Application of Mixed-Effect Modeling to Improve Mechanistic Understanding and Predictability of Oral Absorption

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List of Papers

This thesis is based on the following papers, which are referred to in the text by their Roman numerals.

I Bergstrand M, Söderlind E, Weitschies W, Karlsson MO. Mechanistic modeling of a magnetic marker monitoring study linking gastrointestinal tablet transit, in vivo drug release. and pharmacokinetics. Clin Pharmacol Ther. 2009 Jul;86(1):77-83. II Bergstrand M, Karlsson MO. Handling Data Below the Limit of

Quantification in Mixed Effect Models. AAPS J. 2009 Jun;11(2):371-80.

III Bergstrand M, Hooker AC, Wallin JE, Karlsson MO, Prediction Corrected Visual Predictive Checks for diagnosing nonlinear mixed-effects models. AAPS J. 2011. [Epub ahead of print] IV Bergstrand M, Söderlind E, Eriksson UG, Weitschies W,

Karls-son MO. A semi-mechanistic model to link in vitro and in vivo drug release for modified release formulations. Submitted.

V Bergstrand M, Söderlind E, Eriksson UG, Weitschies W, Karls-son MO. A semi-mechanistic model for characterization of re-gional absorption properties and prospective prediction of plasma concentrations following administration of new mod-ified release formulations. Submitted.

VI Bergstrand M, Visser SA, Sjödin L, Al-Saffar A, Karlsson MO. Semi-mechanistic PK/PD modeling of Paracetamol and Sulfa-pyridine to characterize pharmacological effects on gastric emp-tying and small intestinal transit. In manuscript.

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Abbreviations

ACAT Advanced compartmental absorption and transit ADAM Advanced dissolution, absorption and metabolism AUC Area under the curve (plasma concentration vs. time) BOV Between occasion variability

(also known as inter-individual occasion IOV) BQL Below the quantification limit

BSV Between subject variability

(also known as inter-individual variability IIV) CAT Compartmental absorption and transit

CI Confidence interval

Cmax Maximum concentration

CV Coefficient of variation

DR Delayed release

DV Dependent variable

ER Extended release

FDA Food and Drug Administration (US)

FO First-order method

FOCE First-order conditional method

GE Gastric emptying

GI Gastro intestinal

HPMC Hydroxypropyl methylcellulose

IDV Independent variable

IPRED Individual model prediction

IR Immediate release

i.v. Intravenous IVIVC in vitro - in vivo correlation LLOQ Lower limit of quantification LOQ Limit of quantification

MAR Missing at Random

MCAR Missing Completely at Random

MMC Migrating Motor Complex

MMM Magnetic Marker Monitoring

MNAR Missing Not at Random

MR Modified release

MTT Mean transit time

NDA Dew drug application

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ΔOFV Difference in OFV; likelihood ratio PCM Paracetamol pcVPC Prediction corrected VPC PD Pharmacodynamic PI Prediction interval PK Pharmacokinetic PPC Posterior predictive check

PRED Population typical model prediction PsN Perl-speaks-NONMEM pvcVPC Prediction and variability corrected VPC RSE Relative standard error

RUV Residual unexplained variability SITT Small intestinal transit time SP Sulfapyridine

USP United States Pharmacopeia

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Introduction

The oral route is and will for, a foreseeable future, be the by far most com-mon way of administering pharmacological substances. This is natural given the convenience that it offers and the fact that the gastro intestinal (GI) tract is a natural site for absorption. Oral administration is, however, far from uncomplicated. Absorption from the GI tract is highly variable for different compounds and formulations both with respect to rate and extent of absorp-tion. Absorption properties do not only vary between substances and formu-lations but also from subject to subject and from time to time. A contributing factor to why absorption differs between different formulations and between and within subjects is that factors involved in absorption vary along the GI tract. Examples of factors that can vary along the GI tract are pH, permeabil-ity and intestinal metabolism. These factors can be especially important for modified release (MR) formulations [1].

Several sophisticated techniques to study in vivo GI transit and regional absorption of pharmaceuticals are available and increasingly used. Examples of such methods are imaging techniques such as, gamma scintigraphy or Magnetic Marker Monitoring (MMM), and local drug administration with remote operated capsules like the Bioperm®_{capsule. Another approach is the}

paracetamol and sulfapyridine double marker method which utilizes ob-served plasma concentrations of the two substances as markers for GI transit. Common for all of these methods is that they generate multiple types of ob-servations e.g. tablet GI position, drug release and plasma concentrations of one or more substances. This thesis is based on the hypothesis that applica-tion of mechanistic computer models could facilitate a better understanding of the interrelationship between such variables.

Pharmacometrics is a young scientific discipline focusing on developing and applying mathematical and statistical computer models to characterize, understand and predict a drug’s pharmacokinetics (PK) and pharmacody-namics (PD). The analysis of data from absorption studies has emphasized the need for methodological development which is also of general interest to pharmacometric research. One general problem in model based evaluation of PK and PD is censoring of data. Non random censoring, such as observa-tions below the quantification limit (BQL), can bias estimation of model parameters and can also hamper the assessment of a model’s predictive per-formance. This issue and a more general issue of diagnosing model perfor-mance have been addressed as part of the thesis.

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Pharmacometrics

In the book Pharmacometrics: The Science of Quantitative Pharmacology, edited by Ene I. Ette and Paul J. Williams, pharmacometrics is defined as “the science of developing and applying mathematical and statistical models to characterize, understand and predict a drug’s pharmacokinetics, pharma-codynamics and biomarker-outcome behavior” [2]. Pharmacometrics origi-nates from the field of pharmacokinetic research. PK is often referred to as “what the body does to the drug” in contrast to PD that is “what the drug does to the body” [3]. Methods to characterize the link between drug expo-sure that is governed by PK and pharmacological response (PD) were an essential key to the emergence of the new scientific discipline. In order to accurately understand and characterize PK and PD relationships over time it can be vital to first describe the baseline response in a healthy or diseased biological system. For this reason also modeling of disease progression (DP) and normal physiological functions like the nature of gastro intestinal transit can be important parts of pharmacometric research. Pharmacometrics hence includes a large variety of applications and is foremost defined by a common goal of facilitating more efficient development and usage of pharmaceuticals by application of mathematical and statistical models. Most pharmacometric research is based on mixed-effects models, which are especially useful in application to heterogeneous biological data by its ability to characterize many sources and levels of variability.

A pharmacometric approach to analyzing data from clinical trials of new investigational drugs has become increasingly more common over the last 10 years. It has been shown to influence the approval of new drug applications (NDAs) to FDA (Food and Drug Administration, US) in more than 70% of the cases when it has been applied and to almost always affect a final labe-ling [4]. FDA and other important stakeholders have highlighted the poten-tial of pharmacometric model-based drug development to help turn around the negative trend of less successful NDAs despite increasing investments in pharmacological research [5-7]. The obstacles for a broader application of pharmacometric principles to drug development are currently under discus-sion and it is likely that we are at the start of a paradigm shift from tradition-al biostatistictradition-al to pharmacometric model based evtradition-aluation as a standard [4, 8, 9]. Five key benefits with a model based approach is (1) better opportuni-ties to utilize longitudinal data over time and multiple response variables in making statistical inference [10, 11] (2) increased possibility to incorporate prior knowledge and pool data across studies [12, 13] (3) possibility to inter-polate between investigated doses, dosage regiments etc., and potentially extrapolate to longer treatment times and/or other target populations [14, 15] (4) facilitation of improved study design by optimal design theory and clini-cal trial simulations [16, 17] and (5) a framework for developing

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individua-lized treatments [18, 19]. How these advantages fit in the circular process of scientific learning is illustrated in Figure 1.

Figure 1. Pharmacometric model based scientific learning. Learning in science is a circular process: A study/experiment is initialized to address one or several missing pieces of information. The design of the study is based on previous knowledge and the observations made according to that design constitute the study data.

Interpretation of study data by statistical summarization and comparison generate new information out of the raw data. By integrating different sources of information from the study with previous information new knowledge is generated. Based on the extended knowledge new studies can be designed to address other pieces of missing information. Advantages with a model based approach to scientific learning are pointed out with “+” in the figure.

The circular knowledge generation and propagation presented in Figure 1 fits well with the learn and confirm paradigm for drug development that was introduced by Lewis Shiner in 1997 [20]. A first cycle can represent a learn-ing phase (hypothesis generatlearn-ing) and a second consecutive cycle the con-firming step.

Information

Knowledge

Study

Data

Execution

Interpretation

Integration

Study design

+ Identify what to study + Design optimization + Trial simulation + Facilitate integration of different sources of information + Inter-/extrapolation + Facilitate mechanistic interpretation + Higher power for statistical inference

Model

+ Individualized dosing + Adaptive design

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Nonlinear mixed-effects models

Mathematical models are based on a set of mathematical equations aimed at describing a system of interest. These models can then be used to explore the structure and behavior of the system. One or more dependent variables (DVs) are described as a function of one or more independent variables (IDVs) and a set of model parameters. Most biological processes are best described with models featuring nonlinear functions. Models featuring such functions are referred to as nonlinear models and are commonly used in pharmacometric research.

Mixed-effects models are models featuring a mixture of fixed and random effects. The fixed effects build up the structural model that describes the population typical response (e.g. a typical plasma concentration vs. time curve). The fixed effects therefore describe the variability in the DVs that can be explained by the available information about the IDVs. The remain-ing unexplained variability is described by random effects, which are divided into several different levels; between subject variability (BSV) with regards to model parameters, residual unexplained variability (RUV) i.e. the residual difference between the model prediction and the observations. There is also within subject variability with respect to model parameters, which often is characterized in the form of between occasion variability (BOV). The ran-dom effects are typically estimated in the form of variances around the popu-lation typical parameter (fixed effect) assuming a normal distribution or some transformation of a normal distribution (e.g. log-normal or logit-transform).

The general structure of a mixed-effects model is expressed as follows:

, , ~ 0, (1)

where yijk is the jth observed dependent variable at occasion k in individual i.

yijk is described by a function of a vector of individual parameters Pik and a

vector of independent variables Xijk. Typical influential independent

va-riables in most pharmacometric models are dose and time but the vector Xijk

can contain also many other important predictors often referred to as cova-riates. A relatively unusual covariate that is explored within this thesis is tablet gastrointestinal position. The εijk describes the difference between the

individual prediction and the observation and is referred to as RUV or resi-dual error. In equation 1 the RUV is expressed as a simple additive term, normally distributed with a mean 0 and variance σ2_{. However, residual error}

models can take many different shapes although the most common once are additive, proportional or a combination of the two.

Assuming a log-normal distribution the individual parameter Pik for the ith

individual at the kth_{occasion can be described by the following expression:}

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In which θ is the typical value (fixed effect) of the parameter P in the studied population, and ηi anb κi are the random effects that describe the differences

between the typical value and the individual parameter with respect to the individual and the occasion, respectively. The exponential implementation of the normally distributed random effects results in a log-normal distribution for the individual parameters Pik. Other parameterizations of the random

effects can be used to apply other shapes of distributions [21].

A key advantage with mixed-effects models is that they can be applied to sparse data and/or combinations of sparse and rich data and still characterize several levels of variability [22, 23]. This is a distinct advantage of the mixed-effects modeling approach over other methods such as naïve pooling and standard two-stage approaches. For this reason nonlinear mixed-effects modeling has become the predominant method of choice for population PKPD modeling.

Equation 1 describes the general structure of mixed-effects models ap-plied to continuous data, however mixed-effects models can also be apap-plied to categorical observations or a combination of continuous and categorical observations. An example of combined continuous and categorical observa-tions that is dealt with throughout this thesis (primarily Paper II) is a dataset with plasma concentrations (continuous) and certain observations reported to be below the quantification limit (BQL, i.e. categorical).

Model parameter estimation

The nonlinear mixed-effects modeling software NONMEM (Icon develop-ment Solutions, Ellicot City, MD, USA) [24] was used in all projects in-cluded in this thesis. NONMEM has been an important tool in the develop-ment of pharmacometrics as a scientific discipline and remains the most widely used software in pharmacometric research. Parameter estimation in NONMEM is based on maximum likelihood. The model parameters are estimated by maximizing the likelihood of the data given the model. This is performed by minimization of the extended least squared objective function. The objective function value (OFV) is approximately proportional to -2 times the logarithm of the likelihood of the data. The difference in the OFV (ΔOFV) between two nested models is approximately χ2_{-distributed under}

the assumption that the model is correct and that the errors are normally distributed. The likelihood ratio test can be used to compare nested models (e.g. the inclusion of a covariate effect) where a difference in OFV of 3.84 corresponds to a significance level of p<0.05. The nominal significance level can however be compromised by the approximations within the applied es-timation method and the number of observations [25-27].

Due to the nonlinearity of the model with respect to the random effects the likelihood function can generally not be calculated exactly. An approxi-mation of the likelihood function is therefore obtained by different types of

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linearization. Traditional linearization options available in NONMEM are the first-order method (FO), the first-order conditional estimation method (FOCE) and the Laplacian second-order approximation method. More re-cently a wider range of estimation methods has become available in NON-MEM, however they have not been applied in the projects described in this thesis. These includes maximum likelihood methods that do not rely on li-nearization such as the stochastic approximation expectation maximization method (SAEM) [28, 29] and a full Bayesian estimation method [30].

Mechanistic models

Mechanistic models or “mechanism-based models” attempt to represent phy-siological and pharmacological processes as accurately as possible [31-33]. One purpose of mechanistic models is to better understand the structure of a physiological system and the interplay between biological processes. The mechanistic models are never completely mechanistic but contain different elements of empirical simplifications, and therefore sometimes identified as semi-mechanistic or semi-physiological models [34, 35].

Mechanistic models typically contain a high level of complexity and it is often not possible to estimate all parameters based on observations of one dependent variable from a single experiment. Instead, information about sub-structures and parameter values are obtained from several independent expe-riments or from the literature [32, 36]. Mechanism-based models may allow for hypothesis testing of suggested mechanisms and for learning about sys-tem processes which are not easy to test experimentally. Furthermore, they typically allow for more credible interpolation between, and extrapolation outside, of situations which were the basis for the model [33, 37]. As extra-polations depend on assumptions incorporated into the model, the validity of the assumptions needs to be scrutinized carefully. Sensitivity analysis should be made with regards to less obvious assumptions and limitations to the pre-dictions must always be considered.

Just as there is a gradual scale between completely empirical to highly mechanistic models, there can also be said to be a gradual scale between a ‘bottom-up’ and a ‘top-down’ approach [38, 39]. With a pure ‘top-down’ approach the model is only informed by (trained on) the type of data that it aims to predict, e.g. for PK models typically plasma concentrations. A pure ‘bottom-up’ approach instead takes its basis in information about the system (i.e. human body) and the drug separately. The information about the drug is primarily based on in vitro experiments and physicochemical characteristics. More and more however, a combination of a ‘bottom-up’ and ‘top-down’ approach is used. The development towards such a combined approach comes from two directions. Research groups and software packages that traditionally applied a pure ‘bottom-up’ approach are implementing solu-tions to let their models be informed also by clinical data (e.g. Simcyp Ltd,

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Sheffield, UK, http:www.simcyp.com) [40, 41]. Whereas research groups that previously applied mostly quite empirical models and primarily used a ‘top-down’ approach today apply more and more mechanistic models and hence also include more and more ‘bottom-up’ information [42-44]. This development is made possible by increased availability of computer power and more efficient algorithms for parameter estimation as well as increased awareness of a systems pharmacology approach [45, 46]. Regarding oral absorption the full range of empirical to highly mechanistic models and ‘top-down’ to ‘bottom-up’ approaches are available, which is dwelt upon in a specific section (Oral Drug Absorption, Absorption models).

Handling of censored and missing observations

Censored observations are characterized by the fact the value of the observa-tion is partially missing. This differentiates censored observaobserva-tions from ‘missing observations’, where the value is completely missing. A model based approach is typically less sensitive to censored and missing observa-tions than traditional descriptive statistics and statistical tests [47]. However, censored and missing observations can still be a complicating factor in the analysis of repeated-measures longitudinal study that is typically the case in pharmacometric research. Both in the case of censored and missing observa-tions it is important to understand the mechanism of the missing information. A specific terminology has been adopted to characterize censored and miss-ing data. Censored observations are characterized as left censored, interval censored or right censored (with regards to time-to-event analysis there is further classifications of censoring but that is not relevant for this thesis). Processes generating the missing data are typically classified into 3 catego-ries: Missing Completely at Random (MCAR), Missing at Random (MAR), and Missing Not at Random (MNAR) [48].

A left censored observation is known to be below a certain value but it is unknown by how much. This could for instance be the bioanalytical estimate of a plasma concentration reported to be below the limit of quantification (LOQ). However if logical reasoning allows us to assume that the plasma concentration could not be below 0 we instead have an interval censored observation that has both a lower and upper boundary. Following the same logic a right censored observation is an observation that is larger than a cer-tain known limit. Interval censored observations between 0 and a specific LOQ are the most frequently occurring censoring in the pharmacometric setting. This situation can be transformed into the situation of left censoring by log-transforming the dependent variable before applying the model. Since the natural log of a value that goes towards 0 goes towards minus infinity. Traditional approaches for handling concentration measurements reported as being below the quantification limit (BQL), such as omitting the information or substitution with the LOQ divided by two, have been shown to introduce

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bias in parameter estimates [49, 50]. More informative methods to include the information about censored observations in a maximum likelihood framework were outlined already in 1957 [51]. In 2001, Stuart Beal pub-lished an overview of how this could be applied to a nonlinear mixed-effects model [52] and compared it to the traditional substitution and censoring ap-proaches. The method referred to as M2 in the publication applies condition-al likelihood estimation to the observations above LOQ and the likelihood for the data being above LOQ are maximized with respect to the model pa-rameters. This approach can be implemented in NONMEM by utilization of the YLO functionality [24]. The methods M3 and M4 also suggested by Beal are based on simultaneous modeling of continuous and categorical data where the BQL observations are treated as categorical data. The likelihood for the BQL observations are maximized with respect to the model parame-ters and the likelihood for an observation was taken to be the likelihood that it was indeed below LOQ. The M3 and the M4 methods differ in that the M3 method assumes left censored observations and the M4 method assumes interval censored observations between 0 and LOQ. The likelihood expres-sions for observations above and below LOQ based as implemented with the M2 respectively the M3 method is presented together with a principal illu-stration in Figure 2. A comparison of the different methods to handle BQL observations occurring in three distinctly different patterns and application of an approach to deal with censored observations in simulation based model diagnostics is presented in Paper II.

Figure 2. Likelihood for observations above and below LOQ depending on observed dependent variable y(t), model prediction f(t), residual error variance g(t) and LOQ. Method M3 maximizes the likelihood for BQL observations being indeed BQL (3) simultaneous to maximizing the likelihood for observations above LOQ (2). M2 maximizes the likelihood for observations above BQL conditioned on that they are part of a truncated distribution.

De p e n d e n t V a ri a b le Time M2 for observaon > LOQ

LOQ M3 for observaon > LOQ

2 1 1 ( ( ) ( )) (2) ( ) exp( 2 ( ) 2 ( ) y t f t l t g t g t π ⎛ − ⎞ = _{− ⎜} _⎟ ⎝ ⎠ ( ( )) (3) ( ) ( ) LOQ f t l t g t ⎛ − ⎞ = Φ ⎜ ⎟ ⎝ ⎠

M3 for obs < LOQ

2 1 1 ( ( ) ( )) ( ( )) (1) ( ) exp( / 1 2 ( ) 2 ( ) ( ) y t f t LOQ f t l t g t g t g t π ⎛ ⎞ ⎛ ⎛ − ⎞⎞ ⎛ − ⎞ =⎜ − ⎜ _{⎟ ⎜}⎟ ⎜ − Φ⎜ ⎟⎟_⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎝ ⎠⎠

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Data are missing completely at random if the reason for the missingness is unrelated to the observed and missing response values. An example of this is if samples from a clinical study accidentally are lost, or study drop-out that is unrelated to the investigated dependent variable. This kind of mis-singness does of course, like all mismis-singness and censoring, reduce the over-all information content of the collected data but does not cover-all for any specific measures to avoid biased parameter estimation and assure accurate model diagnostics. Data are MAR if the missingness depends on the response val-ues only through observed components of the response. An example of when MAR can occur in a clinical study is if subjects are automatically taken out of the study if the response variable of interest reaches a certain level. Ob-servations at the following visits are then MAR. This kind of pattern of miss-ing information typically does not bias parameter estimates, given that you are applying a mixed-effects modeling approach, but is important to consider for model diagnostics and clinical trial simulation. Data are MNAR if the missingness depends on both the observed and missing data; that is, the probability that an observation is missing depends on the value of the miss-ing observation itself. Observations MNAR could occur if for example sub-jects are less likely to show up at study visits in the case of poor clinical performance. Observations that are MNAR generally cause more problems and do require careful attention. The MNAR pattern of missingness can se-verely bias parameter estimates and statistical inference between for instance different treatment groups. The way to at least reduce the bias that this pat-tern imposes is to perform joint modeling of the probability of the observa-tion being missing (e.g. subject dropped-out of the study) and the response variable of interest [47, 48, 53].

Model diagnostics

The model building process is often difficult and involves testing, evaluat-ing, and diagnosing a range of plausible models with a major aim to make an adequate inference from the observed data. Establishment and verification of an appropriate model is crucial in order to put confidence in the inferences made based on the model. Graphical diagnostics are extensively used during the model building process and are considered an essential tool for data vi-sualization, inspection of model adequacy, and assumption testing [54, 55]. Graphical diagnostics are considered powerful and are often more or less intuitive to interpret. There is a large range of available graphical approaches to evaluate different aspects of model adequateness. Model diagnostics sel-dom provide a modeler with definitive answers. Thus it is important that a pharmacometrician can interpret the information obtained correctly. To do so the pharmacometrician needs to be aware of each diagnostic’s assump-tions, strengths and weaknesses [56].

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Plots of population typical model predictions (PRED) and individual model predictions (IPRED) versus observations are routinely used as a diag-nostic throughout the model building when dealing with continuous tions. Intuitively an interpreter of these plots looks for how well the observa-tions are centered along the line of identity. The assumption that plots of PRED versus observations should fall uniformly distributed around the line of identity is however flawed. Only the fact that the unexplained parameter variability enter nonlinearly into the model will produce individual predic-tions that are expected to have a mean different from the typical individual prediction (see Equation 2). In addition, factors like censoring and adaptive designs (e.g. therapeutic dose adjustments) can cause an even more skewed distribution [56]. The solution to this problem lies either in relying more heavily on other types of diagnostics or to create reference plots (mirror plots) based on simulations with the model to be diagnosed. If the pattern in the mirror plot for the observed data and the simulated data are similar, no model misspecification is evident from this diagnostic. For plots of IPRED versus observations on the other hand, a seemingly perfect alignment along the line of unity is not necessarily a strong support for model appropriate-ness. A so called “perfect fit phenomenon” occurs especially in the case of studies with sparse sampling. ε-shrinkage is a measure of the over fit that causes the perfect fit phenomenon and should generally be assessed to in-form about the level of appropriateness for diagnostics based on IPRED. An ε-shrinkage greater than 20% has been described to render IPRED versus observations plots essentially uninformative [56, 57].

Residual based diagnostics are commonly used and have the advantage of being useful in diagnosing several aspects of a models performance. Resi-duals can be plotted versus time or some other independent variable to iden-tify possible model misspecifications with regards to the relationship to in-dependent variables. The general interpretation of residual plots is that they should, in the case of adequate model fit, be normally distributed with a mean of 0 across any independent variable. However, the same limitations that have been discussed for PRED and IPRED vs. observations plots do of course apply also to residual based diagnostics that take their basis in the very same quantities (e.g. RES = Observations – PRED, IWRES = (Observa-tions – IPRED)/σ) [56]. Especially IWRES can still be very informative given that these limitations are considered (i.e. ε-shrinkage is verified to be low). Weighted residuals such as WRES and CWRES do not suffer from the same shortcomings as RES and IWRES. However, WRES are weighted based on the FO approximation and hence suffer from the same draw backs that are associated with the crude first-order linearization. It has been dem-onstrated that conditional weighted residuals (CWRES), which are instead based on the FOCE linearization, have better properties [58]. Also CWRES plots have been demonstrated to falsely indicate model misspecifications, in the case of highly non-linear models [56, 59]. Another “residual like” type of

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diagnostic that has been demonstrated to have good, even though not ideal properties, is the Normalized Prediction Distribution Errors (NPDE) [59-62]. The NPDEs are not true residuals but based on the rank order of the observa-tions in relation to multiple model simulaobserva-tions of the original dataset. The interpretation and use of NPDE plots are however very similar to traditional residual plots. Global Uniform Distance (GUD) is a recently suggested diag-nostic tool described to have ideal statistical properties [59]. Further testing is however needed to verify this claim and demonstrate the practical useful-ness.

Simulations based on the model and the underlying design of the ob-served data is increasingly used for model evaluation. The NPDE plots are a special case of a type of diagnostic tools called predictive checks [63]. With this approach multiple simulated replicates of the original dataset are used to create a reference distribution that can be compared to the observations. Some predictive checks focus on secondary statistics (e.g., area under the curve, time above a minimum inhibitory concentration, or the number of responders) that can be derived from both the raw data and the simulated data. This type of diagnostic is useful if such statistics can be accurately calculated and if they pinpoint the primary purpose of the model. Posterior predictive check (PPC) is a predictive check that is based on simulations from the posterior distribution (uncertainty distribution) of the model para-meters rather than only the point estimates [64]. This approach appears to be especially geared towards external validation. The most common form of predictive check is the so called visual predictive check (VPC) [65]. The principle of the VPC is to graphically assess whether simulations from a model of interest are able to reproduce both the central trend (median) and variability in the observed data, when plotted versus an independent variable (typically time). The variably component is typically assessed by comparing observations to simulations for a particular prediction interval (inter-percentile range). The widespread use of VPCs can be attributed to two main advantages of the approach; (1) the principle behind the diagnostic is simple and easily communicated to both modelers and other modeling stakeholders and (2) by the retention of the original y-axis scale the nature and clinical importance of an indicated model misspecification can be easily appreciated. This makes the VPC powerful both as a tool for communication and for guiding model development. As a part of this thesis it is demonstrated how the VPC can be adapted to censored observations and categorical data in general. Ideally a VPC will diagnose both the fixed and random effects of a mixed-effects model. In many cases this can be done by comparing different percentiles of the observed data to percentiles of simulated data. It has been described though that whenever the predictions within a bin differ largely due to different values of other independent variables (e.g. dose, covariates) the diagnosis may be hampered or misleading [66]. Furthermore VPCs have been described to be non-applicable to data following adaptive dosing (e.g.

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therapeutic drug monitoring (TDM)) due to the inherent correlation between the realized design and individual parameters within such studies [56, 67]. As a reaction to these shortcomings of the VPC the principle of prediction corrected VPC (pcVPC) and prediction and variability corrected VPC (pvcVPC) were outlined and tested in Paper III of this thesis. The pcVPC and pvcVPC plots were further applied in Paper IV, V and VI.

Oral drug absorption

Absorption of drugs from the GI tract is complex and often not well unders-tood [68]. The absorption process is influenced by a large number of factors that not only vary between drugs but also between different GI regions [69]. For many of the involved physiological factors there is also a substantial amount of between and within subject variability. The primary physico-chemical factors affecting absorption proprieties of a drug are: pKa, solubili-ty, stabilisolubili-ty, diffusivisolubili-ty, lipophilicisolubili-ty, and salt form. Physiological factors that influence the rate and extent with which orally administered drugs reach the systemic circulation include: pH, ionic strength, influx and efflux trans-porters and gut wall metabolism. All these factors more or less differ along the GI tract. For this reason the GI motility in the form of gastric emptying, small intestinal transit time etc are also very important. One important factor that limits the extent of oral absorption that does not depend on the absorp-tion site along the GI tract is the first pass extracabsorp-tion in the liver. Indepen-dent of the absorption site in the GI tract the substance passes via the portal vein through the liver once before reaching the systemic circulation. There are important interactions between the physiochemical properties of the ac-tive ingredient and the physiological factors such as the fact that solubility often is pH dependent. In the same way there are interactions between for-mulation characterizing factors and physiological factors. Paper I and Pa-per IV of this thesis investigate how drug release from different extended release (ER) formulations varies along the GI tract as a consequence of dif-ferences in physiological factors.

Figure 3 features a schematic representation of important processes in-volved in oral absorption along the GI tract. The structure of that picture is also the mechanistic basis for the models applied in Paper I and Paper V. The picture illustrates how a single piece solid dosage form transits between the different GI regions with discrete movements (e.g. it is only in one place at one time). The movements between the different GI regions can be de-scribed by movement probabilities (MP1-4). The picture have been simpli-fied by assuming small intestine and colon as single characteristic positions but this could typically be divided into several regions.

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Figure 3. Principal figure of processes involved in oral absorption from solid dosage forms. The picture have been simplified by assuming small intestine and colon as single characteristic positions but this could typically divided into several regions.

Figure 4. Summary of some primary determinants for the processes involved in oral absorption from solid dosage forms and available measurements of amount of drug substance throughout the cascade.

Due to differences in physiological conditions in the different GI regions (pH, mechanic stress etc.) the rate of drug release (R1-4) can differ between the GI regions. Released drug substance need to go into solution to be able to be absorbed through the gut wall. The rate of dissolution (S1-4) and precipi-tation (P1-4) can differ along the GI tract for the similar reasons that drug

KA1 KA2 Released substance Dissolved substance S1 S2 S3 S4 KA3 KA4 Gu t W all MP1 MP2 MP3 MP4 MP5 K1 K2 K3 K1 K2 K4 K3 K4 R1 R2 R3 R4 P1 P2 P3 P4 Liv er Sy ste mi c ci rc u lat io n Qpo rt al ve in QH CLGW4 CLH CLR CLGW1 CLGW3 Kef1 Kef2 Kef3 Kef4 K_A Released substance Dissolved substance S1 Gu t W all R1 P1 Liv er K_ef QH Qpor tal ve in CL_GW CL_H CL_R Surface area, Mechanic stress (RPM), pH, Ionic strength pH, Mixing (RPM), Water content Permeability, Active transporter expression Enzyme expression, protein binding ER tablet dose, MMM data IR tablet or powder dose In vitro dissolution experiments Plasma concentrations Systemic circulation

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release can e.g. pH, intestinal water content, ionic strength. The rate in which dissolved drug is absorbed from the gut lumen is dependent on passive diffu-sion as well as influx and efflux transporters (KA/Kef). Efflux transporters are

potentially also of importance for gut wall metabolism since efflux transpor-ters can increase the exposure to metabolizing enzymes in the gut wall [70, 71]. This is best described for efflux protein P-glycoprotein and CYP3A4 that share substrate specificity and act synergistically in preventing drug from passing through the gut wall [72]. Expression of CYP3A4 and other drug metabolizing enzymes in the enterocytes (cells in the gut wall) has been described to differ between the different segments of the GI tract [73, 74]. Solubility, active membrane transport and metabolism in the gut wall and liver are all processes that can be subject to saturation. Such non-linear processes in combination with large within and between subject variability, in many of the involved processes, have often made it difficult to accurately predict oral absorption based on preclinical data and mechanistic models but also difficult to characterize the absorption based on clinical observations [75, 76].

Gastro intestinal transit

As described above the gastro intestinal transit of both solid dosage forms and liquid forms (in solution or suspension) can be of great importance for the absorption of drugs. The gastro intestinal transit is governed largely by GI motility. Studies of GI motility are also important from a pathophysiolog-ical perspective since it is associated with abnormal syndromes like gastro-paresis, constipation and diarrhea [77, 78].

Under fasting conditions the gastro intestinal transit throughout the upper gastro intestinal tract (stomach and small intestine) are primarily governed by the Migrating Motor Complex (MMC). The MMC is a distinct cyclic pattern of electromechanical activity in the mouth muscle that triggers peris-taltic waves that originate from the stomach and propagates through the small intestine. The MMC cycle consists of 4 distinct phases that recurs every 1.5 to 2 hours in the fasting state [79, 80]. Postprandially, MMCs dis-appear to be replaced by a digestive motor activity characterized by regular mixing and propelling movements that optimize nutrient absorption [81].

The GI motility is important in governing the transit of solid oral dosage forms. Larger solid objects such as capsules or single unit tablets have been demonstrated to have significantly different GI transit patterns compared to solutions or small solid units like pellets, especially with respect to gastric emptying and colon transit time [82-84]. With regards to gastric emptying the size effect is most obvious when the dose is administered together with food. In that case smaller units and dissolved drug is emptied significantly faster than larger units. This is in line with the stomachs functionality of grinding the solids down to a manageable size before emptying into the

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duo-denum. For heavy meals in combination with large non-disintegrating cap-sules gastric emptying have been reported as late as 10 h post dosing [84]. When administered in the fasting state gastric emptying is generally fast and any reasonably sized particles are typically emptied within a few minutes [85].

Small intestinal transit is less dependent on the size of the formulation and concomitant food intake. If anything, solid particles appear to transit slightly faster than liquid content [84]. GI fluid is not continuously available throughout the GI tract but is found in clusters. GI transit for a solid dosage form is a heterogonous process, sometimes moving quickly, sometimes slowly, sometimes passing through fluid of varying composition, and being subject to varying peristaltic pressure. A typical small intestinal transit time in healthy subjects is reported to be between 2 and 4 h for solid dosage forms. However, there is a considerable between and within subject variabil-ity, with reports of between 0.5 and 9.5 h. It should be recognized that a considerable part of the small intestinal residence time is spent in rest and not in continuous movement [86].

Before entering the colon solid dosage forms typically stagnate in cecum for a variable period of time. Food intake stimulates emptying of cecum into the colon, a mechanism that is known as the gastro-ileocecal reflex [87, 88]. Further transit of dosage forms through the colon is highly variable and ap-pears to occur during periods of relatively fast movement followed by long periods of rest. The movement periods are stimulated by food intake but can also occur without food stimulation [86]. Small solid pellet particles have been reported to have a slower movement through the colon compared to larger single-unit formulations. For the single-unit formulation the mean (SD) total colon transit time was 15.2 (8.7) h whereas it was 28.4 (14.5) h for the multi-unit formulation [82].

The between and within subject variability is large with respect to GI transit in general, even for a homogenous healthy populations studied under highly controlled conditions. Taking into account the fact that disease and pharmacological treatments can alter the GI transit [83] and the fact that feeding habits generally vary more in natural life the true expected popula-tion variability is likely to be substantially larger.

Modified release formulations

There is a large variety of available oral formulations, oral solutions and suspensions that are utilized to a certain degree but solid dosage forms (i.e. tablets and capsules) are far more frequently used. The solid formulations are primarily divided into immediate release (IR) and modified release (MR) formulations. The MR formulations are further divided into extended release (ER) and delayed release (DR) formulations. Other notations such as “con-trolled release” (synonymous with MR), “prolonged release” and “sustained

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release” (synonymous with ER) have historically been used but these are now gradually disappearing since the IR/MR/ER/DR terminology has been endorsed by FDA and International Conference of Harmonization (ICH) [89-91].

Oral MR formulations are designed with the aim of achieving specific pharmacokinetic profiles, delivering to specific gut localities or reducing the number of drug administrations. MR dosage forms can be formulated either as single-unit or as multiple-units, the latter where the formulation consists of many, often small-sized, units (pellets, beads or granules) which are either filled in a capsule, a sachet or are compressed as tablets which disintegrate to release the individual units [92]. There is a range of different mechanisms that have been used to modify the release for both single and multiple unit formulations. Most mechanisms are aimed at achieving an ER that will sup-port once daily dosing and which result in minimal fluctuations in plasma concentrations [92].

Hydroxypropyl methylcellulose (HPMC), a semi-synthetic cellulose de-rivative, is widely used as a matrix former in single-unit ER formulations [93] and of particular interest to this thesis. The fact that HPMC is “general-ly recognized as safe” (GRAS) by the FDA and also safe from an environ-mental perspective is one of the reasons for its popularity. Furthermore, it is compatible with numerous drugs and can accommodate high levels of drug loading [94]. In contact with water, HPMC swells to form a gel, which serves as a barrier to drug diffusion. Drug release from the HPMC-drug ma-trix involves solvent penetration into the dry mama-trix, gelatinisation of the polymer, dissolution of the drug and diffusion of the solubilised drug through the gel layer. Concomitantly, the outer layers of the tablet become fully hydrated and dissolve, a process generally referred to as erosion. Fac-tors such as the HPMC concentration in the tablet, the viscosity grades of HPMC and the solubility of the active ingredient is important factors mod-ifying the drug release rate from HPMC matrix tablets. The release mechan-ism from HPMC matrix tablets can either be controlled by diffusion, diffu-sion and erodiffu-sion or only erodiffu-sion depending on the choice of viscosity grade and/or addition of additional polymers [95].

A wide range of mathematical models have been applied to describe drug release from HPMC-based pharmaceutical devices [96]. These range from empirical models to characterize in vitro drug release profiles [97, 98] to highly mechanistic models to prospectively predict diffusion, swelling and dissolution (erosion) properties [99].

Absorption models

Models to describe oral absorption exist in many shapes and forms. They range from simplistic and highly empirical models to more complicated and mechanistic models. Typically PK analysis based on sampled plasma

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con-centration has used first or zero-order rate constants with or without lag-time to describe oral absorption [100]. In some cases combinations of two or more first or zero-order process have been applied, either in parallel [101] or sequentially in time [102, 103]. There are also examples of models with mixed zero-order and first-order absorption [104, 105]. These models can be defined as primarily empirical even if a mechanistic interpretation can some-times be made. A range of more complex but still primarily empirical ab-sorption models have also been described and applied to so called ‘atypical absorption profiles’ [100]. Examples of such models are; the Weibull func-tion [106, 107], the inverse Gaussian density input funcfunc-tion [108, 109], tran-sit compartment models [110, 111] and other kinds of time dependent func-tions with or without nonlinear elements [112, 113]. These models are gen-erally more flexible in nature and hence often result in a closer fit to ob-served plasma concentrations. This group of absorption models is sometimes referred to as semi-mechanistic since they are thought to more closely re-semble GI distribution etc. However the simulation properties and extrapola-tion possibilities with these models has generally not been sufficiently ex-plored.

More mechanistic models for oral absorption have existed in parallel with the more empirical one for many years but in contrast have primarily been used for ‘bottom up’ prediction purposes [114, 115]. The basis for these models are physiological information regarding factors such as pH, tissue surface area along the GI tract and available physicochemical information (e.g. permeability, solubility) regarding the substance based either on chemi-cal structure input and/or in vitro experiments.

Most mechanistic absorption models are based on a compartmental struc-ture describing the distribution of drug substance throughout the GI tract. A distinction is typically made between; stomach, duodenum, upper and lower jejunum, one or several ileum compartments (including cecum) and a colon compartment. Early mechanistic models such as the compartmental absorp-tion and transit (CAT) model [68] and the Grass model [116] initially only described the GI distribution of disintegrated drug substance (i.e. in liquid form), dissolution and passive absorption (diffusion). The CAT model was later further developed to also include elements of active transport through the gut wall, intestinal degradation and a simplistic handling of drug release from modified release formulations [117, 118]. The advanced compartmen-tal absorption and transit (ACAT) model was based on the CAT model but included several significant improvements [119]. The model distinguished between six states of drug component; unreleased, undissolved, dissolved, degraded, metabolized, and absorbed substance (similar to Figure 3). First pass metabolism in both gut wall (enterocytes) and the liver are incorporated in the ACAT model.

The ACAT model is the basis for the commercially available software GastroPlusTM_{(Simulations Plus, Inc. Lancaster, CA, USA,}

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http://www.simulations-plus.com) and within that framework the ACAT model has been gradually upgraded to improve the predictions. The compet-ing software solution Simcyp®_{(Simcyp Ltd, Sheffield, UK,}

http://www.simcyp.com) was initially a software primarily designed for the predictions of metabolism but has grown to be a widely applicable database and physiology based simulator of pharmacokinetics, including absorption. Since the release of Simcyp®_{version 7 it has also included an advanced}

dis-solution, absorption and metabolism (ADAM) model [120]. The ADAM model is structurally very similar to the ACAT model but does, for instance, include a more sophisticated dissolution model [121]. In contrast to GastroP-lusTM the Simcyp® solution has naturally incorporated courses of between subject variability to facilitate predictions of population variability in differ-ent demographic groups. PK-Sim® (Bayer Technology Services www.pk-sim.com) is a third software solution for predictions of oral absorption [122]. In PK-Sim® the GI tract is described with a dispersion model [123] that can be seen as a continuous tube with spatially varying properties (pH, surface area etc.) rather than a series of transit compartments.

In vitro - in vivo correlation for oral dosage forms

An in vitro - in vivo correlation (IVIVC) has been defined by the FDA as “a predictive mathematical model describing the relationship between an in vitro property of a dosage form and an in vivo response” [124]. Generally, the in vitro property is the rate or extent of drug dissolution or release while the in vivo response is the plasma drug concentration or amount of drug ab-sorbed. IVIVC plays an important role in product development in that it: (1) can serve as a surrogate for in vivo studies, (2) supports and/or validates the use of dissolution methods and specifications, (3) defines the quality control requirements and (4) guides the selection of appropriate formulations [125].

The Biopharmaceutics Classification System (BCS) suggested by L.A. Amidon, H. Lennernäs et. al. [126] has been used to predict whether in vitro in vivo correlation (IVIVC) can be expected based solely on in vitro dissolu-tion experiments for IR formuladissolu-tions. The BCS classifies drugs into 4 classes based on estimates of solubility and permeability (Table 1).

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Table 1. Biopharmaceutics Classification System (BCS) and associated expectation of IVIVC for IR formulations

Class Solubility Permeability IVIVC based on dissolution rate

I High High IVIVC expected if dissolution rate is slower than gas-_{tric emptying rate, otherwise limited}*_{or no correlation.} II Low High IVIVC expected if in vitro dissolution rate is similar to _{in vivo dissolution rate, unless dose is very high.} III High Low Absorption (permeability) is rate determining and _{limited or no IVIVC expected.} IV Low Low Limited or no IVIVC expected.

*_{A limited correlation means that the dissolution rate while not rate controlling may be} similar to the absorption rate and the extent of correlation will depend on the relative rates. The FDA has adopted the BCS as an approach to grant waiver of in vivo bioavailability and bioequivalence testing (biowaiver) of IR solid dosage forms for Class I high solubility, high permeability drugs when such drug products also exhibit rapid dissolution [127]. A drug substance is considered ‘highly soluble’ when the highest dose strength is soluble in 250 ml or less of aqueous media over a pH range of 1–7.5 at 37○_{C. A drug substance is}

considered to be ‘highly permeable’ when the extent of absorption (parent drug + metabolites) in humans is determined to be ≥90% of an administered dose, based on a mass balance determination or in comparison to an intra-venous reference dose. This can be established in clinical studies or by stu-dies of intestinal permeability in in vitro/in situ permeability stustu-dies. The BCS approach to grant biowaivers has received criticism for using extent of absorption (a thermodynamic measure) and intestinal permeability (a kinetic measure) interchangeably [128, 129].

Table 2. FDA categories of IVIVCs for ER formulations

Level Description

A A functional relationship between in vitro dissolution and the in vivo input rate, _{correlation of profiles, linear or non-linear relationship} B A correlation based on statistical moment analysis (in vitro dissolution time is _{correlated with mean residence time)} C A single point relationship between one dissolution parameter, (e.g. T50%, % dis-_{solved in 4h) and one pharmacokinetic parameter (e.g. AUC, Cmax)} D A multiple Level C correlation relating one or several pharmacokinetic parameters _{of interest to the amount of drug dissolved at several time points.} For ER formulations five correlation levels have been defined in the FDA IVIVC guidance (Table 2) [124]. Even though the IVIVC level terminology was introduced for ER products the same principles appears to also be fre-quently used also for IR formulations of BCS class II and IV. The concept of correlation level is based upon the ability of the applied model to reflect the complete plasma concentration versus time profile based on in vitro dissolu-tion data. The highest correladissolu-tions level (A) represent a direct reladissolu-tionship

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between in vitro dissolution rate and in vivo input rate. This type of correla-tion can have all the previously mencorrela-tioned benefits of established IVIVC including granting of a biowaiver. The lower levels of IVIVC have limited usefulness since they do not guarantee temporally correct relationship be-tween in vitro and in vivo drug release/dissolution.

The FDA guidance states that in order to develop an IVIVC model, at least three drug formulations with a range of release rates, differing from one another by at least 10%, be studied. Assessment of the models predictability can be carried out with internal validation or by external validation based on a fourth or subsequent formulation that was not used in the model develop-ment stage. In conflict with the definition of a level A IVIVC the assessdevelop-ment of the predictability is typically made with respect to the Cmax and AUC.

The conflict lies in that the guidance document states that “the model should predict the entire in vivo time course from the in vitro data” while the as-sessment of Cmax and AUC cannot guarantee that the entire time course is

well described.

There are a number of modeling approaches for establishing IVIVC, in-cluding those based on convolution, compartmental models and most fre-quently used, deconvolution [130, 131]. There are many methods of decon-volution which all rely on similar principles and assume linearity and time invariance of the system being studied [132]. The deconvolution is typically based on observed plasma concentrations following administration of the oral formulations (which depends on dissolution, absorption, distribution, metabolism and excretion of the drug) and observed in vivo reference data i.e. plasma concentration following i.v. dosing or administration of oral solu-tion. The idea of the deconvolution is to isolate the information of interest, that is, the rate at which the dosage unit dissolves in vivo. The exact same sampling time points are needed for the correlation of in vitro and in vivo drug release since no continuous model is used to describe the drug release. The deconvolution should preferably be done on an individual level but fre-quently it is done based on average data. The use of average data is proble-matic from two perspectives; (1) it prohibits identification of inter-subject or inter-dosage unit differences and (2) averaging over several experi-ments/individuals cause bias since average profiles does not reflect a typical profile [133]. The largest problem with the deconvolution approach is how-ever the assumptions of a constant rate and extent of absorption over time (i.e. no differences along the GI tract or saturable processes). However, the deconvolution methods have several other well documented weaknesses, such as the clearly flawed assumption that observations from a single expe-riment or individual are independent [132].

Some of the weaknesses with the deconvolution methods are resolved with a nonlinear mixed-effects modeling approach that incorporates a convo-lution step [131, 134]. This technique models in vitro and in vivo data simul-taneously and allows the prediction of plasma concentration–time profiles on

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an individual subject level using in vitro dissolution data. The assumption of a constant rate and extent of absorption over time is however the same for both convolution and deconvolution based approaches. This does limit the types of formulations and active ingredients for which the approaches can be successfully applied. Differential equation based compartmental models have also in rare cases been applied for establishing IVIVC [130, 135, 136]. Such models can be adapted to take into account nonlinear rate and/or extent of absorption [136] and theoretically also differences along the GI tract.

Conceptual attempts have also been made to demonstrate IVIVC by pros-pective simulations based on ‘bottom up’ mechanistic absorption models [120, 137-139]. With this approach the idea is to make prospective predic-tion of plasma concentrapredic-tions following different oral formulapredic-tions without any fitting to the clinical observations. The predictions are based on in vitro dissolution profiles, a mechanistic absorption model and a model for the disposition of the active substance (possibly based on reference plasma con-centrations following i.v. dosing or administration of oral solution).

In vivo methods to study GI transit and regional absorption

A variety of methods have been used to study GI transit of pharmaceuticals and/or site specific rate and extent of absorption. Perhaps most common, different kinds of intubation techniques that differ in terms of convenience, tolerability and capabilities have been used [140-144]. As an alternative to these methods non-invasive remote operated capsules have been developed [145-148]. After swallowing the capsules are monitored while moving along the GI tract (X-ray, gamma scitigraphy or magnetic labeling) and drug can be released as a solution or powder when activated by an external signal.

A methodology that has introduced the potential of characterizing in vivo behavior of solid dosage forms with respect to GI transit, drug release and regional absorption is gamma scintigraphy [149]. A major advantage of this methodology is the broad availability of the imaging technique [150, 151]. The required imaging equipment as well as the data evaluation methods are essential tools in nuclear medicine and therefore easily accessible. Further-more, gamma scintigraphy can be applied to solid, liquid and semi-solid dosage forms as it is based on the addition of trace amounts of the C-emitting radioisotopes. The temporal and spatial resolution with gamma scintigraphy is limited to approximately a few centimeters and about one minute respectively. However, the major drawback is the ethical problem that healthy subjects become exposed to radiation without having any impor-tant personal benefit, which principally goes against the principals outlined in the declaration of Helsinki [152].

Magnetic Marker Monitoring (MMM) is a non-invasive tool for high res-olution investigation of the gastrointestinal transit of ingested dosage forms without the need to apply radiation [86] that has become an attractive

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alter-native to gamma scinitraphy [153]. MMM is described in larger detail be-low. Similarly, the methodology of intubation with Bioperm®_{capsules and}

the paracetamol and sulfapyridine double marker method, for a simpler cha-racterization of gastric emptying and small intestinal transit, is outlined un-der separate headings.

Magnetic Marker Monitoring

MMM is based on the labeling of solid dosage forms as a magnetic dipole and determination of the location, orientation and strength of the dipole after oral administration using biomagnetic instruments [86]. The magnetic dipole is generated by incorporation of ferromagnetic material in the formulation and subsequently magnetized using a static magnetic field. Black iron oxide (E172), a color pigment that is commonly used as a colorant for food and orally applied dosage forms, can be used as the magnetic material and fol-lowing magnetization results in a dipole moment of about 30-60 μAm2. This weak magnetic field can be detected with an extremely sensitive biomagnet-ic measuring devbiomagnet-ice (multbiomagnet-ichannel SQUID sensor) resulting in three dimen-sional localization and orientation as well as determination of the strength of the magnetic source over time. The obtained three dimensional localization of the labeled formulation is transferred to a coordinate system that refers to the anatomy of the investigated subject (Figure 5). In this way the position in relation to the different religions of the GI tract can be obtained [154].

Figure 5.MMM assessment of GI transit for felodipine ER tablet following fasting administration. The locations of the ER tablets are shown in frontal (left) side (right) view. Each circle represents the mean location of the tablet during a 1 second interval [155]. Reprinted with permission of the copyright owner.

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For dosage forms where the drug release rate is determined by the erosion of the dosage form, the decrease in magnetic moment can be linked to the drug release. In these cases, a relationship between the decrease in magnetic sig-nal and drug release characterized in in vitro experiments can be used to obtain actual in vivo drug release profiles [156].

Bioperm®_{capsule intubation}

Bioperm®_{capsule intubation was recently reported to have been successfully}

applied in 13 phase 1 studies to study regional absorption properties throughout the GI tract [144]. The method features a thin tube introduced through the nose, retrieved from the pharynx, attached to a 30 mm long cap-sule, and swallowed. Peristalsis moves the capsule to the desired location in the gut (monitored by X-ray) where it is anchored before administration via the tube takes place. Substances can be administered in the form of solution or as pellets.

The double marker method

The paracetamol and sulfapyridine double marker technique is based on combined gastric administration of paracetamol and sulfasalazine followed by plasma concentration measurements of paracetamol and sulfapyridine. Paracetamol is poorly absorbed from the stomach but rapidly absorbed from the duodenum. Measurements of paracetamol in plasma can hence be used as a marker gastric emptying (GE) [157]. Sulfasalazine is poorly absorbed in the stomach and small intestine but is rapidly metabolized by the bacterial flora in the large intestine to the metabolite sulfapyridine, which is absorbed. Appearance of sulfapyridine in plasma can therefore be used as a marker to determine the small intestinal transit time (SITT) [158, 159]. The double marker method has mostly been used to study GE and SITT in dog or mon-key [160-162]. However there are also examples of when the methods have been applied to clinical studies [163, 164].

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Aims

The primary aim of the thesis was to improve mechanistic understanding and prospective predictions of oral absorption by establishing nonlinear mixed-effects modeling approaches to analyze observations from advanced in vivo studies of oral absorption. A secondary aim was to advance nonlinear mixed-effects modeling methodology with respect to handling of censored observa-tions and model diagnostics to facilitate the primary aim and pharmacome-tric research in general.

The specific aims were to:

• Outline a suitable integrative approach for quantifying gastro in-testinal tablet transit, in vivo drug release, absorption and disposi-tion based on MMM study observadisposi-tions.

• Characterize the relationship between in vitro and in vivo drug re-lease along the GI tract for hydrophilic matrix ER tablets, by the estimation of the relative mechanic stress in different GI regions. • Develop a model characterizing absorption properties along the

GI tract for the investigational drug AZD0837 and demonstrate how that model in combination with models for drug release and tablet GI transit can be utilized to make prospective predictions of absorption from new ER formulations.

• Demonstrate how semi-mechanistic modeling of GI transit based on paracetamol and sulfapyridine data can facilitate characteriza-tion of pharmacologically induced changes in gastrointestinal transit.

• Evaluate methods for handling censored observations in mixed-effect models to prevent bias in parameter estimates and for diag-nosing model fit using visual predictive checks (VPCs).

• Introduce the concepts of prediction and variability correction in VPCs and highlight situations where this could add significant di-agnostic value.

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Material and Methods

The thesis is based on six papers. Paper I involves the development of a mechanistic model describing the interrelationship between tablet GI transit and in vivo drug release and plasma concentrations of felodipine. The obser-vations of tablet GI transit and in vivo drug release for the felodipine ex-tended release (ER) formulation were made possible by Magnetic Marker Monitoring (MMM). This project can be seen as a pilot study to evaluate the feasibility of applying a mixed-effects modeling approach to data from MMM studies. The successful outcome of that pilot study lead to the initiali-zation of a project described in Paper IV and V. In these two papers an ex-tended version of the methodology outlined in Paper I has been applied to studies of the investigational drug AZD0837, aiming to perform prospective predictions of PK profiles for newly developed ER formulations. Important model building features from these three projects are described in the Model building section. Paper VI features a semi-mechanistic model that characte-rizes pharmacological effects on gastric emptying and small intestinal transit time based on paracetamol and sulfapyridine double marker studies. Impor-tant methodological aspects of that project are described under the subhead-ing Double Marker Model in the Model buildsubhead-ing section.

Paper II and III deal with extensions to pharmacometric methodology concerning censored observations and model diagnostics. These methodo-logical advances were later applied in Paper IV, V and VI. The general me-thodology aspects of these papers are presented in the Mixed-effect modeling methodology section.

Software

Data analysis in all projects included in this thesis were performed with a nonlinear mixed-effects approach as implemented in the NONMEM soft-ware (version 6.1.0 to 7.1.2) [24]. The PsN toolkit [165, 166] was used in conjunction with NONMEM for atomization and post processing purposes (e.g. log-likelihood profiling, VPC). The Xpose 4.3.0 [167, 168] package in R [169] was used for graphical diagnostics. Methodological developments with respect to VPCs presented in Paper II and III have been implemented in PsN and Xpose in line with how it is presented in the papers.