Population pharmacokinetics of tacrolimus whole blood and peripheral blood mononuclear cell concentrations in stable kidney-transplanted patients.

AIM: Therapeutic drug monitoring of tacrolimus based on whole blood drug concentrations is routinely performed. The concentration of tacrolimus in peripheral blood mononuclear cells (PMBCs) is likely to better reflect drug exposure at the treatment target site. We aimed to describe the relationship between tacrolimus whole blood and PBMC concentrations, and the influence of patient characteristics on this relationship by developing a population pharmacokinetic model. METHODS: We prospectively enrolled 63 stable adult kidney-transplanted patients and collected dense (12-h, n = 18) or sparse (4-h, n = 45) pharmacokinetic profiles of tacrolimus. PBMCs were isolated from whole blood (Ficoll density gradient centrifugation), and drug concentrations in whole blood and PBMCs were analysed using liquid chromatography-mass spectrometry. Patient genotype (CYP3A4/5, ABCB1, NR1I2) was assessed with PCR. Population pharmacokinetic modelling and statistical evaluation was performed using NONMEM. RESULTS: Tacrolimus whole blood concentrations were well described using a two-compartment pharmacokinetic model with a lag-time and first-order absorption and elimination. Tacrolimus PBMC concentrations were best estimated from whole blood concentrations with the use of a scaling factor, the ratio of whole blood to PBMC concentrations (RC:PBMC), which was the extent of tacrolimus distribution into PBMC. CYP3A5*1 non-expressors and NR1I2-25 385T allele expressors demonstrated higher RC:PBMC ratios of 42.4% and 60.7%, respectively. CONCLUSION: Tacrolimus PBMC concentration could not be accurately predicted from whole blood concentrations and covariates because of significant residual unexplained variability in the distribution of tacrolimus into PBMCs and may need to be measured directly if required for future studies.

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.

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 optimised 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 digitised, 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.

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.

Pharmacometric modeling of drug adverse effects: an application of mixture models in schizophrenia spectrum disorder patients treated with clozapine.

Clozapine has superior efficacy to other antipsychotics yet is underutilized due to its adverse effects, such as neutropenia, weight gain, and tachycardia. The current investigation aimed to introduce a pharmacometric approach to simultaneously model drug adverse effects, with examples from schizophrenia spectrum patients receiving clozapine. The adverse drug effects were represented as a function of time by incorporating a mixture model to describe individual susceptibility to the adverse effects. Applications of the proposed method were presented by analyzing retrospective data from patients' medical records in Psychiatric Clinic, Penang General Hospital. Tachycardia, weight gain, and absolute neutrophils count (ANC) decrease were best described by an offset, a piecewise linear, and a transient surge function, respectively. 42.9% of the patients had all the adverse effects, including weight gain (0.01 kg/m2 increase every week over a baseline of 24.7 kg/m2 until stabilizing at 279 weeks), ANC decrease (20% decrease from 4540 cells/µL week 12-20.8), and tachycardia (14% constant increase over a baseline of 87.9 bpm for a clozapine maintenance dose of 450 mg daily). 32.5% of the patients had only tachycardia, while the remaining 24.6% had none of the adverse effects. A new pharmacometric approach was proposed to describe adverse drug effects with examples of clozapine-induced weight gain, ANC drop, and tachycardia. The current approach described the longitudinal time changes of continuous data while assessing patient susceptibility. Furthermore, the model revealed the possible co-existence of ANC drop and weight gain; thus, neutrophil monitoring might predict future changes in body weight.

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.

Linking categorical models for prediction of pleasantness score using individual predictions of sweetness and creaminess: An advancement of categorical modeling.

The aim of this work was to develop and evaluate approaches of linked categorical models using individual predictions of probability. A model was developed using data from a study which assessed the perception of sweetness, creaminess, and pleasantness in dairy solutions containing variable concentrations of sugar and fat. Ordered categorical models were used to predict the individual sweetness and creaminess scores and these individual predictions were used as covariates in the model of pleasantness response. The model using individual predictions was compared to a previously developed model using the amount of fat and sugar as covariates driving pleasantness score. The model using the individual prediction of odds of sweetness and creaminess had a lower variability of pleasantness than the model using the content of sugar and fat in the test solutions, which indicates that the individual odds explain part of the variability in pleasantness. Additionally, simultaneous and sequential modeling approaches were compared for the linked categorical model. Parameter estimation was similar, but precision was better with sequential modeling approaches compared to the simultaneous modeling approach. The previous model characterizing the pleasantness response was improved by using individual predictions of sweetness and creaminess rather than the amount of fat and sugar in the solution. The application of this approach provides an advancement within categorical modeling showing how categorical models can be linked to enable the utilization of individual prediction. This approach is aligned with biology of taste sensory which is reflective of the individual perception of sweetness and creaminess, rather than the amount of fat and sugar in the solution.

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.

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 (SI ) and glucose effectiveness (SG ), 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 SI and SG . 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 SI and SG 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 SI and SG than the sparse standard design.

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.

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-HT2c ) 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-HT2c 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.

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.

Sweet/Fat Preference Taste in Subjects Who are Lean, Obese and Very Obese.

PURPOSE: This study assessed the perception of sweetness, creaminess, and pleasantness from a sweet/fat preference test in subjects who are lean (BMI: 19-25), obese (BMI: 30-33) or very obese (BMI: 34-40) using categorical modeling. METHODS: Subjects tasted 16 dairy solutions consisting of 0%, 3.5%, 11.3% and 37.5% fat and each containing 0%, 5%, 10%, or 20% sugar and rated them for sweetness, creaminess and pleasantness. RESULTS: A proportional odds model described the perception of sweetness using an Emax for the effect of sugar and a linear effect for fat. Perception of creaminess was dependent on the fat and sugar content and was described with proportional odds model with linear effects of sugar and fat. Perception of pleasantness increased with sugar and fat but decreased in solutions containing 37.5% fat. A differential odds model using an Emax model for fat and sugar with a negative interaction between them allowed the sugar content to be less than proportional and the fat content to be greater than proportional for pleasantness. CONCLUSIONS: Application of modeling provided understanding of these complex interactions of sugar and fat on the perception of sweetness, creaminess, and pleasantness and provides a tool to investigate obesity and pharmacological intervention.

Dose-Response Mixed Models for Repeated Measures - a New Method for Assessment of Dose-Response.

PURPOSE: In this paper we investigated a new method for dose-response analysis of longitudinal data in terms of precision and accuracy using simulations. METHODS: The new method, called Dose-Response Mixed Models for Repeated Measures (DR-MMRM), combines conventional Mixed Models for Repeated Measures (MMRM) and dose-response modeling. Conventional MMRM can be applied for highly variable repeated measure data and is a way to estimate the drug effect at each visit and dose, however without any assumptions regarding the dose-response shape. Dose-response modeling, on the other hand, utilizes information across dose arms and describes the drug effect as a function of dose. Drug development in chronic kidney disease (CKD) is complicated by many factors, primarily by the slow progression of the disease and lack of predictive biomarkers. Recently, new approaches and biomarkers are being explored to improve efficiency in CKD drug development. Proteinuria, i.e. urinary albumin-to-creatinine ratio (UACR) is increasingly used in dose finding trials in patients with CKD. We use proteinuria to illustrate the benefits of DR-MMRM. RESULTS: The DR-MMRM had higher precision than conventional MMRM and less bias than a dose-response model on UACR change from baseline to end-of-study (DR-EOS). CONCLUSIONS: DR-MMRM is a promising method for dose-response analysis.

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.

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

In the online supplementary.

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.