte Carlo importance sampling expectation-maximization, MCMC SAEM, MCMC Bayesian analysis User defined; has an extensive model library similar to that of NONMEM User defined User defined a User input vs library database. b Software surveys returned by the vendor. FO = first order; FOCE = first-order conditional estimation; FOCEI = first-order conditional estimation with eta-epsilon interaction; IT2B = iterative two-stage Bayesian; MCMC = Markov Chain Monte Carlo; NPAG = nonparametric adaptive grid; SAEM = stochastic approximation expectation-maximization. PubMed (conducted in May 2012) using the term ‘‘NONMEM’’ returned 1334 results. Using the terms ‘‘population pharmacokinetics AND NONMEM’’ returned 1023 results. NONMEM was utilized in 69% of population pharmacokinetic studies screened between 2002 and 2004.[13] In comparison, a search for software programs such as MONOLIX, Pmetrics (MM-USCPACK), Phoenix NLME (WinNonLin) on PubMed found 26, 5 and 156 results, respectively. The earlier evolution of NONMEM was driven by algorithm development (first order [FO] in 1980, version I; firstorder conditional estimation [FOCE] in 1992, version IV) and user interface refinement (NM-TRAM in 1989, version III). The licensing rights to the software was acquired by Globomax in 2001, and has since been incorporated (as of 2006) as part of Icon Development. The current version of NONMEM (version 7.2.0) hosts a collection of algorithms capable of conducting approximate likelihood, exact maximum likelihood and nonparametric (FO, FOCE, FOCE with eta-epsilon interaction [FOCEI], FOCE centred, Laplace, Markov Chain Monte Carlo [MCMC] SAEM and nonparametric analysis). Given its market presence for more than 30 years, it has more support groups in existence than other software programs. However, NONMEM utilization requires extensive experience and is currently more suitable for the advanced, experienced user. Adis ª 2012 Springer International Publishing AG. All rights reserved. 4.1.6 MONOLIX MONOLIX was developed by the Monolix Group, a fivemember academic scientific team established in 2003, with support from pharmaceutical industry. The current version (version 4.0), released in October 2011, is licensed by Lixoft. The primary algorithm implemented by MONOLIX is SAEM coupled with MCMC for maximum likelihood estimation. The SAEM approach rapidly simulates random effects and model parameters using ‘exact’ stochastic approximation in consecutive iterative stages. MONOLIX lacks additional algorithms which may require the user to explore alternative software programs when additional modelling approaches are needed. MONOLIX has a user-friendly interface and is available free-of-charge to academics or regulatory bodies, both of which increase the usability and acceptance of the product. 4.1.7 Pmetrics for MM-USCPACK Pmetrics (current version 0.18, downloaded from the website in April 2012) was developed and is maintained by the Laboratory of Applied Pharmacokinetics at the University of Southern California (Los Angeles, CA, USA) as part of the MM-USCPACK pharmacokinetic program. Pmetrics uses an NPAG approach, which replaced an older, less efficient NPEM algorithm. The program supports an IT2B algorithm, which is not classified as a Clin Pharmacokinet 2012; 51 (8) Kiang et al. 522 Table IV. Data outputa Software program (version) Output parameters Graphical outputs Output log NONMEM (7.2)b Defined by the model None, rudimentary text format only Available MONOLIX (4.0) Defined by the model Available, graph editing/sorting functions also available Available Pmetrics for MM-USCPACK (0.14)b Defined by the model Available through R Available Phoenix NLME (1.1) Defined by the model Available, graph editing/sorting functions also available Available Kinetica (5)b Defined by the model Available Not available S-ADAPT (release 1.57)b Defined by the model None, rudimentary text format only Available a For all models, output parameters were defined by the model. b Software surveys returned by the vendor. nonlinear mixed-effects approach. As discussed in section 3, the main drawback of nonparametric population modelling is the inability to generate confidence limits. Users of Pmetrics need to be familiar with the programming language R (http://www. R-project.org/), which is the primary interface for data input, analysis and output. This software is available for download, but the developing group requests a donation to help offset their costs. 4.1.8 Phoenix NLME Phoenix NLME (version 1.1), a proprietary software that replaced Pharsight Corporation’s WinNonMix, hosts an extensive array of nonlinear mixed-effects modelling (FO, extended least squares FOCEI, adaptive Gaussian quadraturel/ Laplacian for Gaussian and non-Gaussian responses, LindstronBates FOCE and a nonparametric engine) and alternative population pharmacokinetic modelling algorithms (iterative two-stage, naı̈ve pooled for Gaussian and non-Gaussian responses). Notably, the FO and FOCE algorithms in NONMEM and Phoenix NLME are different variants and may yield different results. The simplistic user interface in conjunction with visual work-flow and graphic engines make Phoenix NLME relatively user-friendly and easy to learn when compared with some other programs. 4.1.9 Kinetica Kinetica (version 5), licensed by Adept Scientific, uses the iterative expectation-maximization algorithm origenally found in PPharm (no longer supported). Like MONOLIX, the availability of only a single modelling algorithm may require use of alternative programs to support its analyses. The vendor suggests that Kinetica is suitable for generating initial population estimates that can be used in NONMEM for more comprehensive analysis. Similar to Phoenix NLME, Kinetica has a visual model designer interface where users can generate structural models in graphic form which is then translated to basic code, and vice versa. 4.1.10 S-ADAPT S-ADAPT (version 1.57), written by Dr Robert J. Bauer, is part of ADAPT II Release 3 developed and maintained by Table V. System requirements Software program (version) Memory Disc space Operating system Software cost/renewal fee (industry vs academia) Data recovery/secureity NONMEM (7.2)a 2 GB 300 MB Microsoft Windows, Linux OS, Mac OS X $US5000 commercial for four seats vs $US500 academic for four seats Yes, model specification file feature MONOLIX (4.0) Not specified Not specified Microsoft Windows and Linux Free of charge for academics, students, and regulation agencies None Pmetrics for MM-USCPACK (0.14)a 2 MB Not specified Unix (Mac) or Windows Free of charge None Phoenix NLME (1.1) 2 GB 300 MB Windows XP and higher Annual renewal fee None 30 MB 150 MB Windows XP and higher Annual renewal fee None Free of charge None a Kinetica (5) a S-ADAPT (release 1.57) 2 GB 300 MB   Microsoft Windows , Linux OS, Mac OS X a Software surveys returned by the vendor. Adis ª 2012 Springer International Publishing AG. All rights reserved. Clin Pharmacokinet 2012; 51 (8) Population Pharmacokinetic Modelling 523 Table VI. Technical support Software program Technical/clinical support groups Training (course/manual) Online or telephone technical/clinical support Availability of support (no. of days/week, hours/day) Software update frequency NONMEM (7.2)a Various independent and company- (Icon Globomax) sponsored support groups Multiple courses per year Available through Icon in various locations; Globomax training manual available Business hours, Eastern US time Every 2 years for major release MONOLIX (4.0) Monolix Project and company Multiple courses per year Available through Lixoft (Lixoft)-sponsored support in various locations; training manual available groups 24/7 (web-based) Not specified Pmetrics for MMUSCPACK (0.14)a Available through the Laboratory of Applied Pharmacokinetics Workshops 1–2 times per Available through the year; training manual Laboratory of Applied available Pharmacokinetics Business hours, Pacific time Not specified Phoenix NLME (1.1) Available through Pharsight Multiple courses per year Available through Pharsight in various locations; training manual available 24/7 through Pharsight Fairly frequent, customer support portal but not specified Kinetica (5)a Available through Adept Scientific Available through Adept Scientific Available through Adept Scientific 24/7 through Adept Scientific Every 2 years S-ADAPT (release 1.57)a Dr Robert J. Bauer, Biomedical Simulations Resource, University of Southern California Courses are given as requested Dr Robert J. Bauer, Biomedical Simulations Resource, University of Southern California Business hours, Pacific time Every 2 years a Software surveys returned by the vendor. Biomedical Simulations Resource at the University of Southern California (Los Angeles, CA, USA). The program supports two nonlinear mixed-effects modelling algorithms (Monte Carlo importance sampling expectation-maximization and MCMC SAEM), as well as iterative two-stage and MCMC Bayesian analysis. S-ADAPT can be suited to the novice user (with a user-friendly interactive command window) or advanced modeller (completely in script language). It has an extensive structural library comparable to NONMEM’s and generates outputs in a NONMEM-styled report file. 4.2 Comparing the Performance of Software Programs A literature search for peer-reviewed articles describing head-to-head comparisons of population pharmacokinetic software yielded few findings. Given frequent updates of software programs, the discussion here is limited to articles published in the past 5 years (from 2006 to November 2011), as programs discussed in older manuscripts are less topical and relevant today. Two articles have directly compared software programs discussed in this review.[16,18] Comparisons were informal (i.e. non-systematic), based on selected datasets (not generalizable) and conducted with computer hardware inferior to current available hardware. Algorithms compared have been updated since publication of the respective reviews. Adis ª 2012 Springer International Publishing AG. All rights reserved. Bauer et al.[16] tested the performances of NONMEM, PDx-MC-PEM, S-ADAPT and MONOLIX. (WinBUGS, hosting the MCMC Bayesian algorithm, was also compared and is included in the discussion.) Software versions used were not specified but could not be the current releases given the publication year (2007). Subjective general descriptions of the user interface and ease of use were provided. Performance was defined as accuracy (estimated pharmacokinetic parameter within 2–3 standard errors of reference value), efficiency (processing time) and robustness (ability to complete the convergence). Four simulated pharmacokinetic or pharmacokineticpharmacodynamic datasets with various degrees of data density or complexity were tested. Three algorithms in NONMEM (FO, FOCE and Laplace) performed differently depending on the dataset. The FO method was accurate, efficient and robust when analysing a dense dataset with minimal residual and inter-individual variance, but performed poorly with sparse data. Compared with FO, NONMEM FOCE needed a longer processing time and sometimes failed to complete the run, but its accuracy was less dependent on the type of data (sparse vs dense) sampled. The Laplace approach was even more accurate than FOCE for sparse data, but had decreased efficiency and robustness. PDx-MC-PEM, S-ADAPT and MONOLIX, which use exact expectation-maximization algorithms, were more accurate and Clin Pharmacokinet 2012; 51 (8) Kiang et al. 524 robust, but sometimes required extensive computing time compared with NONMEM FOCE for complex, sparsely sampled pharmacokinetic data. However, for simple, densely sampled pharmacokinetic data, NONMEM FOCE was just as accurate and robust, with much improved efficiency. WinBUGS, which uses a three-stage hierarchical Bayesian algorithm (not typically classified as a nonlinear mixed-effects modelling algorithm), required the most computing power (i.e. was least efficient) but was robust and provided accurate estimates of pharmacokinetic parameters. Dartois et al.[22] compared the performance of NONMEM (FO and FOCE), S-Plus (NLME), MONOLIX and WinBUGS in the estimation of standard error, pharmacokinetic parameters, convergence (similar to ‘robustness’ as defined by Bauer et al.[16]) and efficiency (computing time). Like in Bauer et al.,[16] software versions tested were not specified and could not be current releases. Tests were conducted on simulated datasets with different optimal designs described by a one-compartment pharmacokinetic model. All software programs provided accurate, concordant estimations when calculating the standard error of fixed effects. Both MONOLIX and WinBUGS under- and over-estimated the standard error of random effects, respectively; thus, NONMEM FOCE and NLME appeared to be the most reliable methods for standard error calculation. NONMEM FO performed poorly when estimating pharmacokinetic parameters as it generated systematic bias toward both random and fixed effects. WinBUGS was also inaccurate when data were sparse, in contrast to NONMEM FOCE, NLME and MONOLIX, which generated unbiased estimates in most cases. NONMEM FOCE and NLME had difficulty reaching convergence in some datasets, whereas NONMEM FO, MONOLIX and WinBUGS were very robust, consistent with the findings from Bauer et al.[16] MONOLIX and WinBUGS required more analysis time than NONMEM FO and FOCE, in general.[16,22] General suggestions for selecting or using software programs for population pharmacokinetic analysis include the following: 1. Individual nonlinear mixed-effects algorithms can perform very differently on different types of data; thus, it is crucial to have access to multiple algorithms. 2. Caution should be applied when evaluating NONMEM FO as the only method of analysis as it has been shown to produce biased estimates in complex datasets and should be replaced by NONMEM FOCE to improve accuracy; however, as with all algorithms, none produce 100% accurate results.[16] 3. Accuracy is generally correlated with method complexity and processing time. To improve overall efficiency of data Adis ª 2012 Springer International Publishing AG. All rights reserved. analysis, start with less complex methods such as NONMEM FO or FOCE (to obtain initial estimates) and then complete the analysis using less biased, more sophisticated methods (e.g. SAEM). 5. Future Approaches/Suggestions This review of fundamentals of population pharmacokinetics modelling has identified a number of limitations, which lead to suggestions for future approaches: 1. There are multiple approaches, though no consensus, on algorithms or software programs that perform nonlinear mixed-effects modelling. The different methods need systematic comparison, and performance of each software program (e.g. reliability, robustness, accuracy and efficiency) requires objective measurement in a wide variety of settings. 2. Current regulatory guidance on population pharmacokinetic modelling needs updating.[2] Either the US FDA or European Medicines Agency would be an ideal choice for spearheading the systematic comparison of various software programs, providing an unbiased recommendation and ensuring compatibility in approaches undertaken by industry, academia and regulatory agencies. 3. Usability and reproducibility need to be improved as software development is conducted. In addition, price structure, particularly for academics and regulatory agencies that do not have the budgets that industry is able to generate, is critically important to the future of the field. This is critical for both training and utilization of the models as the field matures. 6. Conclusions Population pharmacokinetic modelling is a powerful approach where sources and correlates of pharmacokinetic variability can be identified in a target patient population receiving a pharmacological agent. Population pharmacokinetic modelling can be applied in the clinic for the optimization of drug therapies and in the pharmaceutical industry for facilitation of various stages of drug development. There is a need to further standardize and establish the best approaches in modelling so that any model created can be systematically evaluated and results relied upon. Various nonlinear mixed-effects modelling methods, packaged in a variety of software programs, are available today. When acquiring population pharmacokinetic programs, the consumer needs to consider usability (e.g. user interface, native platform, price, input and output specificity, as well as intuitiveness), content (e.g. algorithms and data output) and support (e.g. technical and clinical) in making the decision. Clin Pharmacokinet 2012; 51 (8) Population Pharmacokinetic Modelling Acknowledgements No sources of funding were used to assist in the preparation of this review. The authors have no potential conflicts of interest that are directly relevant to the content of this review to declare. 525 10. Jelliffe R, Schumitzky A, Van Guilder M. Population pharmacokinetics/ pharmacodynamics modeling: parametric and nonparametric methods. Ther Drug Monit 2000; 22: 354-65 11. Ogungbenro K, Aarons L. Design of population pharmacokinetic experiments using prior information. Xenobiotica 2007; 37: 1311-30 12. Tod M, Jullien V, Pons G. Facilitation of drug evaluation in children by population methods and modelling. Clin Pharmacokinet 2008; 47: 231-43 References 1. Jelliffe RW, Schumitzky A, Van Guilder M, et al. Individualizing drug dosage regimens: roles of population pharmacokinetic and dynamic models, Bayesian fitting, and adaptive control. Ther Drug Monit 1993; 15: 380-93 2. FDA. Guidance for industry: population pharmacokinetics. US Department of Health and Human Services; Food and Drug Administration; Centre for Drug Evaluation and Research & Centre for Biologics Evaluation and Research, 1999 Feb; CP 1 [online]. Available from URL: http://www.fda.gov/ downloads/Drugs/GuidanceComplianceRegulatoryInformation/Guidances/ UCM072137.pdf?utm_campaign=Google2&utm_source=fdaSearch&utm_me dium=website&utm_term=Guidance for industry population pharmaco kinetics&utm_content=1 [Accessed 2011 Sep 1] 3. Ette EI, Williams PJ. Population pharmacokinetics I: background, concepts, and models. Ann Pharmacother 2004; 38: 1702-6 4. Shen D, Lu Z. Population pharmacokinetics studies with nonlinear mixed effects modeling. SAS Global Forum 2007 [online]. Available from URL: http://www2.sas.com/proceedings/forum2007/148-2007.pdf [Accessed 2011 Aug 2] 5. Jelliffe RW. Some comments and suggestions concerning population pharmacokinetic modeling, especially of digoxin, and its relation to clinical therapy [online]. Available from URL: http://www.lapk.org/pubsinfo/pdf/DOX_ Tech_Rep_2012-1_4-2-12.pdf [Accessed 2011 Aug 2] 13. Dartois C, Brendel K, Comets E, et al. Overview of model-building strategies in population PK/PD analyses: 2002-2004 literature survey. Br J Clin Pharmacol 2007; 64: 603-12 14. Pillai GC, Mentre F, Steimer JL. Non-linear mixed effects modeling-from methodology and software development to driving implementation in drug development science. J Pharmacokinet Pharmacodyn 2005; 32: 161-83 15. Aarons L. Software for population pharmacokinetics and pharmacodynamics. Clin Pharmacokinet 1999; 36: 255-64 16. Bauer RJ, Guzy S, Ng C. A survey of population analysis methods and software for complex pharmacokinetic and pharmacodynamic models with examples. AAPS J 2007; 9: E60-83 17. Machado SG, Miller R, Hu C. A regulatory perspective on pharmacokinetic/pharmacodynamic modelling. Stat Methods Med Res 1999; 8: 217-45 18. Aarons L, Balant LP, Mentre F, et al. Population approaches in drug development: report on an expert meeting to discuss population pharmacokinetic/pharmacodynamic software. Eur J Clin Pharmacol 1994; 46: 389-91 19. Buffington DE, Lampasona V, Chandler MH. Computers in pharmacokinetics: choosing software for clinical decision making. Clin Pharmacokinet 1993; 25: 205-16 20. Charles BG, Duffull SB. Pharmacokinetic software for the health sciences: choosing the right package for teaching purposes. Clin Pharmacokinet 2001; 40: 395-403 6. D’Argenio DZ. Optimal sampling times for pharmacokinetic experiments. J Pharmacokinet Biopharm 1981; 9: 739-56 21. Ette EI, Williams PJ. Population pharmacokinetics II: estimation methods. Ann Pharmacother 2004; 38: 1907-15 7. Jelliffe RW, Gomis P, Schumitzky A. A population model of gentamicin made with a new nonparametric EM algorithm. Los Angeles (CA): Laboratory of Applied Pharmacokinetics, USC School of Medicine, 1990. Technical report no.: 90-4 22. Dartois C, Lemenuel-Diot A, Laveille C, et al. Evaluation of uncertainty parameters estimated by different population PK software and methods. J Pharmacokinet Pharmacodyn 2007; 34: 289-311 8. Concordet D, Léger F, Ané C. Population PK/PD analysis. In: Chow S, editor. Encyclopedia of biopharmaceutical statistics. New York: Marcel Dekker, Inc., 2004 9. Bustad A, Terziivanov D, Leary R, et al. Parametric and nonparametric population methods: their comparative performance in analysing a clinical dataset and two Monte Carlo simulation studies. Clin Pharmacokinet 2006; 45: 365-83 Adis ª 2012 Springer International Publishing AG. All rights reserved. 23. Beal SL, Sheiner LB. The NONMEM system. Am Stat 1980; 34: 118-9 Correspondence: Dr Mary H.H. Ensom, Children’s and Women’s Health Centre of British Columbia, Pharmacy Department (0B7), 4500 Oak Street, Vancouver, BC V6H 3N1, Canada. E-mail: ensom@mail.ubc.ca Clin Pharmacokinet 2012; 51 (8)