Pharmacostatistical Model Research Articles

Leveraging magnetic resonance imaging - annualized relapse rate relationship to aid early decision making in multiple sclerosis clinical drug development

Currently, go/no-go decision making in proof-of-concept (POC) multiple sclerosis (MS) trials for promising drug/dose selection are predominantly qualitative in nature. POC trials employ placebo corrected magnetic resonance imaging lesion counts (MRI-T2 counts) as endpoint, whereas, phase 3 trials employ annualized relapse rate at 24 months (ARR-24) as the efficacy endpoint. The objective of the current investigation is to provide a quantitative framework that can aid informed decision making in MS clinical drug development. Blinded summary level data on MRI-T2 lesions at 12 months and aggregate ARR-24 across six clinical development programs digitized from a Food and Drug Administration (FDA)’s 2012 science day presentation were utilized to develop a pharmaco-statistical model linking the MRI-T2 lesions at 12 months with ARR-24. The developed MRI-T2-ARR-24 model was further evaluated by clinical trial simulations and was used to predict the probability of phase 3 clinical trial success given the MRI results in POC trial. The MRI-T2-ARR-24 model suggested that for a unit increase in the MRI-T2 counts, the mean predicted ARR-24 increased by 10%. The model correctly predicted the trial outcomes of four out of the six published MS trials with individual trial predicted ARR-24 values within ± 60% bias. Clinical trial simulations indicated that at least 60% reduction in MRI-T2 counts from placebo in proof-of-concept trials (at any dose or regimen) is needed to achieve a minimum of 80% probability of technical success in the phase 3 trial. Given the competitive landscape in the MS drug development, the decision tool kit could aid in reducing the failure rate in MS phase 3 trials and provide a quantitative framework for more informed dose selection. Further it is anticipated that for significant formulation changes post approval, the MRI-T2-ARR-24 model may be used for bridging efficacy (ARR-24) based only on MRI-T2 data.

Evaluation of factors important in modeling plasma concentrations of tetracycline hydrochloride administered in water in swine

To model the plasma tetracycline concentrations in swine (Sus scrofa domestica) treated with medication administered in water and determine the factors that contribute to the most accurate predictions of measured plasma drug concentrations. Plasma tetracycline concentrations measured in blood samples from 3 populations of swine. Data from previous studies provided plasma tetracycline concentrations that were measured in blood samples collected from 1 swine population at 0, 4, 8, 12, 24, 32, 48, 56, 72, 80, 96, and 104 hours and from 2 swine populations at 0, 12, 24, 48, and 72 hours hours during administration of tetracycline hydrochloride dissolved in water. A 1-compartment pharmacostatistical model was used to analyze 5 potential covariate schemes and determine factors most important in predicting the plasma concentrations of tetracycline in swine. 2 models most accurately predicted the tetracycline plasma concentrations in the 3 populations of swine. Factors of importance were body weight or age of pig, ambient temperature, concentration of tetracycline in water, and water use per unit of time. The factors found to be of importance, combined with knowledge of the individual pharmacokinetic and chemical properties of medications currently approved for administration in water, may be useful in more prudent administration of approved medications administered to swine. Factors found to be important in pharmacostatistical models may allow prediction of plasma concentrations of tetracycline or other commonly used medications administered in water. The ability to predict in vivo concentrations of medication in a population of food animals can be combined with bacterial minimum inhibitory concentrations to decrease the risk of developing antimicrobial resistance.

Evaluation of Vancomycin Dosing Regimens in Preterm and Term Neonates Using Monte Carlo Simulations

To compare four common dosing regimens for vancomycin in preterm and term neonates by assessing the probability that each regimen would achieve the widely used therapeutic target serum trough concentrations of 5-15 mg/L and the newly suggested target of 15-20 mg/L. Retrospective population pharmacokinetic analysis using therapeutic drug monitoring data obtained from 1990-2007, with a subsequent simulation study performed on the pharmacokinetic model. Tertiary-care children's hospital. One hundred thirty-four preterm (66%) and term (34%) neonates, with a postnatal age of 1-121 days and postmenstrual age of 24.6-44 weeks. Therapeutic drug monitoring data for vancomycin were used to develop a population pharmacokinetic model in the target population. Parameter estimates for the derived pharmacostatistical model were used to perform Monte Carlo simulations for four recommended dosing regimens: a standard dose for all neonates, postmenstrual age-based dosing, postmenstrual and postnatal age-based dosing, and serum creatinine-based dosing. Multivariate age-weight distributions were established for term and preterm neonates using Centers for Disease Control and Prevention growth charts and intrauterine and postnatal growth charts from the literature, respectively. Each dosing regimen was treated as a separate scenario in which 200 replicates with 100 patients/replicate were simulated. The 5-15-mg/L target trough serum concentration was achieved in 34% (90% confidence interval [CI] 20-53%), 42% (90% CI 31-55%), 52% (90% CI 43-60%), and 63% (90% CI 54-72%) of patients receiving the standard dose, postmenstrual age-based dose, postmenstrual and postnatal age-based dose, and serum creatinine-based dose, respectively. Serum creatinine-based dosing produced trough concentrations predominantly in the 5-15-mg/L target range, with the smallest variability in both term and preterm neonates. As expected, when the target range was narrow and higher (15-20 mg/L), only 13-21% of patients were within the range across the four dosing regimens. Monte Carlo simulations based on our population pharmacokinetic model suggest that vancomycin dosing guidelines based on serum creatinine concentration have a greater likelihood of achieving trough concentrations in the 5-15-mg/L range compared with other evaluated dosing regimens. None of the four dosing regimens is suitable to produce target trough concentration of 15-20 mg/L in an acceptable number of patients.

Population pharmacokinetics of pregabalin in healthy subjects and patients with chronic pain or partial seizures

Pregabalin, a high-affinity ligand for α2δ subunits of voltage-gated calcium channels, is a novel pharmacotherapy for chronic pain, partial seizures, and other disorders. The present study investigated the population pharmacokinetics of pregabalin following single and multiple doses in healthy volunteers and patient populations. Using nonlinear mixed-effect modeling, 5,583 plasma pregabalin concentration-time samples from 1,723 subjects were analyzed: 2,868 samples from healthy volunteers or subjects with renal impairment (n = 123), 1,513 from patients with partial seizures (n = 626), and 1,202 from patients with chronic pain (n = 974). A one-compartment model with first-order elimination and absorption processes and absorption lag time was used. This pharmacostatistical model showed that: (1) pregabalin oral clearance (CL/F) was directly proportional to creatinine clearance (CLcr), but was independent of gender, race, age, female hormonal status, daily dose, and dosing regimen; (2) apparent volume of distribution was dependent on body weight and gender; (3) absorption rate was decreased when given with food; and (4) coadministration with marketed antiepileptic drugs (AEDs) had no significant effect on pregabalin CL/F. Pregabalin CL/F is related to CLcr, and this relationship is similar among healthy volunteers and patients with either partial seizures or chronic pain disorders. The only factor having a clinically significant influence on steady-state plasma pregabalin concentrations is renal function.

Population pharmacokinetics of caffeine in healthy male adults using mixed-effects models

Caffeine has been shown to maintain or improve the performance of individuals, but its pharmacokinetic profile for Asians has not been well characterized. In this study, a population pharmacokinetic model for describing the pharmacokinetics of caffeine in Singapore males was developed. The data were also analysed using non-compartmental models. Data gathered from 59 male volunteers, who each ingested a single caffeine capsule in two clinical trials (3 or 5 mg/kg), were analysed via non-linear mixed-effects modelling. The participants' covariates, including age, body weight, and regularity of caffeinated-beverage consumption or smoking, were analysed in a stepwise fashion to identify their potential influence on caffeine pharmacokinetics. The final pharmacostatistical model was then subjected to stochastic simulation to predict the plasma concentrations of caffeine after oral (204, 340 and 476 mg) dosing regimens (repeated dosing every 6, 8 or 12 h) over a hypothetical 3-day period. The data were best described by a one-compartmental model with first-order absorption and first-order elimination. Smoking status was an influential covariate for clearance: clearance (mL/min) = 110*SMOKE + 114, where SMOKE was 0 and 1 for the non-smoker and the smoker respectively. Interoccasion variability was smaller compared to interindividual variability in clearance, volume and absorption rate (27% vs. 33%, 10% vs. 15% and 23% vs. 51% respectively). The extrapolated elimination half-lives of caffeine in the non-smokers and the smokers were 4.3 +/- 1.5 and 3.0 +/- 0.7 h respectively. Dosing simulations indicated that dosing regimens of 340 mg (repeated every 8 h) and 476 mg (repeated every 6 h) should achieve population-averaged caffeine concentrations within the reported beneficial range (4.5-9 microg/mL) in the non-smokers and the smokers respectively over 72 h. The population pharmacokinetic model satisfactorily described the disposition and variability of caffeine in the data. Mixed-effects modelling showed that the dose of caffeine depended on cigarette smoking status.

Pharmacokinetics and pharmacodynamics of gatifloxacin in children with recurrent otitis media: application of sparse sampling in clinical development

Gatifloxacin is a 4th-generation fluoroquinolone previously under investigation for the treatment of otitis media in infants and children. These analyses were designed to evaluate the extent of drug exposure relative to adult populations and to examine the relationship between drug exposure and response to therapy in children with recurrent otitis media or early treatment failures of acute otitis media. The patient population included 187 patients from an open-label, multicenter, noncomparative study using gatifloxacin 10 mg/kg once daily. Gatifloxacin exposure was estimated using a single steady-state blood sample in conjunction with a pharmacostatistical model developed using a separate pediatric data set. Gatifloxacin exposure was equivalent to that in adults given 400 mg daily. Of the 41 patients who had Streptococcus pneumoniae from middle ear culture, there were only 3 bacteriologic failures; there was no relationship between plasma fu AUC 0–24:MIC ratio and outcome. In conclusion, population pharmacokinetic/pharmacodynamic methods allowed estimation of drug exposure using one sample per patient.

Clinical Utility of a Pharmacostatistical Model for Ibandronate in Postmenopausal Osteoporosis

Ibandronate, a potent, nitrogen-containing bisphosphonate for the treatment of postmenopausal osteoporosis, is the subject of an ongoing clinical development program to explore novel oral and intravenous (i.v.) dosing regimens. As part of this program, an extensive modeling and simulation project was undertaken to develop and validate a pharmacologically realistic mathematical model for ibandronate in osteoporosis, the aim being to identify practical dosing regimens for clinical evaluation. A simplified kinetics of drug action or kinetic-pharmacodynamic (K-PD) model (developed from a 4-compartment pharmacokinetic-pharmacodynamic [PK-PD] model) accurately described the urinary excretion of the C-telopeptide of the alpha-chain of type I collagen (uCTX). The model was extended to consider the effects of supplemental calcium therapy and allow simultaneous fitting of i.v. and oral ibandronate data, and then externally validated. This model was used successfully in the selection of appropriate once-monthly doses for further clinical evaluation and recent clinical studies have confirmed the efficacy of the doses identified. Further development of the model may include investigating the effects of ibandronate on bone mineral density and fracture risk, which would further enhance its clinical utility and predictive value. Although modeling and simulation has been used to explore the efficacy of other bisphosphonates, the extensive program with ibandronate has produced a comprehensively validated model that is the first to be prospectively tested by evaluating novel dosing regimens.

A Population Pharmacokinetic Model for Montelukast Disposition in Adults and Children

The purpose was to develop a population pharmacokinetic model for montelukast after intravenous administration. Clinical trial simulations were conducted using the model developed to identify the lowest intravenous dose in 6- to 14-year-old children that would give montelukast systemic exposures that were comparable to those found to be associated with efficacy in adults. Two clinical studies were conducted where montelukast was administered intravenously as a 7-mg dose to adults and as a 3.5-mg dose to children aged 6 to 14 years. Model development included defining the base pharmacostatistical model and investigating the effects of demographic variables [age and total body weight (TBW)] on the structural parameters, using a nonlinear mixed effect modeling approach. A linear three-compartment pharmacokinetic model was found to best describe the disposition of montelukast. Inclusion of TBW as a covariate caused a 35% and 63% decrease in the interindividual variabilities on clearance and central volume of distribution, respectively. Trial simulations suggested that a 5.25-mg intravenous dose of montelukast should be chosen in children aged 6 to 14 years. The model developed can adequately describe the intravenous pharmacokinetics of montelukast and can be used as a useful tool for dose selection in pediatric subpopulations.

Pharmacokinetic modelling of cefotaxime and desacetylcefotaxime--a population study in 25 elderly patients.

To develop a pharmacostatistical model to simultaneously characterise the pharmacokinetics of cefotaxime and its main metabolite, desacetylcefotaxime, in elderly patients. Cefotaxime, 1 g, was infused three times daily to 25 elderly patients, 66-93 years old. Cefotaxime and desacetylcefotaxime plasma concentrations (289 and 304 samples, respectively), along with demographic and physiological characteristics, were analysed using a population approach. Cefotaxime pharmacokinetics was best described by a two-compartment open model in which desacetylcefotaxime was produced from the central compartment. The final parameter estimates were derived from simultaneous fit of parent/metabolite data. Cefotaxime clearance, mean 5.5 l/h, was positively influenced by body weight and serum protein concentration and negatively influenced by serum creatinine and age. In contrast, desacetylcefotaxime elimination was only decreased by age. The mean terminal half-lives of cefotaxime and desacetylcefotaxime were 1.7 h and 2.6 h, respectively. The stability and predictive performance of the final population pharmacokinetic model was assessed using 200 bootstrap samples of the original data. Cefotaxime and desacetylcefotaxime elimination decreased with increasing age above 60 years. This decreased elimination was related to individual characteristics that are typically related to renal function.

Population kinetics of tobramycin in neonates.

The population kinetics of tobramycin were studied in 140 neonates (100/40 patients for the index/validation groups, respectively) of 30 to 42 weeks' gestational age and 0.8 to 4.25 kg current body weight in their first 2 weeks of life, undergoing routine therapeutic drug monitoring of their tobramycin serum levels. The 365 tobramycin concentration measurements obtained were analyzed by use of NONMEM according to a one-compartment open model with zero-order absorption and first-order elimination. The effect of a variety of demographic, developmental, and clinical factors (gender, height, birth weight, current weight, gestational age, postnatal age, postconceptional age, and serum creatinine concentration) on clearance and volume of distribution was investigated. Forward selection and backward elimination regression identified significant covariates. The final pharmacostatistical model with influential covariates was as follows (full population): clearance (L/h) = 0.0508 x current weight (kg), multiplied by 0.843 if birth weight was 2.5 kg or less (low-birthweight infants), and volume of distribution (L) = 0.533 x current weight (kg). Using the proportional error model for the random-effects parameters, interindividual variability for clearance and for volume of distribution was determined to be 25.8% and 21.9%, respectively, and the residual variability was 19.2%. In this study, the use of the NONMEM gave significant and consistent information on the pharmacokinetics and the determinants of the pharmacokinetic variability of tobramycin in neonates when compared with available bibliographic information. Moreover, the final population pharmacokinetic model may be used to design a priori recommendations for tobramycin and to improve the dosing readjustments through Bayesian estimation.

Selecting reliable pharmacokinetic data for explanatory analyses of clinical trials in the presence of possible noncompliance.

For single-dose concentration-time data collected in clinical trials to be useful for explanatory pharmacokinetic (PK) or pharmacokinetic-pharmacodynamic (PK-PD) analyses, the following two assumptions on the data must hold: (i) the times of the concentration (PK) observations are known, and (ii) the patient's recent past dosing history (times and amounts) is known. If either (or both) of these assumptions does not hold, and data analysis proceeds as if it did, biased estimates may result. Assumption (i) usually does hold as study personnel observe and record PK sampling times. Assumption (ii) is a problem when, as is often the case of outpatient studies, one must rely on patient recall for past dosing history. This paper presents a technique to avoid assumption (ii) by identifying for deletion those PK observation occasions likely exhibiting unreliable preceding dose histories. To so identify occasions, a Bayes objective function (posterior density) for the data is maximized in its parameters for each individual. The likelihood factor of this function is a mixture pharmacostatistical model expressing the likelihood of the observed concentration(s) under three mutually exclusive events: the prescribed dose preceding the occasion was not taken at all (NT), the prescribed dose was taken at the specified time (T), or the prescribed dose was taken at an unspecified time (U). Suspect observations are identified as those whose maximum corresponding likelihood component is other than T. The approach as defined here relies on the following assumptions in addition to (i): (ii) population PK (i.e., the distribution of PK parameters in the population being sampled) is known, at least approximately. (iii) PK samples (at least 1 or 2 per occasion) are available, (iv) doses taken are of the stated magnitude, and (v) the drug has a short half-life. Simulations reveal that especially when more than one PK sample is available per study occasion, the methodology chooses a set of PK observations that should perform better in subsequent explanatory analyses, or as a basis for estimating individual PK parameters, than do other simpler methods.

Screening for basiliximab exposure–response relationships in renal allotransplantation

The immunosuppressant basiliximab--a chimeric monoclonal antibody specific to the interleukin-2 receptor on activated T-lymphocytes--significantly reduces the incidence of acute cellular rejection following renal transplantation. Screening for exposure-response relationships was performed within a randomized, blinded, placebo-controlled efficacy trial in which patients received 40 mg basiliximab (20 mg on days 0 and 4) by intravenous infusion in addition to cyclosporine and corticosteroids. In a subset of patients, serum samples were collected pre-transplant and once in weeks 2, 3 and 4 for determination of basiliximab concentrations. A population pharmacostatistical model was used to derive individual empirical Bayes estimates of each patient's pharmacokinetic parameters. Biopsy-confirmed acute rejection episodes were recorded to month 6 post-transplant. Forty basiliximab-treated patients were evaluated, 30 men and 10 women, aged 48 +/- 12 yr (range, 24-73) and weighing 72.4 +/- 12.9 kg (range, 52.5-107.5). The basiliximab distribution volume was 7.5 +/- 1.7 L, the half-life 7.5 +/- 2.5 d and the clearance 33 +/- 12 mL/h. There was no clinically relevant influence of weight, age, or gender on basiliximab disposition. Receptor-saturating serum basiliximab concentrations (> 0.2 microgram/mL) were maintained for 41 +/- 23 d. Twenty-five patients remained rejection-free over the 6-month observation period, while a total of 26 biopsy-confirmed acute rejection episodes occurred in the remaining 14 patients. Of these episodes, 12 occurred during receptor blockade. No apparent relationship to basiliximab concentration on the day of onset was observed range, 0.1-9.0 microgram/mL) nor did the time of suppression offset represent a period of increased risk for rejection episodes. Fourteen rejection episodes occurred after basiliximab had cleared from the serum. The durations of receptor suppression preceding these events did not differ compared with those in patients who remained rejection-free: 32 +/- 11 versus 45 +/- 26 d, respectively (p = 0.1269). Given the durations of receptor saturation achieved with the chosen basiliximab regimen, this screen for exposure-response relationships did not identify the duration of receptor saturation in peripheral blood as a predictive factor for acute rejection episodes. Further exploration for exposure-effect relationships in a larger population is warranted.

Effect of variability in hepatic clearance on the bioequivalence parameters of a drug and its metabolite: simulations using a pharmacostatistical model

A semi-physiological pharmacostatistical model was developed and used to study the manner in which intra-individual variability in hepatic clearance is transmitted to the area-under the plasma concentration-time curve from zero to infinity (AUC) of a drug and its metabolite. In order to clarify the effects, the model contained no other sources of variability. As the drug's hepatic extraction ratio increased, the coefficient of variation (CV) of the AUC of the drug increased, whereas that of the metabolite decreased. The AUC of the metabolite increased as the drug's non-hepatic clearance increased. In contrast, at low extraction ratios, the CV of the AUC of the drug decreased as the drug's non-hepatic clearance increased. At high extraction ratios, the CV of the AUC of the drug was insensitive to the contributions of other forms of clearance. The results suggest that under certain circumstances, smaller samples sizes could be used in bioequivalence studies for highly variable drugs if the test were based on the metabolite rather than the parent drug.

Population Pharmacokinetic Parameters of Valproic Acid; Conventional and Slow Release Formulation.

A population pharmacokinetic analysis of valproic acid in conventional and slow release formulations was carried out. Three hundred and forty-four points in two hundred and fifteen patients were analyzed. The pharmacokinetic model, which took into account the age of the patients and the absorption lag time of the slow release formula tions, and a pharmacostatistical model with individual and residual variability were evaluated. The influence of the age of the patients and the absorption lag time on the valproic acid pharmacokinetics was significant based on the results of the statistical test. The ka of slow release formulations was 0.230 (1/h), the ka of conventional formulations was 8.14 (1/h), the Vd of the conventional and slow release formulations was 0.212 (L/kg) and the ke of the conventional and slow release formulations was 0.0495 (1/h) in adults (≥12 years) and the lag time of the slow release formulations was 1.25 (h). The ka changed with the patient's age. The ka was different for conventional and slow release formulations. Though conventional formulations did not have a lag time, the slow release formulations had a lag time. The patient age and the lag time are thought to be included in the population pharmacokinetic model using a slow release formulation. The findings suggest that the values obtained for these population pharmacokinetic parameters will be useful in optimizing valproic acid therapy for individual patients.

Population Pharmacokinetics of Intravenous Amiodarone and Comparison with Two-Stage Pharmacokinetic Analysis

The disposition of amiodarone, an antiarrhythmic agent was evaluated after a single intravenous infusion (5 mg/kg over 15 minutes) in patients of various ages and with various degrees of renal function and left ventricular function. The plasma concentration-time data were obtained from three clinical studies with similar protocols. The data were analyzed by nonlinear mixed-effects modeling (NONMEM) to estimate the population pharmacokinetic parameters of amiodarone and to determine the significant demographic covariates affecting these parameters. The pharmacokinetic parameters of amiodarone (weight-corrected) also were calculated using two-stage analysis and were compared with the results obtained from the mixed-effects analysis. The population plasma concentration-time profile of amiodarone was best described by a four-compartment model. Demographic covariates (i.e., creatinine clearance and ejection fraction) did not improve the final pharmacostatistical model significantly. The results from the two-stage analysis showed no significant relationship between amiodarone pharmacokinetic parameters and age, gender, renal function, or ejection fraction. The results from one study, however, demonstrated that advanced age (> or = 65 years) resulted in reduced amiodarone clearance coupled with a prolonged elimination half-life. No such correlation was detected with NONMEM analysis, which may be partly attributable to the small number of elderly patients. Overall, the results from NONMEM analysis validated the results obtained from the two-stage analysis.

Population pharmacokinetics of caffeine in premature neonates.

To determine population pharmacokinetic parameters of caffeine in premature neonates. This population analysis was done using 145 serum concentration measurements gathered from 75 hospitalized patients during their routine clinical care. The data were analysed by use of NONMEM (mixed effects modeling) according to a one-compartment open model with either zero or first-order absorption and first-order elimination. The effect of a variety of developmental, demographic and clinical factors (gender, birth weight, current weight, gestational age, postnatal age, postconceptional age and concurrent treatment with phenobarbital and parenteral nutrition) on clearance and volume of distribution was investigated. Forward selection and backward elimination regression identified significant covariates. The final pharmacostatistical model with influential covariates were as follows: clearance (m1.h-1) = 5.81-current weight (kg) + 1.22.postnatal age (weeks), multiplied by 0.757 if gestational age < or = 28 weeks and 0.836 if the current primary source of patients' nutrition is parenteral nutrition, and volume of distribution (ml) = 911.current weight (kg). The inter-individual variability in clearance and the residual variability, expressed as coefficients of variation, were 14.8%, and 18.44%, respectively. Due to the lack of information on the data set we were unable to characterize the interindividual variability for volume of distribution. In this study, which involved on average only two serum concentrations of caffeine per patient, the use of NONMEM gave us significant and consistent information about the pharmacokinetic profile of caffeine when compared with available bibliographic information. Additionally, parenteral nutrition and low gestational age (< or = 28 weeks) may even come to be considered as risk factors, and their presence may serve as an indicator of the need for periodic monitoring of caffeine concentrations in premature infants.

Predictive performance of the Bayesian analysis: Effects of blood sampling time, population parameters, and pharmacostatistical model

The present paper reports theoretical equations for the predictive performance of the Bayesian forecasting method. The precision of parameter estimates and predicted concentrations for an individual was described by general equations with the aid of a variance-covariance matrix of parameter estimates that involved the Bayes theorem. The equations were applied to assess the predictive performance of the one-point Bayesian method in association with blood sampling time, the population parameters, and the pharmacostatistical model. The simulation study showed that the prediction error in parameter estimates essentially depended upon the sampling time but the magnitude of dependency was affected by the size of inter- and intraindividual variances. With a smaller value of interindividual variance, the dependency on sampling time was less apparent. Effects of sampling time were further examined using clinical data obtained from 20 patients taking theophylline, and the results were in good agreement with the theoretical consideration. The present general equations are useful to investigate the sampling strategy as well as structural and variance modeling on the predictive performance of the Bayesian method.