Maria C. Kjellsson

Mechanistic modeling of pitavastatin disposition in sandwich-cultured human hepatocytes: a proteomics-informed bottom-up approach

Isolated human hepatocytes are commonly used to predict transporter-mediated clearance in vivo. Such predictions, however, do not provide estimations of transporter contributions and consequently do not allow predictions of the outcome resulting from a change in the activity of a certain transporter, for example, by inhibition or a genetic variant with reduced function. Pitavastatin is a drug that is heavily dependent on hepatic transporters for its elimination, and it is excreted mainly as unchanged drug in the bile. For this reason, pitavastatin was used as a model drug to demonstrate the applicability of a bottom-up approach to predict transporter-mediated disposition in sandwich-cultured human hepatocytes (SCHHs), allowing for the estimation of transporter contributions. Transport experiments in transfected human embryonic kidney cells (HEK293 cell lines) and inverted membrane vesicles overexpressing each of the relevant transport proteins were used to generate parameter estimates for the mechanistic model. By adjusting for differences in transporter abundance between the in vitro systems and individual SCHH batches, the model successfully predicted time profiles of medium and intracellular accumulation. Our predictions of pitavastatin bile accumulation could not be confirmed, however, because of a very low biliary excretion of pitavastatin in relation to the hepatic uptake in our SCHHs. This study is, to our knowledge, the first to successfully simulate transporter-mediated processes in a complex system such as SCHHs at the level of individual transport proteins using a bottom-up approach.

Estimating bias in population parameters for some models for repeated measures ordinal data using NONMEM and NLMIXED.

The application of proportional odds models to ordered categorical data using the mixed-effects modeling approach has become more frequently reported within the pharmacokinetic/pharmacodynamic area during the last decade. The aim of this paper was to investigate the bias in parameter estimates, when models for ordered categorical data were estimated using methods employing different approximations of the likelihood integral; the Laplacian approximation in NONMEM (without and with the centering option) and NLMIXED, and the Gaussian quadrature approximations in NLMIXED. In particular, we have focused on situations with non-even distributions of the response categories and the impact of interpatient variability. This is a Monte Carlo simulation study where original data sets were derived from a known model and fixed study design. The simulated response was a four-category variable on the ordinal scale with categories 0, 1, 2 and 3. The model used for simulation was fitted to each data set for assessment of bias. Also, simulations of new data based on estimated population parameters were performed to evaluate the usefulness of the estimated model. For the conditions tested, Gaussian quadrature performed without appreciable bias in parameter estimates. However, markedly biased parameter estimates were obtained using the Laplacian estimation method without the centering option, in particular when distributions of observations between response categories were skewed and when the interpatient variability was moderate to large. Simulations under the model could not mimic the original data when bias was present, but resulted in overestimation of rare events. The bias was considerably reduced when the centering option in NONMEM was used. The cause for the biased estimates appears to be related to the conditioning on uninformative and uncertain empirical Bayes estimate of interindividual random effects during the estimation, in conjunction with the normality assumption.

The impact of misspecification of residual error or correlation structure on the type I error rate for covariate inclusion

It has been shown that when using the FOCE method in NONMEM, the likelihood ratio test (LRT) can be sensitive to the use of an inappropriate estimation method in that ignoring an existing η–ε interaction leads to actual significance levels for type I errors being higher than the nominal levels. The objective of this study was to assess through simulations the LRT sensitivity to various types of residual error model misspecifications in both continuous and categorical data. The study contained two parts, simulations based on continuous and categorical data. Data sets containing 250 individuals with up to 24 observations per individual were simulated multiple times (1000) with different types of residual error models for the continuous data and different strength of correlation between observations for the categorical data. The data sets were analyzed using either the correct or a simpler (incorrect) model with or without addition of a covariate. The type I error rate of inclusion of the non-informative covariate on the 5% level was calculated as the number of runs where the drop in the objective function value (OFV) was larger than 3.84 when the covariate relationship was included in the model using the correct or the incorrect model. The difference in OFV between the model with the correct and the incorrect structure was also calculated as a measure of the residual error model misspecification. For continuous data the FOCE method was used in most cases (with interaction when appropriate). The Laplacian estimation method was used for one of the continuous models and for categorical data. The results showed that the residual error model misspecifications when the erroneous model was used were pronounced, as indicated by the OFV being substantially higher than for the corresponding correct models. The significance levels of the LRT with the incorrect model were appropriate in all cases but ignoring (serial) correlations between observations (continuous and categorical data) as well as when the η–ε interaction was ignored (which has previously been shown, continuous data). When ignoring correlation, the type I error rates were shown to be sensitive to the correlation strength, the number of observations per individual and the magnitude of the inter-individual variability on clearance. We conclude that the LRT appears robust towards all tested cases, but ignoring (serial) correlations between observations and η–ε interaction.

Comparison of proportional and differential odds models for mixed-effects analysis of categorical data

In this work a model for analyzing categorical data is presented; the differential odds model. Unlike the commonly used proportional odds model, this model does not assume that a covariate affects all categories equally on the log odds scale. The differential odds model was compared to the proportional odds model, by assessing statistical significance and improvement of predictive performance when applying the differential odds model to data previously analyzed using the proportional odds model. Three clinical studies; 3-category T-cell receptor density data, 5-category diarrhea data and 6-category sedation data, were re-analyzed with the differential odds model. As expected, no improvements were seen with T-cell receptor density and diarrhea data. However, for the more complex measurement sedation, the differential odds model provided both statistical improvements and improvements in simulation properties. The estimated actual critical value was for all data lower than the nominal value, using the number of added parameters as the degree of freedom, i.e. the differential odds model is statistically indicated to a less extent than expected. The differential odds model had the desired property of not being indicated when not necessary, but it may provide improvements when the data does not represent a categorization of continuous data.

A Model-Based Approach to Predict Longitudinal HbA1c, Using Early Phase Glucose Data From Type 2 Diabetes Mellitus Patients After Anti-Diabetic Treatment

Predicting late phase outcomes from early‐phase findings can help inform decisions in drug development. If the measurements in early‐phase differ from those in late phase, forecasting is more challenging. In this paper, we present a model‐based approach for predicting glycosylated hemoglobin (HbA1c) in late phase using glucose and insulin concentrations from an early‐phase study, investigating an anti‐diabetic treatment. Two previously published models were used; an integrated glucose and insulin (IGI) model for meal tolerance tests and an integrated glucose‐red blood cell‐HbA1c (IGRH) model predicting the formation of HbA1c from the average glucose concentration (Cg,av). Output from the IGI model was used as input to the IGRH model. Parameters of the IGI model and drug effects were estimated using data from a phase1 study in 59 diabetic patients receiving various doses of a glucokinase activator. Cg,av values were simulated according to a Phase 2 study design and used in the IGRH model for predictions of HbA1c. The performance of the model‐based approach was assessed by comparing the predicted to the actual outcome of the Phase 2 study. We have shown that this approach well predicts the longitudinal HbA1c response in a 12‐week study using only information from a 1‐week study where glucose and insulin concentrations were measured.

Longitudinal Modeling of the Relationship Between Mean Plasma Glucose and HbA1c Following Antidiabetic Treatments

Late‐phase clinical trials within diabetes generally have a duration of 12–24 weeks, where 12 weeks may be too short to reach steady‐state glycated hemoglobin (HbA1c). The main determinant for HbA1c is blood glucose, which reaches steady state much sooner. In spite of this, few publications have used individual data to assess the time course of both glucose and HbA1c, for predicting HbA1c. In this paper, we present an approach for predicting HbA1c at end‐of‐trial (24–28 weeks) using glucose and HbA1c measurements up to 12 weeks. The approach was evaluated using data from 4 trials covering 12 treatment arms (oral antidiabetic drug, glucagon‐like peptide‐1, and insulin treatment) with measurements at 24–28 weeks to evaluate predictions vs. observations. HbA1c percentage was predicted for each arm at end‐of‐trial with a mean prediction error of 0.14% [0.01;0.24]. Furthermore, end points in terms of HbA1c reductions relative to comparator were accurately predicted. The proposed model provides a good basis to optimize late‐stage clinical development within diabetes.

Evaluation of the nonparametric estimation method in NONMEM VI

PURPOSE In NONMEM VI, a novel method exists for estimation of a nonparametric parameter distribution. The parameter distributions are approximated by discrete probability density functions at a number of parameter values (support points). The support points are obtained from the empirical Bayes estimates from a preceding parametric estimation step, run with the First Order (FO) or First Order Conditional Estimation (FOCE) methods. The purpose of this work is to evaluate this new method with respect to parameter distribution estimation. METHODS The performance of the method, with special emphasis on the analysis of data with non-normal distribution of random effects, was studied using Monte Carlo (MC) simulations. RESULTS The mean value (and ranges) of absolute relative biases (ARBs, %) in parameter distribution estimates with nonparametric methods preceded with FO and FOCE were 0.80 (0.1-3.7) and 0.70 (0-3), respectively, while for parametric methods, these values were 23.74 (3.3-97.5) and 4.38 (0.1-17.9), for FO and FOCE, respectively. The nonparametric estimation method in NONMEM could identify non-normal parameter distributions and correct bias in parameter estimates seen when applying the FO estimation method. CONCLUSIONS The method shows promising properties when analyzing different types of pharmacokinetic (PK) data with both the FO and FOCE methods as preceding steps.

Semimechanistic model describing gastric emptying and glucose absorption in healthy subjects and patients with type 2 diabetes

The integrated glucose‐insulin (IGI) model is a previously published semimechanistic model that describes plasma glucose and insulin concentrations after glucose challenges. The aim of this work was to use knowledge of physiology to improve the IGI models description of glucose absorption and gastric emptying after tests with varying glucose doses. The developed models performance was compared to empirical models. To develop our model, data from oral and intravenous glucose challenges in patients with type 2 diabetes and healthy control subjects were used together with present knowledge of small intestinal transit time, glucose inhibition of gastric emptying, and saturable absorption of glucose over the epithelium to improve the description of gastric emptying and glucose absorption in the IGI model. Duodenal glucose was found to inhibit gastric emptying. The performance of the saturable glucose absorption was superior to linear absorption regardless of the gastric emptying model applied. The semiphysiological model developed performed better than previously published empirical models and allows better understanding of the mechanisms underlying glucose absorption. In conclusion, our new model provides a better description and improves the understanding of dynamic glucose tests involving oral glucose.

Modeling of 24-hour glucose and insulin profiles in patients with type 2 diabetes mellitus treated with biphasic insulin aspart.

Insulin therapy for diabetes patients is designed to mimic the endogenous insulin response of healthy subjects and thereby generate normal blood glucose levels. In order to control the blood glucose in insulin‐treated diabetes patients, it is important to be able to predict the effect of exogenous insulin on blood glucose. A pharmacokinetic/pharmacodynamic model for glucose homoeostasis describing the effect of exogenous insulin would facilitate such prediction. Thus the aim of this work was to extend the previously developed integrated glucose–insulin (IGI) model to predict 24‐hour glucose profiles for patients with Type 2 diabetes following exogenous insulin administration. Clinical data from two trials were included in the analysis. In both trials, 24‐hour meal tolerance tests were used as the experimental setup, where exogenous insulin (biphasic insulin aspart) was administered in relation to meals. The IGI model was successfully extended to include the effect of exogenous insulin. Circadian variations in glucose homeostasis were assessed on relevant parameters, and a significant improvement was achieved by including a circadian rhythm on the endogenous glucose production in the model. The extended model is a useful tool for clinical trial simulation and for elucidating the effect profile of new insulin products.

Requirements for multi-level systems pharmacology models to reach end-usage: the case of type 2 diabetes

We are currently in the middle of a major shift in biomedical research: unprecedented and rapidly growing amounts of data may be obtained today, from in vitro, in vivo and clinical studies, at molecular, physiological and clinical levels. To make use of these large-scale, multi-level datasets, corresponding multi-level mathematical models are needed, i.e. models that simultaneously capture multiple layers of the biological, physiological and disease-level organization (also referred to as quantitative systems pharmacology—QSP—models). However, todays multi-level models are not yet embedded in end-usage applications, neither in drug research and development nor in the clinic. Given the expectations and claims made historically, this seemingly slow adoption may seem surprising. Therefore, we herein consider a specific example—type 2 diabetes—and critically review the current status and identify key remaining steps for these models to become mainstream in the future. This overview reveals how, today, we may use models to ask scientific questions concerning, e.g., the cellular origin of insulin resistance, and how this translates to the whole-body level and short-term meal responses. However, before these multi-level models can become truly useful, they need to be linked with the capabilities of other important existing models, in order to make them ‘personalized’ (e.g. specific to certain patient phenotypes) and capable of describing long-term disease progression. To be useful in drug development, it is also critical that the developed models and their underlying data and assumptions are easily accessible. For clinical end-usage, in addition, model links to decision-support systems combined with the engagement of other disciplines are needed to create user-friendly and cost-efficient software packages.