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Estimating the parameters of the operational model of pharmacological agonism.

The aim of this work is practical. We show that the parameters of the widely used operational model of pharmacological agonism are difficult to estimate from single dose-response curves. The parameters can be estimated using pairs of dose-response curves (usually treatment and control) sharing some parameters. Confidence bands for the estimators are developed. In the case of multiple dose-response curve pairs one can employ a non-linear mixed effects model to allow for inter-individual variation. The point estimates and the confidence intervals thus obtained are similar to the more naive construction based on mean and standard errors of parameter estimates. To test for difference of certain parameters between treatment and control we employ a permutation test and Wald's test.

Animals↗

Phase I population pharmacokinetics of irofulven.

Our aim was to develop a population pharmacokinetic model for irofulven and to assess covariates that might affect irofulven pharmacokinetics. Irofulven was administered by 5- or 30-min i.v. infusion to cancer patients during a phase I study. Blood samples were collected over 4 h. Plasma samples were analyzed to quantitate irofulven by high-performance liquid chromatography. Population pharmacokinetic analysis was performed using a non-linear mixed effects modeling program, MP2. Fifty-nine patients were available for pharmacokinetic analysis. Irofulven plasma concentration-time profiles were best described by a two-compartment pharmacokinetic model. Clearance and central volume of distribution were not significantly influenced by individual characteristics, i.e. body weight (BW), body surface area (BSA), age and gender. Final parameter estimates of clearance and central volume of distribution were 616 l/h and 37 l, respectively, resulting in a very short terminal half-life of less than 10 min. A relatively high level of variability was observed in irofulven pharmacokinetics, which was mainly due to a significant residual variability, 39%. For a 30-min irofulven infusion, the optimal sampling schedule for clearance estimation using the Bayesian method was the three time points 0.35-0.45, 0.80 and 1-1.2 h from the beginning of a 30-min infusion. We conclude that after i.v. infusion of irofulven, plasma clearance was high and not dependent upon patient age, gender, BSA or BW.

Adult↗

Mixed-effect models to assess consistency and reliability across multiple evaluations.

The issue of consistency and reliability arises frequently in applied clinical trials, and there is a considerable amount of literature on this topic. For a continuous random variable, we describe a process to assess whether the mean and variance are the same from one evaluation to the other and we derive the intraclass correlation (ICC) for evaluating consistency in the distributions of paired data. Mixed-effects linear models are applied, and these procedures are illustrated using dietary recall data from the Girls health Enrichment Multi-site Studies (GEMS). The SAS program code for performing the statistical analysis is provided. The models can be generalized to account for more design factors and other applicable covariates.

Clinical Trials as Topic↗

Heart rate variability in dairy cows-influences of breed and milking system.

Heart rate variability parameters in the time, frequency and nonlinear domains were investigated in two breeds of dairy cows (Austrian Simmental and Brown Swiss) milked either in an automatic milking system with partially forced cow traffic or in a herringbone milking parlour. Recordings were made of 24 cows (six of each breed and milking system) during lying, standing idle, and standing being milked, and analysed with linear mixed effects models taking the covariates time of day, live body weight, milk yield, stage of lactation and stage of pregnancy into account. Heart rate and nonlinear deterministic shares were higher, and heart rate variability in the time and frequency domains was lower, later in the day, in cows with higher body weight and in Simmental compared to Brown Swiss cows. Differences in the linear and nonlinear domains during lying indicated an increased level of chronic stress in cows in the automatic milking system with partially forced cow traffic, compared to cows milked in the herringbone milking parlour. No effects of milking system were found during milking, indicating that the stressor in the automatic milking system was not the milking process itself.

Analysis of Variance↗

Population pharmacokinetic modeling of steady state clearance of carbamazepine and its epoxide metabolite from sparse routine clinical data.

OBJECTIVE: To develop a population pharmacokinetic model to evaluate the effects of variety of covariates on clearance of carbamazepine (CBZ) and its main metabolite carbamazepine-10,11-epoxide (CBZE) in Chinese population. METHODS: Serum samples at steady trough state (n = 459) were collected prospectively from 408 compliant outpatients during their routine clinical care. CBZ and CBZE concentrations were simultaneously determined by high performance liquid chromatography. Population clearance (CL) of CBZ and CBZE were estimated by non-linear mixed effect modeling and NONMEM program with a one-compartment model of first-order absorption and elimination. RESULTS: Total body weight (TBW), dose and concomitant medication were all important determinants of CL of CBZ and CBZE. The final regression model for CBZ was: where VPA = 1 for patients comedicated with valproic acid and its dose greater than 18 mg/kg, otherwise VPA = 0; PHT = 1 for patients comedicated with phenytoin, otherwise PHT = 0; PB = 1 for patients comedicated with phenytoin, otherwise PB = 0. The final regression CL model for the CBZE was: where VPA = 1 for patients comedicated with valproic acid, otherwise VPA = 0. CONCLUSION: The current models, which describe CL of CBZ and CBZE in terms of patient specific details, can be used as a reference to optimize CBZ therapy in Chinese epilepsy patients.

Administration, Oral↗

Application of a combined effect compartment and binding model for gastric acid inhibition of AR-HO47108: a potassium competitive acid blocker, and its active metabolite AR-HO47116 in the dog.

The effect of AR-HO47108, a potassium competitive acid blocker, and its active metabolite AR-HO47116 was studied in Heidenhain pouch dogs following administration of single oral and intravenous doses of the two compounds. The histamine-stimulated acid secretion was measured in different periods after dose up to 24h. All data obtained in the different studies was pooled and analyzed by non-linear mixed effects modelling. It was found that there is a delay between the plasma concentration-time peak and the maximum inhibitory effect and that the effect persisted longer than anticipated from the plasma concentration half-lives of the compounds. In addition, it was found that the peak effect was reached earlier at higher doses. The effect data was well described by a combined effect compartment and binding model and both distribution to the biophase i.e. the canaliculus of the parietal cell and a rate limiting binding interaction between drug and enzyme appear to contribute to the observed delay. In addition, a secretion rate dependent washout from the biophase may contribute. Furthermore, because the parent compound and metabolite bind to the same enzyme, the effect is determined by competition between the two for the same enzyme. The metabolite was found to be less potent than the parent compound, with Kd values of the combined model of 125 and 11.2 nM for the metabolite and parent compound, respectively. However, the metabolite is generated in high concentrations that rapidly exceed the concentration of parent compound after oral administration of parent compound, and this together with its longer plasma half-life will make its contribution to the overall effect increase with time and slightly prolong the duration of the effect.

Animals↗

Population pharmacokinetic modelling of darifenacin and its hydroxylated metabolite using pooled data, incorporating saturable first-pass metabolism, CYP2D6 genotype and formulation-dependent bioavailability.

AIMS: A model describing the population pharmacokinetics of darifenacin and its hydroxylated metabolite was developed from a combined analysis of 18 studies. The relationships between explanatory covariates and pharmacokinetic parameters were explored. METHODS: Plasma concentration data from 337 individuals were pooled from 17 Phase 1 studies (median 28/33 darifenacin/metabolite observations per healthy subject), and one Phase 2 study (median 7/7 darifenacin/metabolite observations per subject) encompassing one intravenous and five different oral formulations (1-45 mg). RESULTS: Non-linear Mixed Effects Models (NONMEM Version VI) described both the population pharmacokinetics of darifenacin and its hydroxylated metabolite with a two-compartment disposition model with first order absorption. The values (mean +/- standard error of the mean) for clearance (CL) and volume of distribution of the central compartment were 40.2 +/- 2.0 l h-1 and 34.7 +/- 4.6 l h-1, respectively, in a typical male CYP2D6 homozygote-extensive metabolizer (Hom-EM). The absolute bioavailability (F) of darifenacin in a Hom-EM after doses of 7.5, 15 or 30 mg extended release formulation (CR) was 15, 19 and 25%, respectively. Factors influencing F were formulation (70-110% higher for CR compared with immediate release following equivalent daily doses), CYP2D6 genotype [heterozygote-extensive metabolizers (Het-EM) and poor metabolizers (PM) experienced 40 and 90%, respectively, higher exposure than Hom-EM irrespective of dose administered] and saturable first-pass metabolism (dose nonlinearity 1.05-1.43-fold). Race affected F, which was 56% lower in Japanese males. The CYP3A4 inhibitors ketoconazole and erythromycin increased F to approximately 100% and ketoconazole decreased CL by 67.5%. CL was 31% lower in females and 10% lower at night. Formulation affected the metabolite absorption/formation rate. Ketoconazole and erythromycin administration resulted in a decrease of 61.2 and 28.8% in exposure to the metabolite, respectively. The covariates race, gender and circadian rhythm accounted for only approximately half of the variability in the estimated exposures to darifenacin. CONCLUSIONS: The pooled analysis provided a descriptive integration of all characteristics and covariates of the pharmacokinetics of darifenacin and its metabolite, enabling interpolation and extrapolation of these key factors.

Adolescent↗

Longitudinal random effects models for genetic analysis of binary data with application to mastitis in dairy cattle.

A Bayesian analysis of longitudinal mastitis records obtained in the course of lactation was undertaken. Data were 3341 test-day binary records from 329 first lactation Holstein cows scored for mastitis at 14 and 30 days of lactation and every 30 days thereafter. First, the conditional probability of a sequence for a given cow was the product of the probabilities at each test-day. The probability of infection at time t for a cow was a normal integral, with its argument being a function of "fixed" and "random" effects and of time. Models for the latent normal variable included effects of: (1) year-month of test + a five-parameter linear regression function ("fixed", within age-season of calving) + genetic value of the cow + environmental effect peculiar to all records of the same cow + residual. (2) As in (1), but with five parameter random genetic regressions for each cow. (3) A hierarchical structure, where each of three parameters of the regression function for each cow followed a mixed effects linear model. Model 1 posterior mean of heritability was 0.05. Model 2 heritabilities were: 0.27, 0.05, 0.03 and 0.07 at days 14, 60, 120 and 305, respectively. Model 3 heritabilities were 0.57, 0.16, 0.06 and 0.18 at days 14, 60, 120 and 305, respectively. Bayes factors were: 0.011 (Model 1/Model 2), 0.017 (Model 1/Model 3) and 1.535 (Model 2/Model 3). The probability of mastitis for an "average" cow, using Model 2, was: 0.06, 0.05, 0.06 and 0.07 at days 14, 60, 120 and 305, respectively. Relaxing the conditional independence assumption via an autoregressive process (Model 2) improved the results slightly.

Animals↗

Foundation for nonlinear models with thresholds for longitudinal data.

Threshold models first appeared in the literature nearly half a century ago. Threshold segments have been added to many commonly used forms of models from linear models and generalized linear models through mixed models for the analysis of cross-sectional data. Nonlinear models with thresholds for cross-sectional data are less prevalent in the literature. Nonlinear models with thresholds for longitudinal data are new. The historical developments leading to this point are reviewed as a means of introducing terms necessary for discussing features of these newer models. Nonlinear models for longitudinal data with thresholds are presented and discussed.

Algorithms↗

Genome-Wide Association Analyses of Bitter Food Preferences Link Genetic Loci to Sensory and Metabolic Pathways.

BACKGROUND: Genetic variation is implicated in individual preferences for bitter-tasting foods. However, previous studies have focused on candidate genes and limited varieties of bitter-tasting foods and have treated food preference scale responses as continuous data. OBJECTIVES: The present investigation aimed to identify genetic variants associated with preferences for bitter-tasting foods using ordinal multinomial regression models in genome-wide association studies (GWAS). In addition, post-GWAS functional annotation and mapping, genetic correlations, and associations with dietary intake were examined. METHODS: Food preference and genome-wide genotyping data were used from the UK Biobank (n = 125,578). Preference data from Likert scale rankings (from 1 to 9) for 12 individual foods were analyzed using ordinal multinomial regression GWAS. In addition, 1 composite continuous variable was created for preference for cruciferous vegetables as a group and analyzed using a linear mixed-model GWAS to enable the calculation of a polygenic score (PGS) for cruciferous vegetable preference. Convergent validity of GWAS results was assessed with dietary intake data for the same food items in the CARTaGENE cohort (n = 8176). Post-GWAS gene-level and pathway-level association analyses were conducted in MAGMA (Multimarker Analysis of GenoMic Annotation). RESULTS: Forty-six single-nucleotide polymorphisms (SNPs) were identified for preferences for 11 bitter-tasting foods at a genome-wide significance level (P < 7.14 &#xd7; 10-9). Gene-set analysis for enrichment identified pathways related to caffeine metabolism and bitter taste perception for preference of coffee without sugar and grapefruit, respectively. Genes with higher expression in brain tissues showed stronger genetic associations with cruciferous vegetable preference. The PGS for cruciferous vegetable preference was weakly correlated with intake (r = 0.05, P < 0.0001), but individual SNPs were not associated with intake in a consistent manner. CONCLUSIONS: Genetic variation contributes to preferences for bitter-tasting foods among adults, and some links with food intake are detectable. Nevertheless, effect sizes are small and inconsistent, reflecting the multifactorial complexity of food intake.

bitter taste↗

Modelling of residual variability in toxicokinetic studies with sparse sampling: the case of tetrahydronaphthalene.

The present study describes the kinetics of tetrahydronaphthalene in male and female rats (five animals per dose per sex) at three dose levels (15, 50, and 150 mg/kg daily). Plasma concentration measurements were performed in the course of a subacute toxicity study of 28 days duration in an enriched study design. Two blood samples per animal were taken at different time points after application at day 1 and 16 (150 mg/kg daily) and at day 3 and 18 (15 and 50 mg/kg daily), respectively. Tetrahydronaphthalene was assayed by gas chromatography-mass spectrometry (GC-MS) after extraction. The data of plasma concentration time were analysed using non-linear mixed effects modelling as implemented in NONMEM. The structural model with the best fit employed one compartment kinetics with instantaneous drug input. Interindividual variability in both k and V was found to be very small [k, 0.201 h(-1), 0.013; V, 16.19 (kg), 1.77; population mean and SE]. No unequivocal evidence of dose dependence could be found. The kinetic parameter with the highest extent of variability was the extent of bioavailability which showed an coefficient of variation (CV) of 96%. Both gender and dose had no influence on the variability. The present approach is concluded to offer more insight into the relationship between dose, concentration and effect and into factors which explain variability in kinetics without additional testing or additional animals. Proposals for a refined sampling schedule are made.

Animals↗

Non-linear pharmacokinetics of irinotecan in mice.

Irinotecan (CPT-11) is a topoisomerase I inhibitor used in the treatment of metastatic colorectal cancer. Its conversion by carboxyl esterases is necessary to form the active metabolite SN-38. The aims of the study were to evaluate the linearity of CPT-11 pharmacokinetics and the influence of the schedule of administration of CPT-11 in mice, using a population pharmacokinetic approach with the NON-linear Mixed Effects Model (NONMEM) program. Mice were treated using two doses and two schedules of administration [10 mg/kg/day (dailyx5)x2 or 50 mg/kg/day on days 1 and 12]. Plasma concentrations of both CPT-11 and SN-38 were determined by HPLC. A pharmacokinetic model based on both immediate conversion of CPT-11 to SN-38 for a fraction of the administered dose and saturable process for the remaining fraction fitted the data well. Refinements of the model allowed us to evaluate both the impacts of the dose and the schedule of administration on the pharmacokinetic parameters. We conclude that the pharmacokinetics of CPT-11 is not linear in mice. Extrapolation of both pharmacokinetic and pharmacodynamic preclinical results to humans may be limited by species particularities for this drug.

Animals↗

Estimating correlation coefficient between two variables with repeated observations using mixed effects model.

We estimate the correlation coefficient between two variables with repeated observations on each variable, using linear mixed effects (LME) model. The solution to this problem has been studied by many authors. Bland and Altman (1995) considered the problem in many ad hoc methods. Lam, Webb and O'Donnell (1999) solved the problem by considering different correlation structures on the repeated measures. They assumed that the repeated measures are linked over time but their method needs specialized software. However, they never addressed the question of how to choose the correlation structure on the repeated measures for a particular data set. Hamlett et al. (2003) generalized this model and used Proc Mixed of SAS to solve the problem. Unfortunately, their method also cannot implement the correlation structure on the repeated measures that is present in the data. We also assume that the repeated measures are linked over time and generalize all the previous models, and can account for the correlation structure on the repeated measures that is present in the data. We study how the correlation coefficient between the variables gets affected by incorrect assumption of the correlation structure on the repeated measures itself by using Proc Mixed of SAS, and describe how to select the correlation structure on the repeated measures. We also extend the model by including random intercept and random slope over time for each subject. Our model will also be useful when some of the repeated measures are missing at random.

Algorithms↗

Acetaminophen analgesia in children: placebo effect and pain resolution after tonsillectomy.

BACKGROUND: Pharmacodynamic models of acetaminophen analgesia in children have not explored the efficacy of single oral doses greater than 40 mg/kg. METHODS: Children aged 9.0 +/- 3.0 years (+/- SD) and weight 37.9+/- 16.6 kg undergoing outpatient tonsillectomy were randomised to receive acetaminophen elixir 40 mg/kg (n = 12). high dose acetaminophen elixir 100 mg/kg (n =20) or placebo (n=30) 0.5 -1 h preoperatively. No other analgesics were given. Individual acetaminophen serum concentrations and pain scores [visual analogue scale (VAS) 0-10] were measured over a 4-8 h postoperative period. These data were pooled with data from a previous study investigating acetaminophen pharmacodynamics (n = 120) and analysed using a non-linear mixed effect model. Placebo effects and drug effects were modelled using effect-site concentration models. RESULTS: A one-compartment model with first-order input, lag time and first-order elimination was used to describe the population pharmacokinetics of acetaminophen. Pharmacokinetic parameter estimates were similar to those previously described. Pharmacodynamic population parameter estimates [population variability coefficient of variation (CV)] for a maximum analgesic effect (Emax) model, in which the greatest possible pain relief (VAS 0-10) equates to an Emax of 10, were Emax 5.17 (64%) and 50% effective concentration 9.98 mg/l (107%). The equilibration half-life (t(eq)) of the analgesic effect compartment was 53 min (217%). A placebo drug model for the effects of placebo response had a t(eq) of 1.96 h (40%), an elimination half-life of 2.06 h (50%) and a potency of 1.54 pain relief units (24%). CONCLUSIONS: High dose acetaminophen (100 mg/kg) was no more effective than 40 mg/kg and was associated with increased nausea and vomiting. A target effect compartment concentration of 10 mg/l is expected to produce a pain reduction of 2.6 units. The placebo model accounted for a maximum pain reduction of 5.6 units at 3 h. The combination of placebo effect and preoperative acetaminophen 40 mg/kg results in pain scores below 4 units for 5 h postoperatively.

Acetaminophen↗

Group sequential comparison of changes: ad-hoc versus more exact method.

There are many clinical trials in which we are interested in comparing changes in responses between two treatment groups sequentially. Investigators might assume a simple linear model, take the average of the ordinary least square estimators of slope within each treatment group, and use the standardized difference between these two averages as the test statistic at each interim analysis. Ad-hoc construction of the boundary values for interim analysis might be based on group sequential methods which assume that the interim test statistics have independent increments even though it may not be true when a response variable is measured repeatedly over time for each subject. This ad-hoc method is very simple and appealing, and thus has been used in a clinical trial setting. Lee and DeMets (1991, Journal of the American Statistical Association 86, 757-762) have proposed a more exact group sequential method for comparing rates of change. Under the assumption that the response follows the linear mixed effects model, they have derived the asymptotic joint distribution of the sequentially computed statistics. Construction of group sequential boundaries is based on this distribution theory. By simulation studies, we first study the robustness of the more exact method to violations of the typical assumptions. In addition, we compare the ad-hoc method with the more exact method and examine how well these two methods work for various situations. The relationship between two different information times, Fisher information and a surrogate information, are also discussed from the simulation studies.

Analysis of Variance↗

Effectiveness of cleaning and health education in reducing childhood lead poisoning among children residing near superfund sites in Missouri.

In this study, the authors evaluated whether a combination of tailored education, lead dust removal by trained cleaning specialists, and family follow-up visits would be more effective than conventional health educational programs in reducing elevated blood lead levels in children living in or near lead mining hazardous waste sites. The authors randomized children between 6 and 72 mo of age with blood lead levels between 10 and 20 microg/dl into 3 groups: standard care, tailored newsletters, or tailored newsletters and specialized cleaning. The authors obtained questionnaires, blood lead levels, and environmental lead samples during initiation and compared them with the same items obtained at 3, 6, and 9 mo follow-up. They used a linear mixed effect model to evaluate the intervention effect. Blood lead levels decreased overall 1.54 microg/dl (12.1%) during the study. The authors found that tailored newsletters and specialized cleaning produced the greatest decline in blood lead levels, but no statistical differences were found among the methodologies. The small decline observed in blood lead levels reduced levels to below 10 microg/dl for 40% of the children.

Child↗

A mixed approach and a distribution-free multiple imputation technique for the estimation of a multivariate probit model with missing values.

In the present paper a mixed generalized estimating/pseudo-score equations (GEPSE) approach together with a distribution-free multiple imputation technique is proposed for the estimation of regression and correlation structure parameters of multivariate probit models with missing values for an ordered categorical time-invariant variable. Furthermore, a generalization of the squared trace correlation (RT2) for multivariate probit models, denoted by pseudo-RT2, is proposed. A simulation study was conducted, simulating a probit model with an equicorrelation structure in the errors of an underlying regression model and using two different missing mechanisms. For a low 'true' correlation the difference between the GEPSE, a generalized estimating equations (GEE) and a maximum likelihood (ML) estimator were negligible. For a high 'true' correlation the GEPSE estimator turned out to be more efficient than the GEE and very efficient relative to the ML estimator. Furthermore, the pseudo-RT2 was close to RT2 of the underlying linear model. The mixed approach is illustrated using a psychiatric data set of depressive in-patients. The results of this analysis suggest that the depression score at discharge from a psychiatric hospital and the occurrence of stressful life events seem to increase the probability of having an episode of major depression within a one-year interval after discharge. Furthermore, the correlation structure points to short-time effects on having or not having a depressive episode, not accounted for in the systematic part of the regression model.

Depressive Disorder↗

Decline in lung function in the Busselton Health Study: the effects of asthma and cigarette smoking.

Asthma in adults may be associated with chronic airflow obstruction, possibly resulting from airway disease in early life and/or a greater rate of decline in lung function in adult life compared with those with asthma. Treatment and cigarette smoking may also influence the rate of decline of lung function. The aim of this analysis was to examine the level and rate of decline in lung function in relationship to asthma and cigarette smoking in adults. Subjects (n = 9,317) had participated as adults (> 18 years) in one or more of the cross-sectional Busselton Health Surveys between 1966 and 1981 or in the follow-up study of 1994/1995. The effects of sex, doctor-diagnosed asthma, smoking status, and anthropometric data on the level and rate of decline in FEV1 were examined in a linear mixed effects model. At the age of 19 years, FEV1 was reduced in subjects with asthma but was similar in smokers and nonsmokers. Males, taller subjects, smokers, and subjects with asthma had greater declines in FEV1 with age. Smoking and asthma had additive but not multiplicative effects on decline. Thus, asthma is associated with reduced lung function at the beginning of adult life as well as an increased rate of decline during adult life.

Adult↗