Evaluation of covariate effects in item response theory models

Item response theory (IRT) models are usually the best way to analyze composite or rating scale data. Standard methods to evaluate covariate or treatment effects in IRT models do not allow to identify item-specific effects. Finding subgroups of patients who respond differently to certain items could be very important when designing inclusion or exclusion criteria for clinical trials, and aid in understanding different treatment responses in varying disease manifestations. We present a new method to investigate item-specific effects in IRT models, which is based on inspection of residuals. The method was investigated in a simulation exercise with a model for the Epworth Sleepiness Scale. We also provide a detailed discussion as a guidance on how to build a robust covariate IRT model.

Item response theory analysis of daytime sleepiness as a symptom of obstructive sleep apnea

Obstructive sleep apnea (OSA) is a sleep disorder which is linked to many health risks. The gold standard to evaluate OSA in clinical trials is the Apnea-Hypopnea Index (AHI). However, it is time-consuming, costly, and disregards aspects such as quality of life. Therefore, it is of interest to use patient-reported outcomes like the Epworth Sleepiness Scale (ESS), which measures daytime sleepiness, as surrogate end points. We investigate the link between AHI and ESS, via item response theory (IRT) modeling. Through the developed IRT model it was identified that AHI and ESS are not correlated to any high degree and probably not measuring the same sleepiness construct. No covariate relationships of clinical relevance were found. This suggests that ESS is a poor choice as an end point for clinical development if treatment is targeted at improving AHI, and especially so in a mild OSA patient group.

Evaluation of postprandial total triglycerides within the TIGG model for characterizing postprandial response of glucose, insulin, and GLP-1

The TIGG model is the first model to integrate glucose and insulin regulation, incretin effect, and triglyceride (TG) response in the lipoprotein subclasses of chylomicrons and VLDL-V6. This model described the response following a high-fat meal in individuals who are lean, obese, and very obese and provided insights into the possible regulation of glucose homeostasis in the extended period following a meal. Often, total TGs are analyzed within clinical studies, instead of lipoprotein subclasses. We extended the existing TIGG model to capture the observed total TGs and determined if this model could be used to predict the postprandial TG response of chylomicron and VLDL-V6 when only total TGs are available. To assess if the lipoprotein distinction was important for the model, a second model (tTIGG) was developed using only the postprandial response in total TGs, instead of postprandial TG response in chylomicrons and VLDL-V6. The two models were compared on their predictability to characterize the postprandial response of glucose, insulin, and active GLP-1. Both models were able to characterize the postprandial TG response in individuals who are lean, obese, or very obese following a high-fat meal. The extended TIGG model resulted in a better model fit of the glucose data compared to the tTIGG model, indicating that chylomicron and VLDL-V6 provided additional information compared to total TGs. Furthermore, the expanded TIGG model was able to predict the postprandial TG response of chylomicrons and VLDL-V6 using the total TGs and could therefore be used in studies where only total TGs were collected.

Altered glucose-dependent secretion of glucagon and ACTH is associated with insulin resistance, assessed by population analysis

This study aimed to characterize how the dysregulation of counter-regulatory hormones can contribute to insulin resistance and potentially to diabetes. Therefore, we investigated the association between insulin sensitivity and the glucose- and insulin-dependent secretion of glucagon, adrenocorticotropic hormone (ACTH), and cortisol in non-diabetic individuals using a population model analysis. Data, from hyperinsulinemic-hypoglycemic clamps, were pooled for analysis, including 52 individuals with a wide range of insulin resistance (reflected by glucose infusion rate 20-60 min; GIR20-60min). Glucagon secretion was suppressed by glucose and, to a lesser extent, insulin. The GIR20-60min and BMI were identified as predictors of the insulin effect on glucagon. At normoglycemia (5 mmol/L), a 90% suppression of glucagon was achieved at insulin concentrations of 16.3 and 43.4 µU/mL in individuals belonging to the highest and lowest quantiles of insulin sensitivity, respectively. Insulin resistance of glucagon secretion explained the elevated fasting glucagon for individuals with a low GIR20-60min. ACTH secretion was suppressed by glucose and not affected by insulin. The GIR20-60min was superior to other measures as a predictor of glucose-dependent ACTH secretion, with 90% suppression of ACTH secretion by glucose at 3.1 and 3.5 mmol/L for insulin-sensitive and insulin-resistant individuals, respectively. This difference may appear small but shifts the suppression range into normoglycemia for individuals with insulin resistance, thus, leading to earlier and greater ACTH/cortisol response when the glucose falls. Based on modeling of pooled glucose-clamp data, insulin resistance was associated with generally elevated glucagon and a potentiated cortisol-axis response to hypoglycemia, and over time both hormonal pathways may therefore contribute to dysglycemia and possibly type 2 diabetes.

Optimal dosing of gliclazide - a model-based approach

Gliclazide was approved as a treatment for type 2 diabetes in an era before model-based drug development and consequently the recommended doses were not optimized with modern methods. To investigate various dosing regimens of gliclazide, we used publicly available data to characterise the dose-response relationship using pharmacometric models. A literature search identified 21 published gliclazide pharmacokinetic (PK) studies with full profiles. These were digitized and a PK model was developed for immediate- (IR) and modified-release (MR) formulations. Data from a gliclazide dose-ranging study of postprandial glucose were used to characterise the concentration-response relationship, using the integrated glucose-insulin model. Simulations from the full model showed that the maximum effect was 44% of the patients achieving HbA1c<7 % with 11% experiencing glucose<3 mmol/L and the most sensitive patients (i.e., 5% most extreme) experiencing 35 min of hypoglycaemia. Simulations revealed that the recommended IR dose (320 mg) was appropriate with no efficacy gain with increased dose. However, the recommended dose for the MR formulation may be increased to 270 mg, with more patients achieving HbA1c goals (i.e., HbA1c<7%) without a hypoglycaemic risk higher than the resulting risk from the recommended IR dose.

Optimization of trial duration to predict long-term HbA1c change with therapy: A pharmacometrics simulation-based evaluation

Glycated hemoglobin (HbA1c) is the main biomarker of diabetes drug development. However, because of its delayed turnover, trial duration is rarely shorter than 12 weeks, and being able to predict long-term HbA1c with precision using data from shorter studies would be beneficial. The feasibility of reducing study duration was therefore investigated in this study, assuming a model-based analysis. The aim was to investigate the predictive performance of 24- and 52-week extrapolations using data from up to 4, 6, 8 or 12 weeks, with six previously published pharmacometric models of HbA1c. Predictive performance was assessed through simulation-based dose-response predictions and model averaging (MA) with two hypothetical drugs. Results were consistent across the methods of assessment, with MA supporting the results derived from the model-based framework. The models using mean plasma glucose (MPG) or nonlinear fasting plasma glucose (FPG) effect, driving the HbA1c formation, showed good predictive performance despite a reduced study duration. The models, using the linear effect of FPG to drive the HbA1c formation, were sensitive to the limited amount of data in the shorter studies. The MA with bootstrap demonstrated strongly that a 4-week study duration is insufficient for precise predictions of all models. Our findings suggest that if data are analyzed with a pharmacometric model with MPG or FPG with a nonlinear effect to drive HbA1c formation, a study duration of 8 weeks is sufficient with maintained accuracy and precision of dose-response predictions.

Impact of Obesity on Postprandial Triglyceride Contribution to Glucose Homeostasis, Assessed with a Semimechanistic Model

The integrated glucose-insulin model is a semimechanistic model describing glucose and insulin after a glucose challenge. Similarly, a semiphysiologic model of the postprandial triglyceride (TG) response in chylomicrons and VLDL-V6 was recently published. We have developed the triglyceride-insulin-glucose-GLP-1 (TIGG) model by integrating these models and active GLP-1. The aim was to characterize, using the TIGG model, the postprandial response over 13 hours following a high-fat meal in 3 study populations based on body mass index categories: lean, obese, and very obese. Differential glucose and lipid regulation were observed between the lean population and obese or very obese populations. A population comparison revealed further that fasting glucose and insulin were elevated in obese and very obese when compared with lean; and euglycemia was achieved at different times postmeal between the obese and very obese populations. Postprandial insulin was incrementally elevated in the obese and very obese populations compared with lean. Postprandial chylomicrons TGs were similar across populations, whereas the postprandial TGs in VLDL-V6 were increased in the obese and very obese populations compared with lean. Postprandial active GLP-1 was diminished in the very obese population compared with lean or obese. The TIGG model described the response following a high-fat meal in individuals who are lean, obese, and very obese and provided insight into the possible regulation of glucose homeostasis in the extended period after the meal by utilizing lipids. The TIGG-model is the first model to integrate glucose and insulin regulation, incretin effect, and postprandial TGs response in chylomicrons and VLDL-V6.

Postprandial triglyceride reduction following acute treatment of a selective 5-hydroxytryptamine-2c agonist and characterization using a semi-physiological model

AIM

To investigate the tolerability, pharmacokinetics (PK) and postprandial triglyceride (TG) response of single, escalating oral doses of a selective 5-hydroxytryptamine-2c (5-HT_2c ) agonist in subjects with overweight/obesity and apply mechanistic population pharmacokinetic-pharmacodynamic modelling to identify a plausible drug mechanism of action.

MATERIALS AND METHODS

This phase 1, single-centre, double-blind, randomized, placebo-controlled, four-period, two-alternating cohorts study evaluated single escalating oral doses ranging from 5 to 130 mg of LY2140112 (LY) in subjects with overweight/obesity (body mass index: 27-39 kg/m² ). Postprandial TG response (total TG, chylomicrons and very low-density lipoprotein particles [VLDL]-V6) following a high-fat meal were assessed for 11 h postmeal for each dose level. The PK profile was assessed for 96 h postdose. Drug exposure and TG concentrations in chylomicrons and VLDL-V6 were used to characterize the drug mechanism of action using non-linear mixed-effect modelling.

RESULTS

Seventeen subjects entered the study and 16 subjects received at least one dose of LY. LY2140112 was generally well tolerated up to 75 mg. The PK of LY were described by a two-compartment model with first-order elimination. The 100 and 130 mg dose levels of LY significantly reduced the postprandial TG of VLDL-V6 by approximately 50%, while total TG and chylomicrons were not significantly different from placebo. The application of a published lipokinetic model successfully described the postprandial TG response in this study and indicated that LY reduced the conversion of TGs from chylomicron to VLDL-V6.

CONCLUSIONS

LY significantly reduced the postprandial TG of VLDL-V6 following a single dose, when food consumption was controlled. The data indicate that a selective 5-HT_2c agonist alters lipid metabolism, beyond the reported reduction in satiety. The application of a semi-physiological lipokinetic model enabled identification of a plausible drug mechanism of action of LY.

An Item Response Theory-Informed Strategy to Model Total Score Data from Composite Scales

Composite scale data is widely used in many therapeutic areas and consists of several categorical questions/items that are usually summarized into a total score (TS). Such data is discrete and bounded by nature. The gold standard to analyse composite scale data is item response theory (IRT) models. However, IRT models require item-level data while sometimes only TS is available. This work investigates models for TS. When an IRT model exists, it can be used to derive the information as well as expected mean and variability of TS at any point, which can inform TS-analyses. We propose a new method: IRT-informed functions of expected values and standard deviation in TS-analyses. The most common models for TS-analyses are continuous variable (CV) models, while bounded integer (BI) models offer an alternative that respects scale boundaries and the nature of TS data. We investigate the method in CV and BI models on both simulated and real data. Both CV and BI models were improved in fit by IRT-informed disease progression, which allows modellers to precisely and accurately find the corresponding latent variable parameters, and IRT-informed SD, which allows deviations from homoscedasticity. The methodology provides a formal way to link IRT models and TS models, and to compare the relative information of different model types. Also, joint analyses of item-level data and TS data are made possible. Thus, IRT-informed functions can facilitate total score analysis and allow a quantitative analysis of relative merits of different analysis methods.

Comparison of Precision and Accuracy of Five Methods to Analyse Total Score Data

Total score (TS) data is generated from composite scales consisting of several questions/items, such as the Movement Disorder Society-Unified Parkinson's Disease Rating Scale (MDS-UPDRS). The analysis method that most fully uses the information gathered is item response theory (IRT) models, but these are complex and require item-level data which may not be available. Therefore, the TS is commonly analysed with standard continuous variable (CV) models, which do not respect the bounded nature of data. Bounded integer (BI) models do respect the data nature but are not as extensively researched. Mixed models for repeated measures (MMRM) are an alternative that requires few assumptions and handles dropout without bias. If an IRT model exists, the expected mean and standard deviation of TS can be computed through IRT-informed functions-which allows CV and BI models to estimate parameters on the IRT scale. The fit, performance on external data and parameter precision (when applicable) of CV, BI and MMRM to analyse simulated TS data from the MDS-UPDRS motor subscale are investigated in this work. All models provided accurate predictions and residuals without trends, but the fit of CV and BI models was improved by IRT-informed functions. The IRT-informed BI model had more precise parameter estimates than the IRT-informed CV model. The IRT-informed models also had the best performance on external data, while the MMRM model was worst. In conclusion, (1) IRT-informed functions improve TS analyses and (2) IRT-informed BI models had more precise IRT parameter estimates than IRT-informed CV models.

A Time-to-Event Model Relating Integrated Craving to Risk of Smoking Relapse Across Different Nicotine Replacement Therapy Formulations

Smoking increases the risk of cancer and other diseases, causing an estimated 7 million deaths per year. Nicotine replacement therapy (NRT) reduces craving for smoking, therefore, increasing an individual's probability to remain abstinent. In this work, we for the first time quantitatively described the relationship between craving and smoking abstinence, using retrospectively collected data from 19 studies, including 3 NRT formulations (inhaler, mouth spray, and patch) and a combination of inhaler and patch. Smokers motivated to quit were included in the NRT or placebo arms. Integrated craving (i.e., craving over a period of time) was assessed with 4-category, 5-category, or 100-mm visual analogue scale. The bounded integer model was used to assess latent craving from all scales. A time-to-event model linked predicted integrated craving to the hazard of smoking relapse. Available data included 9,323 adult subjects, observed for 3 weeks up to 2 years. At the study end, 9% (11% for NRT and 5% for placebo), on average, remained abstinent according to the protocol definition. A Gompertz-Makeham hazard best described the data, with a hazard of smoking relapse decreasing over time. Latent integrated craving was positively related to the hazard of smoking relapse, through a sigmoidal maximum effect function. For the same craving, being on NRT was found to reduce the hazard of relapse by an additional 30% compared with placebo. This work confirmed that low craving is associated with a high probability of remaining smoking abstinent and that NRT, in addition to reducing craving, increases the probability of remaining smoking abstinent.

Optimal Designs for Model-Based Assessment of Insulin Sensitivity and Glucose Effectiveness

The integrated minimal model allows assessment of clinical diagnosis indices, for example, insulin sensitivity (S_I ) and glucose effectiveness (S_G ), from data of the insulin-modified intravenous glucose tolerance test (IVGTT), which is laborious with an intense sampling schedule, up to 32 samples. The aim of this study was to propose a more informative, although less laborious, IVGTT design to be used for model-based assessment of S_I and S_G . The IVGTT design was optimized simultaneously for all design variables: glucose and insulin infusion doses, time of glucose dose and start of insulin infusion, insulin infusion duration, sampling times, and number of samples. Design efficiency was used to compare among different designs. The simultaneously optimized designs showed a profound higher efficiency than both standard rich (32 samples) and sparse (10 samples) designs. The optimized designs, after removing replicate sample times, were 1.9 and 7.1 times more efficient than the standard rich and sparse designs, respectively. After including practical aspects of the designs, for example, sufficient duration between samples and avoidance of prolonged hypoglycemia, we propose 2 practical designs with fewer sampling times and lower input of glucose and insulin than standard designs, constrained to prevent hypoglycemia. The optimized practical rich design is equally efficient in assessing S_I and S_G as the rich standard design, but with half the number of the samples, while the optimized practical sparse design has 1 less sample and requires 4.6 times fewer individuals for equal certainty when assessing S_I and S_G than the sparse standard design.

Relating Nicotine Plasma Concentration to Momentary Craving Across Four Nicotine Replacement Therapy Formulations

Tobacco use is a major health concern. To assist smoking cessation, nicotine replacement therapy (NRT) is used to reduce nicotine craving. We quantitatively described the relationship between nicotine pharmacokinetics (PKs) from NRTs and momentary craving, linking two different pharmacodynamic (PD) scales for measuring craving. The dataset comprised retrospective data from 17 clinical studies and included 1,077 adult smokers with 39,802 craving observations from four formulations: lozenge, gum, mouth spray, and patch. A PK/PD model was developed that linked individual predicted nicotine concentrations with the categorical and visual analogue PD scales through a joint bounded integer model. A maximum effect model, accounting for acute tolerance development, successfully related nicotine concentrations to momentary craving. Results showed that all formulations were similarly effective in reducing craving, albeit with a fourfold lower potency for the patch. Women were found to have a higher maximal effect of nicotine to reduce craving, compared with men.

A Bounded Integer Model for Rating and Composite Scale Data

Rating and composite scales are commonly used to assess treatment efficacy. The two main strategies for modelling such endpoints are to treat them as a continuous or an ordered categorical variable (CV or OC). Both strategies have disadvantages, including making assumptions that violate the integer nature of the data (CV) and requiring many parameters for scales with many response categories (OC). We present a method, called the bounded integer (BI) model, which utilises the probit function with fixed cut-offs to estimate the probability of a certain score through a latent variable. This method was successfully implemented to describe six data sets from four different therapeutic areas: Parkinson's disease, Alzheimer's disease, schizophrenia, and neuropathic pain. Five scales were investigated, ranging from 11 to 181 categories. The fit (likelihood) was better for the BI model than for corresponding OC or CV models (ΔAIC range 11-1555) in all cases but one (∆AIC - 63), while the number of parameters was the same or lower. Markovian elements were successfully implemented within the method. The performance in external validation, assessed through cross-validation, was also in favour of the new model (ΔOFV range 22-1694) except in one case (∆OFV - 70). A residual for diagnostic purposes is discussed. This study shows that the BI model respects the integer nature of data and is parsimonious in terms of number of estimated parameters.

Translation Between Two Models; Application with Integrated Glucose Homeostasis Models

PURPOSE

For some biological systems, there exist several models with somewhat different features and perspectives. We propose an evaluation method for NLME models by analyzing real and simulated data from the model of main interest using a structurally different, but similar, NLME model. We showcase this method using the Integrated Glucose Insulin (IGI) model and the Integrated Minimal Model (IMM). Additionally, we try to map parameters carrying similar information between the two models.

METHODS

A bootstrap of real data and simulated datasets from both the IMM and IGI models were analyzed with the two models. Important parameters of the IMM were mapped to IGI parameters using a large IMM simulated dataset analyzed under the IGI model.

RESULTS

Comparison of the parameters estimated from real data and data simulated with the IMM and analyzed with the IGI model demonstrated differences between real and IMM-simulated data. Comparison of the parameters estimated from real data and data simulated with the IGI model and analyzed with the IMM also demonstrated differences but to a lower extent. The strongest parameter correlations were found for: insulin-dependent glucose clearance (IGI) ~ insulin sensitivity (IMM); insulin-independent glucose clearance (IGI) ~ glucose effectiveness (IMM); and insulin effect parameter (IGI) ~ insulin action (IMM).

CONCLUSIONS

We demonstrated a new approach to investigate models' ability to simulate real-life-like data, and the information captured in each model in comparison to real data, and the IMM clinically used parameters were successfully mapped to their corresponding IGI parameters.

Variability Attribution for Automated Model Building

We investigated the possible advantages of using linearization to evaluate models of residual unexplained variability (RUV) for automated model building in a similar fashion to the recently developed method “residual modeling.” Residual modeling, although fast and easy to automate, cannot identify the impact of implementing the needed RUV model on the imprecision of the rest of model parameters. We used six RUV models to be tested with 12 real data examples. Each example was first linearized; then, we assessed the agreement in improvement of fit between the base model and its extended models for linearization and conventional analysis, in comparison to residual modeling performance. Afterward, we compared the estimates of parameters’ variabilities and their uncertainties obtained by linearization to conventional analysis. Linearization accurately identified and quantified the nature and magnitude of RUV model misspecification similar to residual modeling. In addition, linearization identified the direction of change and quantified the magnitude of this change in variability parameters and their uncertainties. This method is implemented in the software package PsN for automated model building/evaluation with continuous data.

Model-Based Conditional Weighted Residuals Analysis for Structural Model Assessment

Nonlinear mixed effects models are widely used to describe longitudinal data to improve the efficiency of drug development process or increase the understanding of the studied disease. In such settings, the appropriateness of the modeling assumptions is critical in order to draw correct conclusions and must be carefully assessed for any substantial violations. Here, we propose a new method for structure model assessment, based on assessment of bias in conditional weighted residuals (CWRES). We illustrate this method by assessing prediction bias in two integrated models for glucose homeostasis, the integrated glucose-insulin (IGI) model, and the integrated minimal model (IMM). One dataset was simulated from each model then analyzed with the two models. CWRES outputted from each model fitting were modeled to capture systematic trends in CWRES as well as the magnitude of structural model misspecifications in terms of difference in objective function values (ΔOFV_Bias). The estimates of CWRES bias were used to calculate the corresponding bias in conditional predictions by the inversion of first-order conditional estimation method’s covariance equation. Time, glucose, and insulin concentration predictions were the investigated independent variables. The new method identified correctly the bias in glucose sub-model of the integrated minimal model (IMM), when this bias occurred, and calculated the absolute and proportional magnitude of the resulting bias. CWRES bias versus the independent variables agreed well with the true trends of misspecification. This method is fast easily automated diagnostic tool for model development/evaluation process, and it is already implemented as part of the Perl-speaks-NONMEM software.

Model-Based Residual Post-Processing for Residual Model Identification

The purpose of this study was to investigate if model-based post-processing of common diagnostics can be used as a diagnostic tool to quantitatively identify model misspecifications and rectifying actions. The main investigated diagnostic is conditional weighted residuals (CWRES). We have selected to showcase this principle with residual unexplained variability (RUV) models, where the new diagnostic tool is used to scan extended RUV models and assess in a fast and robust way whether, and what, extensions are expected to provide a superior description of data. The extended RUV models evaluated were autocorrelated errors, dynamic transform both sides, inter-individual variability on RUV, power error model, t-distributed errors, and time-varying error magnitude. The agreement in improvement in goodness-of-fit between implementing these extended RUV models on the original model and implementing these extended RUV models on CWRES was evaluated in real and simulated data examples. Real data exercise was applied to three other diagnostics: conditional weighted residuals with interaction (CWRESI), individual weighted residuals (IWRES), and normalized prediction distribution errors (NPDE). CWRES modeling typically predicted (i) the nature of model misspecifications, (ii) the magnitude of the expected improvement in fit in terms of difference in objective function value (ΔOFV), and (iii) the parameter estimates associated with the model extension. Alternative metrics (CWRESI, IWRES, and NPDE) also provided valuable information, but with a lower predictive performance of ΔOFV compared to CWRES. This method is a fast and easily automated diagnostic tool for RUV model development/evaluation process; it is already implemented in the software package PsN.

Study Design Selection in Early Clinical Anti-Hyperglycemic Drug Development: A Simulation Study of Glucose Tolerance Tests

In antidiabetic drug development, phase I studies usually involve short‐term glucose provocations. Multiple designs are available for these provocations (e.g., meal tolerance tests (MTTs) and graded glucose infusions (GGIs)). With a highly nonlinear, complex system as the glucose homeostasis, the various provocations will contribute with different information offering a rich choice. Here, we investigate the most appropriate study design in phase I for several hypothetical mechanisms of action of a study drug. Five drug effects in diabetes therapeutic areas were investigated using six study designs. Power to detect drug effect was assessed using the likelihood ratio test, whereas precision and accuracy of the quantification of drug effect was assessed using stochastic simulation and estimations. An overall summary was developed to aid designing the studies of antihyperglycemic drug development using model‐based analysis. This guidance is to be used when the integrated glucose insulin model is used, involving the investigated drug mechanisms of action.

Evidence-Based Design of Fixed-Dose Combinations: Principles and Application to Pediatric Anti-Tuberculosis Therapy

BACKGROUND AND OBJECTIVES

Fixed-dose combination formulations where several drugs are included in one tablet are important for the implementation of many long-term multidrug therapies. The selection of optimal dose ratios and tablet content of a fixed-dose combination and the design of individualized dosing regimens is a complex task, requiring multiple simultaneous considerations.

METHODS

In this work, a methodology for the rational design of a fixed-dose combination was developed and applied to the case of a three-drug pediatric anti-tuberculosis formulation individualized on body weight. The optimization methodology synthesizes information about the intended use population, the pharmacokinetic properties of the drugs, therapeutic targets, and practical constraints. A utility function is included to penalize deviations from the targets; a sequential estimation procedure was developed for stable estimation of break-points for individualized dosing. The suggested optimized pediatric anti-tuberculosis fixed-dose combination was compared with the recently launched World Health Organization-endorsed formulation.

RESULTS

The optimized fixed-dose combination included 15, 36, and 16% higher amounts of rifampicin, isoniazid, and pyrazinamide, respectively. The optimized fixed-dose combination is expected to result in overall less deviation from the therapeutic targets based on adult exposure and substantially fewer children with underexposure (below half the target).

CONCLUSION

The development of this design tool can aid the implementation of evidence-based formulations, integrating available knowledge and practical considerations, to optimize drug exposures and thereby treatment outcomes.

Comparison of Power, Prognosis, and Extrapolation Properties of Four Population Pharmacodynamic Models of HbA1c for Type 2 Diabetes

Reusing published models saves time; time to be used for informing decisions in drug development. In antihyperglycemic drug development, several published HbA1c models are available but selecting the appropriate model for a particular purpose is challenging. This study aims at helping selection by investigating four HbA1c models, specifically the ability to identify drug effects (shape, site of action, and power) and simulation properties. All models could identify glucose effect nonlinearities, although for detecting the site of action, a mechanistic glucose model was needed. Power was highest for models using mean plasma glucose to drive HbA1c formation. Insulin contribution to power varied greatly depending on the drug target; it was beneficial only if the drug target was insulin secretion. All investigated models showed good simulation properties. However, extrapolation with the mechanistic model beyond 12 weeks resulted in drug effect overprediction. This investigation aids drug development in decisions regarding model choice if reusing published HbA1c models.

Semi-physiological model of postprandial triglyceride response in lean, obese and very obese individuals after a high-fat meal

AIMS

To quantify the postprandial triglyceride (TG) response of chylomicrons and very-low-density lipoprotein-V6 (VLDL-V6) after a high-fat meal in lean, obese and very obese healthy individuals, using a mechanistic population lipokinetic modelling approach.

METHODS

Healthy individuals from three body mass index population categories: lean (18.5-24.9 kg/m² ), obese (30-33 kg/m² ), and very obese (34-40 kg/m² ) were enrolled in a clinical study to assess the TG response after a high-fat meal, containing 60% fat. Non-linear mixed-effect modelling was used to analyse the TG concentrations of chylomicrons and large VLDL-V6 particles.

RESULTS

The TGs in chylomicrons and VLDL-V6 particles had a prominent postprandial peak and represented the majority of the postprandial response; only the VLDL-V6 showed a difference across the populations. A turn-over model successfully described the TG concentration-time profiles of both chylomicrons and large VLDL-V6 particles after the high-fat meal. This model consisted of four compartments: two transit compartments for the lag between meal consumption and appearance of TGs in the blood, and one compartment each for the chylomicrons and large VLDL-V6 particles. The rate constants for the production of chylomicrons and elimination of large VLDL-V6 particles, along with the conversion rate of chylomicrons to large VLDL-V6 particles were well defined.

CONCLUSIONS

This is the first lipokinetic model to describe the absorption of TGs from dietary fats into the blood stream and compares the dynamics of TGs in chylomicrons and large VLDL-V6 particles among lean, obese and very obese people. Such a model can be used to identify where pharmacological therapies act, thereby improving the determination of efficacy, and identifying complementary mechanisms for combinational drug therapies.

Model-Based Interspecies Scaling of Glucose Homeostasis

Being able to scale preclinical pharmacodynamic response to clinical would be beneficial in drug development. In this work, the integrated glucose insulin (IGI) model, developed on clinical intravenous glucose tolerance test (IVGTT) data, describing dynamic glucose and insulin concentrations during glucose tolerance tests, was scaled to describe data from similar tests performed in healthy rats, mice, dogs, pigs, and humans. Several approaches to scaling the dynamic glucose and insulin were investigated. The theoretical allometric exponents of 0.75 and 1, for clearances and volumes, respectively, could describe the data well with some species-specific adaptations: dogs and pigs showed slower first phase insulin secretion than expected from the scaling, pigs also showed more rapid insulin dependent glucose elimination, and rodents showed differences in glucose effectiveness. The resulting scaled IGI model was shown to accurately predict external preclinical IVGTT data and may be useful in facilitating translations of preclinical research into the clinic.

Implications for Drug Characterization in Glucose Tolerance Tests Without Insulin: Simulation Study of Power and Predictions Using Model-Based Analysis

In antihyperglycemic drug development, drug effects are usually characterized using glucose provocations. Analyzing provocation data using pharmacometrics has shown powerful, enabling small studies. In preclinical drug development, high power is attractive due to the experiment sizes; however, insulin is not always available, which potentially impacts power and predictive performance. This simulation study was performed to investigate the implications of performing model-based drug characterization without insulin. The integrated glucose-insulin model was used to simulate and re-estimated oral glucose tolerance tests using a crossover design of placebo and study compound. Drug effects were implemented on seven different mechanisms of action (MOA); one by one or in two-drug combinations. This study showed that exclusion of insulin may severely reduce the power to distinguish the correct from competing drug effect, and to detect a primary or secondary drug effect, however, it did not affect the predictive performance of the model.

Application of the integrated glucose-insulin model for cross-study characterization of T2DM patients on metformin background treatment

AIM

The integrated glucose-insulin (IGI) model is a semi-mechanistic physiological model which can describe the glucose-insulin homeostasis system following various glucose challenge settings. The aim of the present work was to apply the model to a large and diverse population of metformin-only-treated type 2 diabetes mellitus (T2DM) patients and identify patient-specific covariates.

METHODS

Data from four clinical studies were pooled, including glucose and insulin concentration-time profiles from T2DM patients on stable treatment with metformin alone following mixed-meal tolerance tests. The data were collected from a wide range of patients with respect to the duration of diabetes and level of glycaemic control.

RESULTS

The IGI model was expanded by four patient-specific covariates. The level of glycaemic control, represented by baseline glycosylated haemoglobin was identified as a significant covariate for steady-state glucose, insulin-dependent glucose clearance and the magnitude of the incretin effect, while baseline body mass index was a significant covariate for steady-state insulin levels. In addition, glucose dose was found to have an impact on glucose absorption rate. The developed model was used to simulate glucose and insulin profiles in different groups of T2DM patients, across a range of glycaemic control, and it was found accurately to characterize their response to the standard oral glucose challenge.

CONCLUSIONS

The IGI model was successfully applied to characterize differences between T2DM patients across a wide range of glycaemic control. The addition of patient-specific covariates in the IGI model might be valuable for the future development of antidiabetic treatment and for the design and simulation of clinical studies.

Modeling the Disease Progression from Healthy to Overt Diabetes in ZDSD Rats

Studying the critical transitional phase between healthy to overtly diabetic in type 2 diabetes mellitus (T2DM) is of interest, but acquiring such clinical data is impractical due to ethical concerns and would require a long study duration. A population model using Zucker diabetic Sprague-Dawley (ZDSD) rats was developed to describe this transition through altering insulin sensitivity (IS, %) as a result of accumulating excess body weight and β-cell function (BCF, %) to affect glucose-insulin homeostasis. Body weight, fasting plasma glucose (FPG), and fasting serum insulin (FSI) were collected biweekly over 24 weeks from ZDSD rats (n = 23) starting at age 7 weeks. A semi-mechanistic model previously developed with clinical data was adapted to rat data with BCF and IS estimated relative to humans. Non-linear mixed-effect model estimation was performed using NONMEM. Baseline IS and BCF were 41% compared to healthy humans. BCF was described with a non-linear rise which peaked at 14 weeks before gradually declining to a negligible level. A component for excess growth reflecting obesity was used to affect IS, and a glucose-dependent renal effect exerted a two- to sixfold increase on the elimination of glucose. A glucose-dependent weight loss effect towards the end of experiment was implemented. A semi-mechanistic model to describe the dynamics of glucose and insulin was successfully developed for a rat population, transitioning from healthy to advanced diabetes. It is also shown that weight loss can be modeled to mimic the glucotoxicity phenomenon seen in advanced hyperglycemia.

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, today's 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.

Weight-HbA1c-insulin-glucose model for describing disease progression of type 2 diabetes

A previous semi‐mechanistic model described changes in fasting serum insulin (FSI), fasting plasma glucose (FPG), and glycated hemoglobin (HbA1c) in patients with type 2 diabetic mellitus (T2DM) by modeling insulin sensitivity and β‐cell function. It was later suggested that change in body weight could affect insulin sensitivity, which this study evaluated in a population model to describe the disease progression of T2DM. Nonlinear mixed effects modeling was performed on data from 181 obese patients with newly diagnosed T2DM managed with diet and exercise for 67 weeks. Baseline β‐cell function and insulin sensitivity were 61% and 25% of normal, respectively. Management with diet and exercise (mean change in body weight = −4.1 kg) was associated with an increase of insulin sensitivity (30.1%) at the end of the study. Changes in insulin sensitivity were associated with a decrease of FPG (range, 7.8–7.3 mmol/L) and HbA1c (6.7–6.4%). Weight change as an effector on insulin sensitivity was successfully evaluated in a semi‐mechanistic population model.

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 model's description of glucose absorption and gastric emptying after tests with varying glucose doses. The developed model's 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.

Nonlinear mixed-effects modelling for single cell estimation: when, why, and how to use it

Background

Studies of cell-to-cell variation have in recent years grown in interest, due to improved bioanalytical techniques which facilitates determination of small changes with high uncertainty. Like much high-quality data, single-cell data is best analysed using a systems biology approach. The most common systems biology approach to single-cell data is the standard two-stage (STS) approach. In STS, data from each cell is analysed in a separate sub-problem, meaning that only data from the same cell is used to calculate the parameter values within that cell. Because only parts of the data are considered, problems with parameter unidentifiability are exaggerated in STS. In contrast, a related approach to data analysis has been developed for the studies of patient-to-patient variations. This approach, called nonlinear mixed-effects modelling (NLME), makes use of all data, when estimating the patient-specific parameters. NLME would therefore be advantageous compared to STS also for the study of cell-to-cell variation. However, no such systematic evaluation of the two approaches exists.

Results

Herein, such a systematic comparison between STS and NLME has been performed. Different examples, both linear and nonlinear, and both simulated and real experimental data, have been examined. With informative data, there is no significant difference in the results for either parameter or noise estimation. However, when data becomes uninformative, NLME is significantly superior to STS. These results hold independently of whether the loss of information is due to a low signal-to-noise ratio, too few data points, or a bad input signal. The improvement is shown to come from both the consideration of a joint likelihood (JLH) function, describing all parameters and data, and from an a priori postulated form of the population parameters. Finally, we provide a small tutorial that shows how to use NLME for single-cell analysis, using the free and user-friendly software Monolix.

Conclusions

When considering uninformative single-cell data, NLME yields more accurate parameter and noise estimates, compared to more traditional approaches, such as STS and JLH.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0203-x) contains supplementary material, which is available to authorized users.

The Effects of a GLP-1 Analog on Glucose Homeostasis in Type 2 Diabetes Mellitus Quantified by an Integrated Glucose Insulin Model

In recent years, several glucagon-like peptide-1 (GLP-1)-based therapies for the treatment of type 2 diabetes mellitus (T2DM) have been developed. The aim of this work was to extend the semimechanistic integrated glucose-insulin model to include the effects of a GLP-1 analog on glucose homeostasis in T2DM patients. Data from two trials comparing the effect of steady-state liraglutide vs. placebo on the responses of postprandial glucose and insulin in T2DM patients were used for model development. The effect of liraglutide was incorporated in the model by including a stimulatory effect on insulin secretion. Furthermore, for one of the trials an inhibitory effect on glucose absorption was included to account for a delay in gastric emptying. As other GLP-1 receptor agonists have similar modes of action, it is believed that the model can also be used to describe the effect of other receptor agonists on glucose homeostasis.

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.

Abscess penetration of cefpirome: concentrations and simulated pharmacokinetic profiles in pus

PURPOSE

Abscess patients frequently receive antibiotic therapy when incision cannot be performed or in addition to incision. However, antibiotic concentrations in human abscesses are widely unknown.

METHODS

Pharmacokinetics of cefpirome in 12 human abscesses located in different body regions was studied. Cefpirome (2 g) was administered as an intravenous short infusion, and concentrations were measured in plasma over an 8-h period and in abscesses at incision. A pharmacokinetic two-stage model was applied.

RESULTS

At abscess incision performed 158 ± 112 min after the start of the infusion, the cefpirome concentrations in the abscess fluid varied markedly, ranging from ≤0.1 (limit of quantification) to 47 (mean 8.4 ± 14.1 ) mg/L. Cefpirome was detectable in nine of 12 abscesses. Maximum concentrations were calculated to be 183 ± 106 mg/L in plasma and 12 ± 16 mg/L in the abscess. A cefpirome concentration of 2 mg/L, which is the minimum concentration inhibiting growth of 90% of the most relevant bacterial pathogens, was exceeded spontaneously in six of 12 abscesses after a single dose. Cefpirome concentrations in the abscess did not correlate with either the pH or the ratio of surface area to volume of the abscesses, nor with plasma pharmacokinetics.

CONCLUSIONS

Cefpirome may be useful to treat abscess patients because it was detectable in most abscesses after a single dose. However, the penetration of cefpirome into abscesses is extremely variable and cannot be predicted by measuring other available covariates.

Good penetration of moxifloxacin into human abscesses

Abscesses are often treated with antibiotics in addition to incision or when incision is unfeasible, but accurate information about antibiotic abscess penetration in humans is missing. This study aimed at evaluating the penetration of moxifloxacin into human abscesses. After administration of a single dose of 400 mg moxifloxacin, drug concentrations were measured in 10 differently located abscesses at incision, and in plasma over 8 h. At incision performed 0.9-4.8 h after administration, moxifloxacin concentrations in abscesses ranged from ≤0.01 to 9.2 mg/l (1.9 ± 3.4 mg/l), indicating pronounced drug accumulation in some abscesses. The degree of abscess penetration could not be explained by covariates like the ratio of surface area to volume or pH of abscesses, or by moxifloxacin plasma concentrations. Concluding, moxifloxacin was detectable in most abscesses and may be a useful antibiotic for this indication. However, antibiotic abscess penetration was highly variable and unpredictable, suggesting surgical abscess incision whenever possible.

Modeling sleep data for a new drug in development using markov mixed-effects models

PURPOSE

To characterize the time-course of sleep in insomnia patients as well as placebo and concentration-effect relationships of two hypnotic compounds, PD 0200390 and zolpidem, using an accelerated model-building strategy based on mixed-effects Markov models.

METHODS

Data were obtained in a phase II study with the drugs. Sleep stages were recorded during eight hours of sleep for two nights per treatment for the five treatments. First-order Markov models were developed for one transition at a time in a sequential manner; first a baseline model, followed by placebo and lastly the drug models. To accelerate the process, predefined models were selected based on a priori knowledge of sleep, including inter-subject and inter-occasion variability.

RESULTS

Baseline sleep was described using piece-wise linear models, depending on time of night and duration of sleep stage. Placebo affected light sleep stages; drugs also affected slow-wave sleep. Administering PD 0200390 30 min earlier than standard dosing was shown through simulations to reduce latency to persistent sleep by 40%.

CONCLUSION

The proposed accelerated model-building strategy resulted in a model well describing sleep patterns of insomnia patients with and without treatments.

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.

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 back-step method--method for obtaining unbiased population parameter estimates for ordered categorical data

A significant bias in parameters, estimated with the proportional odds model using the software NONMEM, has been reported. Typically, this bias occurs with ordered categorical data, when most of the observations are found at one extreme of the possible outcomes. The aim of this study was to assess, through simulations, the performance of the Back-Step Method (BSM), a novel approach for obtaining unbiased estimates when the standard approach provides biased estimates. BSM is an iterative method involving sequential simulation-estimation steps. BSM was compared with the standard approach in the analysis of a 4-category ordered variable using the Laplacian method in NONMEM. The bias in parameter estimates and the accuracy of model predictions were determined for the 2 methods on 3 conditions: (1) a nonskewed distribution of the response with low interindividual variability (IIV), (2) a skewed distribution with low IIV, and (3) a skewed distribution with high IIV. An increase in bias with increasing skewness and IIV was shown in parameters estimated using the standard approach in NONMEM. BSM performed without appreciable bias in the estimates under the 3 conditions, and the model predictions were in good agreement with the original data. Each BSM estimation represents a random sample of the population; hence, repeating the BSM estimation reduces the imprecision of the parameter estimates. The BSM is an accurate estimation method when the standard modeling approach in NONMEM gives biased estimates.