Dynamic population pharmacokinetic-pharmacodynamic modelling and simulation supports similar efficacy in glycosylated haemoglobin response with once or twice-daily dosing of canagliflozin.

AIM: Canagliflozin is an SGLT2 inhibitor approved for the treatment of type-2 diabetes. A dynamic population pharmacokinetic-pharmacodynamic (PK/PD) model relating 24-h canagliflozin exposure profiles to effects on glycosylated haemoglobin was developed to compare the efficacy of once-daily and twice-daily dosing. METHODS: Data from two clinical studies, one with once-daily, and the other with twice-daily dosing of canagliflozin as add-on to metformin were used (n = 1347). An established population PK model was used to predict full 24-h profiles from measured trough concentrations and/or baseline covariates. The dynamic PK/PD model incorporated an Emax relationship between 24-h canagliflozin exposure and HbA1c-lowering with baseline HbA1c affecting the efficacy. RESULTS: Internal and external model validation demonstrated that the model adequately predicted HbA1c-lowering for canagliflozin once-daily and twice-daily dosing regimens. The differences in HbA1c reduction between the twice-daily and daily mean profiles were minimal (at most 0.023% for 100 mg total daily dose [TDD] and 0.011% for 300 mg TDD, up to week 26, increasing with time and decreasing with TDD) and not considered clinically meaningful. CONCLUSIONS: Simulations using this model demonstrated the absence of clinically meaningful between-regimen differences in efficacy, supported the regulatory approval of a canagliflozin-metformin immediate release fixed-dose combination tablet and alleviated the need for an additional clinical study.

Oxygen Mass Transport in Stented Coronary Arteries.

Oxygen deficiency, known as hypoxia, in arterial walls has been linked to increased intimal hyperplasia, which is the main adverse biological process causing in-stent restenosis. Stent implantation has significant effects on the oxygen transport into the arterial wall. Elucidating these effects is critical to optimizing future stent designs. In this study the most advanced oxygen transport model developed to date was assessed in two test cases and used to compare three coronary stent designs. Additionally, the predicted results from four simplified blood oxygen transport models are compared in the two test cases. The advanced model showed good agreement with experimental measurements within the mass-transfer boundary layer and at the luminal surface; however, more work is needed in predicting the oxygen transport within the arterial wall. Simplifying the oxygen transport model within the blood flow produces significant errors in predicting the oxygen transport in arteries. This study can be used as a guide for all future numerical studies in this area and the advanced model could provide a powerful tool in aiding design of stents and other cardiovascular devices.

Population Pharmacokinetic Modeling of Canagliflozin in Healthy Volunteers and Patients with Type 2 Diabetes Mellitus.

BACKGROUND AND OBJECTIVES: Canagliflozin is an orally active, reversible, selective sodium-glucose co-transporter-2 inhibitor. A population pharmacokinetic (popPK) model of canagliflozin, including relevant covariates as sources of inter-individual variability, was developed to describe phase I, II, and III data in healthy volunteers and in patients with type 2 diabetes mellitus (T2DM). METHODS: The final analysis included 9061 pharmacokinetic (PK) samples from 1616 volunteers enrolled in nine phase I, two phase II, and three phase III studies and was performed using NONMEM(®) 7.1. Inter-individual variability was evaluated using an exponential model and the residual error model was additive in the log domain. The first-order conditional estimation method with interaction was applied and the model was parameterized in terms of rate constants. Covariate effects were explored graphically on empirical Bayes estimates of PK parameters, as shrinkage was low. Clinical relevance of statistically significant covariates was evaluated. The predictive properties of the model were illustrated by prediction-corrected visual predictive checks. RESULTS: A two-compartment PK model with lag-time and sequential zero- and first-order absorption and first-order elimination best described the observed data. Sex, age, and weight on apparent volume of distribution of the central compartment, body mass index on first-order absorption rate constant, and body mass index and over-encapsulation on lag-time, and estimated glomerular filtration rate (eGFR, by MDRD equation), dose, and genetic polymorphism (carriers of UGT1A9*3 allele) on elimination rate constant were identified as statistically significant covariates. The prediction-corrected visual predictive checks revealed acceptable predictive performance of the model. CONCLUSION: The popPK model adequately described canagliflozin PK in healthy volunteers and in patients with T2DM. Because of the small magnitude of statistically significant covariates, they were not considered clinically relevant. However, dosage adjustments are recommended for T2DM patients with renal impairment (eGFR ≥60 mL/min/1.73 m(2): 100 or 300 mg/day; eGFR of 45 to <60 mL/min/1.73 m(2): 100 mg/day).

The method of averaging applied to pharmacokinetic/pharmacodynamic indirect response models.

The computational effort required to fit the pharmacodynamic (PD) part of a pharmacokinetic/pharmacodynamic (PK/PD) model can be considerable if the differential equations describing the model are solved numerically. This burden can be greatly reduced by applying the method of averaging (MAv) in the appropriate circumstances. The MAv gives an approximate solution, which is expected to be a good approximation when the PK profile is periodic (i.e. repeats its values in regular intervals) and the rate of change of the PD response is such that it is approximately constant over a single period of the PK profile. This paper explains the basis of the MAv by means of a simple mathematical derivation. The NONMEM® implementation of the MAv using the abbreviated FORTRAN function FUNCA is described and explained. The application of the MAv is illustrated by means of an example involving changes in glycated hemoglobin (HbA1c%) following administration of canagliflozin, a selective sodium glucose co-transporter 2 inhibitor. The PK/PD model applied to these data is fitted with NONMEM® using both the MAv and the standard method using a numerical differential equation solver (NDES). Both methods give virtually identical results but the NDES method takes almost 8 h to run both the estimation and covariance steps, whilst the MAv produces the same results in less than 30 s. An outline of the NONMEM® control stream and the FORTRAN code for the FUNCA function is provided in the appendices.

Mixed-effects beta regression for modeling continuous bounded outcome scores using NONMEM when data are not on the boundaries.

Beta regression models have been recommended for continuous bounded outcome scores that are often collected in clinical studies. Implementing beta regression in NONMEM presents difficulties since it does not provide gamma functions required by the beta distribution density function. The objective of the study was to implement mixed-effects beta regression models in NONMEM using Nemes' approximation to the gamma function and to evaluate the performance of the NONMEM implementation of mixed-effects beta regression in comparison to the commonly used SAS approach. Monte Carlo simulations were conducted to simulate continuous outcomes within an interval of (0, 70) based on a beta regression model in the context of Alzheimer's disease. Six samples per subject over a 3 years period were simulated at 0, 0.5, 1, 1.5, 2, and 3 years. One thousand trials were simulated and each trial had 250 subjects. The simulation-reestimation exercise indicated that the NONMEM implementation using Laplace and Nemes' approximations provided only slightly higher bias and relative RMSE (RRMSE) compared to the commonly used SAS approach with adaptive Gaussian quadrature and built-in gamma functions, i.e., the difference in bias and RRMSE for fixed-effect parameters, random effects on intercept, and the precision parameter were <1-3 %, while the difference in the random effects on the slope was <3-7 % under the studied simulation conditions. The mixed-effect beta regression model described the disease progression for the cognitive component of the Alzheimer's disease assessment scale from the Alzheimer's Disease Neuroimaging Initiative study. In conclusion, with Nemes' approximation of the gamma function, NONMEM provided comparable estimates to those from SAS for both fixed and random-effect parameters. In addition, the NONMEM run time for the mixed beta regression models appeared to be much shorter compared to SAS, i.e., 1-2 versus 20-40 s for the model and data used in the manuscript.

Shrinkage in nonlinear mixed-effects population models: quantification, influencing factors, and impact.

Shrinkage of empirical Bayes estimates (EBEs) of posterior individual parameters in mixed-effects models has been shown to obscure the apparent correlations among random effects and relationships between random effects and covariates. Empirical quantification equations have been widely used for population pharmacokinetic/pharmacodynamic models. The objectives of this manuscript were (1) to compare the empirical equations with theoretically derived equations, (2) to investigate and confirm the influencing factor on shrinkage, and (3) to evaluate the impact of shrinkage on estimation errors of EBEs using Monte Carlo simulations. A mathematical derivation was first provided for the shrinkage in nonlinear mixed effects model. Using a linear mixed model, the simulation results demonstrated that the shrinkage estimated from the empirical equations matched those based on the theoretically derived equations. Simulations with a two-compartment pharmacokinetic model verified that shrinkage has a reversed relationship with the relative ratio of interindividual variability to residual variability. Fewer numbers of observations per subject were associated with higher amount of shrinkage, consistent with findings from previous research. The influence of sampling times appeared to be larger when fewer PK samples were collected for each individual. As expected, sample size has very limited impact on shrinkage of the PK parameters of the two-compartment model. Assessment of estimation error suggested an average 1:1 relationship between shrinkage and median estimation error of EBEs.

A time scaling approach to develop an in vitro-in vivo correlation (IVIVC) model using a convolution-based technique.

In vitro-in vivo correlation (IVIVC) models prove very useful during drug formulation development, the setting of dissolution specifications and bio-waiver applications following post approval changes. A convolution-based population approach for developing an IVIVC has recently been proposed as an alternative to traditional deconvolution based methods, which pose some statistical concerns. Our aim in this study was to use a time-scaling approach using a convolution-based technique to successfully develop an IVIVC model for a drug with quite different in vitro and in vivo time scales. The in vitro and the in vivo data were longitudinal in nature with considerable between subject variation in the in vivo data. The model was successfully developed and fitted to the data using the NONMEM package. Model utility was assessed by comparing model-predicted plasma concentration-time profiles with the observed in vivo profiles. This comparison met validation criteria for both internal and external predictability as set out by the regulatory authorities. This study demonstrates that a time-scaling approach may prove useful when attempting to develop an IVIVC for data with the aforementioned properties. It also demonstrates that the convolution-based population approach is quite versatile and that it is capable of producing an IVIVC model with a big difference between the in vitro and in vivo time scales.

Impact of low percentage of data below the quantification limit on parameter estimates of pharmacokinetic models.

The objectives of the simulation study were to evaluate the impact of BQL data on pharmacokinetic (PK) parameter estimates when the incidence of BQL data is low (e.g. ≤10%), and to compare the performance of commonly used modeling methods for handling BQL data such as data exclusion (M1) and likelihood-based method (M3). Simulations were performed by adapting the method of a recent publication by Ahn et al. (J Phamacokinet Pharmacodyn 35(4):401-421, 2008). The BQL data in the terminal elimination phase were created at frequencies of 1, 2.5, 5, 7.5, and 10% based on a one- and a two-compartment model. The impact of BQL data on model parameter estimates was evaluated based on bias and imprecision. The simulations demonstrated that for the one-compartment model, the impact of ignoring the low percentages of BQL data (≤10%) in the elimination phase was minimal. For the two-compartment model, when the BQL incidence was less than 5%, omission of the BQL data generally did not inflate the bias in the fixed-effect parameters, whereas more pronounced bias in the estimates of inter-individual variability (IIV) was observed. The BQL data in the elimination phase had the greatest impact on the volume of distribution estimate of the peripheral compartment of the two-compartment model. The M3 method generally provided better parameter estimates for both PK models than the M1 method. However, the advantages of the M3 over the M1 method varied depending on different BQL censoring levels, PK models and parameters. As the BQL percentages decreased, the relative gain of the M3 method based on more complex likelihood approaches diminished when compared to the M1 method. Therefore, it is important to balance the trade-off between model complexity and relative gain in model improvement when the incidence of BQL data is low. Understanding the model structure and the distribution of BQL data (percentage and location of BQL data) allows selection of an appropriate and effective modeling approach for handling low percentages of BQL data.

A population approach to in vitro-in vivo correlation modelling for compounds with nonlinear kinetics.

Developing an In Vitro-In Vivo Correlation (IVIVC) model is becoming an important part of the drug development process. Traditional methods such as deconvolution and convolution make the assumption of linearity of the system being studied and are, therefore, unsuitable for use with compounds exhibiting nonlinear kinetics. This study proposes the use of a compartmental approach which may be based on systems of differential equations, a method which can comfortably accommodate nonlinearity. This technique can easily be implemented using existing NONMEM libraries and is an accurate, fast and straightforward method of developing an IVIVC model.

A dose-finding trial of the effect of long-term folic acid intervention: implications for food fortification policy.

BACKGROUND: The lowest dose of folic acid required to achieve effective reductions in homocysteine is controversial but important for food fortification policy given recent concerns about the potential adverse effects of overexposure to this vitamin. OBJECTIVE: We compared the effectiveness of 0.2 mg folic acid/d with that of 0.4 and 0.8 mg/d at lowering homocysteine concentrations over a 6-mo period. DESIGN: A randomized dose-finding trial with folic acid was conducted. Of 203 participants screened, 101 patients with ischemic heart disease and 71 healthy volunteers completed the study. Participants were randomly assigned to receive placebo or folic acid at doses of 0.2, 0.4, or 0.8 mg/d for 26 wk; subsamples of patients with ischemic heart disease were also examined at 6 or 12 wk. RESULTS: Participants with higher baseline homocysteine concentrations had the greatest reductions in homocysteine in response to folic acid doses of 0.2 mg (-20.6%), 0.4 mg (-20.7%), and 0.8 mg (-27.8%); in those with lower baseline homocysteine concentrations, the responses were -8.2%, -8.9%, and -8.3%, respectively. No significant differences in homocysteine responses to the different doses were observed. In the patient group sampled at intervals during the intervention, the maximal homocysteine response appeared to be achieved by 6 wk in the 0.8-mg/d group and by 12 wk in the 0.4-mg/d group. However, the homocysteine response was suboptimal in the 0.2-mg/d group at both 6 and 12 wk compared with that at 26 wk. CONCLUSIONS: A folic acid dose as low as 0.2 mg/d can, if administered for 6 mo, effectively lower homocysteine concentrations. Higher doses may not be necessary because they result in no further significant lowering, whereas doses even lower than 0.2 mg/d may be effective in the longer term. Previous trials probably overestimated the folic acid dose required because of a treatment duration that was too short. This trial was registered at clinicaltrials.gov as ISRCTN45296887.

The effects of averaging on accuracy of IVIVC model predictions.

When using the method of deconvolution to establish an IVIVC model, the choice of whether or not to average the data before analysis is a crucial one. Averaging the data leads to a loss of information and current advice on best practise suggests that deconvolution take place at the individual subject level. This study compares each approach and concludes that averaging has a detrimental effect on the accuracy of predictions produced.

Combined models for data from in vitro-in vivo correlation experiments.

A method is presented to describe the in vitro-in vivo correlation (IVIVC) of an extended release drug formulation. This extended release drug product is overencapsulated with immediate release material. The heterogeneity of the capsule is modelled using a combined model of an extended release and an immediate release pharmacokinetic profile. Whereas an IVIVC is conventionally performed using a two-stage procedure, the model uses a one-stage convolution-based method. The method is applied to a Galantamine controlled release formulation, an acetylcholinesterase inhibitor for the treatment of Alzheimer's disease. The average percentage prediction error indicated a good fit of the new model.

Likelihood based approaches to handling data below the quantification limit using NONMEM VI.

PURPOSE: To evaluate the likelihood-based methods for handling data below the quantification limit (BQL) using new features in NONMEM VI. METHODS: A two-compartment pharmacokinetic model with first-order absorption was chosen for investigation. Methods evaluated were: discarding BQL observations (M1), discarding BQL observations but adjusting the likelihood for the remaining data (M2), maximizing the likelihood for the data above the limit of quantification (LOQ) and treating BQL data as censored (M3), and like M3 but conditioning on the observation being greater than zero (M4). These four methods were compared using data simulated with a proportional error model. M2, M3, and M4 were also compared using data simulated from a positively truncated normal distribution. Successful terminations and bias and precision of parameter estimates were assessed. RESULTS: For the data simulated with a proportional error model, the overall performance was best for M3 followed by M2 and M1. M3 and M4 resulted in similar estimates in analyses without log transformation. For data simulated with the truncated normal distribution, M4 performed better than M3. CONCLUSIONS: Analyses that maximized the likelihood of the data above the LOQ and treated BQL data as censored provided the most accurate and precise parameter estimates.

The level of carbonation of a sugar-sweetened beverage preload affects satiety and short-term energy and food intakes.

The consumption of sugar-sweetened beverages is associated with increased incidence of overweight and obesity, and a factor underlying this putative link could be the relatively low levels of satiety that may be induced by these beverages. Although many sugar-sweetened beverages are carbonated, little attention has been given to the potential effects of level of carbonation on satiety and subsequent intakes. We hypothesized that increasing the level of carbonation in a sugar-sweetened beverage would increase satiety and decrease intakes in the short term. Using a randomized, within-subject cross-over design, thirty non-obese subjects (fifteen women, fifteen men) participated on three occasions, 1 week apart. Following a standard breakfast, subjects consumed a beverage preload 10 min before consuming a lunch ad libitum. Preloads were the same sugar-sweetened beverage (400 ml, 639 kJ) with three levels of carbonation, which were low (1.7 volumes), medium (2.5 volumes) and high (3.7 volumes). Satiety was assessed using visual analogue scales and intakes were measured at the lunch and for the rest of the day. Compared with the beverage with low carbonation, consumption of the beverages with medium and high carbonation led to significantly (P < 0.05) higher satiety until lunch, when intakes of food and energy were significantly (P < 0.05) lower. There were no significant effects on satiety following lunch or on intakes for the rest of the day. This short-term study suggests that the level of carbonation may need to be taken into account when assessing potential effects of beverages on satiety and intake.

A comparison of the prediction accuracy of two IVIVC modelling techniques.

The goal when developing an in vitro-in vivo correlation (IVIVC) model is the ability to accurately predict the in vivo plasma concentration profile of a drug formulation using only its in vitro dissolution data. The prediction accuracy of any model depends on the reliability of the method used to develop it. Some statistical concerns regarding methods based on deconvolution have been highlighted and a convolution based technique has been proposed as an alternative. This comparison shows, by means of a simulation study, that the modelling approach which uses convolution produces far more accurate results, accurately predicting the observed plasma concentration-time profile and, therefore, comfortably meeting the FDA validation criteria. The fact that the model developed using the deconvolution based technique fails to describe the simulated data and thus fails the FDA validation test when it ought to pass should be of great concern to those currently implementing this method.

Effect of a voluntary food fortification policy on folate, related B vitamin status, and homocysteine in healthy adults.

BACKGROUND: Mandatory folic acid fortification of food is effective in reducing neural tube defects and may even reduce stroke-related mortality, but it remains controversial because of concerns about potential adverse effects. Thus, it is virtually nonexistent in Europe, albeit many countries allow food fortification on a voluntary basis. OBJECTIVE: The objective of the study was to examine the effect of a voluntary but liberal food fortification policy on dietary intake and biomarker status of folate and other homocysteine-related B vitamins in a healthy population. DESIGN: The study was a cross-sectional study. From a convenience sample of 662 adults in Northern Ireland, those who provided a fasting blood sample and dietary intake data were examined (n = 441, aged 18-92 y). Intakes of both natural food folate and folic acid from fortified foods were estimated; we used the latter to categorize participants by fortified food intake. RESULTS: Fortified foods were associated with significantly higher dietary intakes and biomarker status of folate, vitamin B-12, vitamin B-6, and riboflavin than were unfortified foods. There was no difference in natural food folate intake (range: 179-197 microg/d) between the fortified food categories. Red blood cell folate concentrations were 387 nmol/L higher and plasma total homocysteine concentrations were 2 micromol/L lower in the group with the highest fortified food intake (median intake: 208 microg/d folic acid) than in the nonconsumers of fortified foods (0 microg/d folic acid). CONCLUSIONS: These results show that voluntary food fortification is associated with a substantial increase in dietary intake and biomarker status of folate and metabolically related B vitamins with potential beneficial effects on health. However, those who do not consume fortified foods regularly may have insufficient B vitamin status to achieve the known and potential health benefits.

The effects of the fibre content and physical structure of carrots on satiety and subsequent intakes when eaten as part of a mixed meal.

Previous research indicates that vegetables yield relatively high satiety scores, and that fibre content and structure may both contribute to these effects. This study evaluated the effects of the fibre content and physical structure (gross anatomy and cell structure) of carrots on postprandial satiety and subsequent food intakes when consumed as part of a mixed meal. Using a randomised, repeated-measures, within-subject cross-over design, young women consumed a standardised breakfast and test lunches on three occasions, 4 weeks apart. The test lunches (3329 kJ) comprised boiled rice (200 g) with sweet and sour sauce (200 g) that included chicken (200 g) and carrots (200 g) in three conditions: whole carrots (fibre and structure; n 34), blended carrots (fibre but no structure; n 34) or carrot nutrients (no fibre or structure; n 32). The carrot nutrients had the same energy, major nutrients and portion weight as the other two conditions. Post-lunch satiety was assessed by visual analogue scales. Intakes were covertly weighed at a meal eaten ad libitum (3 h later), and for the remainder of the day using food diaries. Compared with the meal with carrot nutrients, meals with whole carrots and blended carrots resulted in significantly (P<0.05) higher satiety. There were significant (P<0.05) differences between conditions in intakes at the meal eaten ad libitum and for the remainder of the day, and intakes consistently decreased in the order: carrot nutrients, blended carrots, whole carrots, indicating that both fibre content and structure played a role in these effects.

Riboflavin lowers homocysteine in individuals homozygous for the MTHFR 677C->T polymorphism.

BACKGROUND: Meta-analyses predict that a 25% lowering of plasma homocysteine would reduce the risk of coronary heart disease by 11% to 16% and stroke by 19% to 24%. Individuals homozygous for the methylenetetrahydrofolate reductase (MTHFR) 677C-->T polymorphism have reduced MTHFR enzyme activity resulting from the inappropriate loss of the riboflavin cofactor, but it is unknown whether their typically high homocysteine levels are responsive to improved riboflavin status. METHODS AND RESULTS: From a register of 680 healthy adults 18 to 65 years of age of known MTHFR 677C-->T genotype, we identified 35 with the homozygous (TT) genotype and age-matched individuals with heterozygous (CT, n=26) or wild-type (CC, n=28) genotypes to participate in an intervention in which participants were randomized by genotype group to receive 1.6 mg/d riboflavin or placebo for a 12-week period. Supplementation increased riboflavin status to the same extent in all genotype groups (8% to 12% response in erythrocyte glutathione reductase activation coefficient; P<0.01 in each case). However, homocysteine responded only in the TT group, with levels decreasing by as much as 22% overall (from 16.1+/-1.5 to 12.5+/-0.8 micromol/L; P=0.003; n=32) and markedly so (by 40%) in those with lower riboflavin status at baseline (from 22.0+/-2.9 and 13.2+/-1.0 micromol/L; P=0.010; n=16). No homocysteine response was observed in the CC or CT groups despite being preselected for suboptimal riboflavin status. CONCLUSIONS: Although previously overlooked, homocysteine is highly responsive to riboflavin, specifically in individuals with the MTHFR 677 TT genotype. Our findings might explain why this common polymorphism carries an increased risk of coronary heart disease in Europe but not in North America, where riboflavin fortification has existed for >50 years.

Mixed effects versus fixed effects modelling of binary data with inter-subject variability.

The question of whether or not a mixed effects model is required when modelling binary data with inter-subject variability and within subject correlation was reported in this journal by Yano et al. (J. Pharmacokin. Pharmacodyn. 28:389-412 [2001]). That report used simulation experiments to demonstrate that, under certain circumstances, the use of a fixed effects model produced more accurate estimates of the fixed effect parameters than those produced by a mixed effects model. The Laplace approximation to the likelihood was used when fitting the mixed effects model. This paper repeats one of those simulation experiments, with two binary observations recorded for every subject, and uses both the Laplace and the adaptive Gaussian quadrature approximations to the likelihood when fitting the mixed effects model. The results show that the estimates produced using the Laplace approximation include a small number of extreme outliers. This was not the case when using the adaptive Gaussian quadrature approximation. Further examination of these outliers shows that they arise in situations in which the Laplace approximation seriously overestimates the likelihood in an extreme region of the parameter space. It is also demonstrated that when the number of observations per subject is increased from two to three, the estimates based on the Laplace approximation no longer include any extreme outliers. The root mean squared error is a combination of the bias and the variability of the estimates. Increasing the sample size is known to reduce the variability of an estimator with a consequent reduction in its root mean squared error. The estimates based on the fixed effects model are inherently biased and this bias acts as a lower bound for the root mean squared error of these estimates. Consequently, it might be expected that for data sets with a greater number of subjects the estimates based on the mixed effects model would be more accurate than those based on the fixed effects model. This is borne out by the results of a further simulation experiment with an increased number of subjects in each set of data. The difference in the interpretation of the parameters of the fixed and mixed effects models is discussed. It is demonstrated that the mixed effects model and parameter estimates can be used to estimate the parameters of the fixed effects model but not vice versa.