Analysis of Melanoma Onset: Assessing Familial Aggregation by Using Estimating Equations and Fitting Variance Components via Bayesian Random Effects Models

We investigate whether relative contributions of genetic and shared environmental factors are associated with an increased risk in melanoma. Data from the Queensland Familial Melanoma Project comprising 15,907 subjects arising from 1912 families were analyzed to estimate the additive genetic, common and unique environmental contributions to variation in the age at onset of melanoma. Two complementary approaches for analyzing correlated time-to-onset family data were considered: the generalized estimating equations (GEE) method in which one can estimate relationship-specific dependence simultaneously with regression coefficients that describe the average population response to changing covariates; and a subject-specific Bayesian mixed model in which heterogeneity in regression parameters is explicitly modeled and the different components of variation may be estimated directly. The proportional hazards and Weibull models were utilized, as both produce natural frameworks for estimating relative risks while adjusting for simultaneous effects of other covariates. A simple Markov Chain Monte Carlo method for covariate imputation of missing data was used and the actual implementation of the Bayesian model was based on Gibbs sampling using the free ware package BUGS. In addition, we also used a Bayesian model to investigate the relative contribution of genetic and environmental effects on the expression of naevi and freckles, which are known risk factors for melanoma.

Population pharmacokinetics of metformin in late pregnancy

The pharmacokinetic disposition of metformin in late pregnancy was studied together with the level of fetal exposure at birth. Blood samples were obtained in the third trimester of pregnancy from women with gestational diabetes or type 2 diabetes, 5 had a previous diagnosis of polycystic ovary syndrome. A cord blood sample also was obtained at the delivery of some of these women, and also at delivery of others who had been taking metformin during pregnancy but from whom no blood had been taken. Plasma metformin concentrations were assayed by a new, validated, reverse-phase HPLC method, A 2-compartment, extravascular maternal model with transplacental partitioning of drug to a fetal compartment was fitted to the data. Nonlinear mixed-effects modeling was performed in'NONMEM using FOCE with INTERACTION. Variability was estimated using logarithmic interindividual and additive residual variance models; the covariance between clearance and volume was modeled simultaneously. Mean (range) metformin concentrations in cord plasma and in maternal plasma were 0.81 (range, 0.1-2.6) mg/L and 1.2 (range, 0. 1-2.9) mg/L, respectively. Typical population values (interindividual variability, CV%) for allometrically scaled maternal clearance and volume of distribution were 28 L/h/70 kg (17.1%) and 190 L/70 ka (46.3%), giving a derived population-wide half-life of 5.1 hours. The placental partition coefficient for metformin was 1.07 (36.3%). Neither maternal age nor weight significantly influenced the pharmacokinetics. The variability (SD) of observed concentrations about model-predicted concentrations was 0.32 mg/L. The pharmacokinetics were similar to those in nonpregnant patients and, therefore, no dosage adjustment is warranted. Metformin readily crosses the placenta, exposing the fetus to concentrations approaching those in the maternal circulation. The sequelae to such exposure, ea, effects on neonatal obesity and insulin resistance, remain unknown.

A D-optimal designed population pharmacokinetic study of itraconazole capsules and solution in adults with cystic fibrosis

Background: Oral itraconazole (ITRA) is used for the treatment of allergic bronchopulmonary aspergillosis in patients with cystic fibrosis (CF) because of its antifungal activity against Aspergillus species. ITRA has an active hydroxy-metabolite (OH-ITRA) which has similar antifungal activity. ITRA is a highly lipophilic drug which is available in two different oral formulations, a capsule and an oral solution. It is reported that the oral solution has a 60% higher relative bioavailability. The influence of altered gastric physiology associated with CF on the pharmacokinetics (PK) of ITRA and its metabolite has not been previously evaluated. Objectives: 1) To estimate the population (pop) PK parameters for ITRA and its active metabolite OH-ITRA including relative bioavailability of the parent after administration of the parent by both capsule and solution and 2) to assess the performance of the optimal design. Methods: The study was a cross-over design in which 30 patients received the capsule on the first occasion and 3 days later the solution formulation. The design was constrained to have a maximum of 4 blood samples per occasion for estimation of the popPK of both ITRA and OH-ITRA. The sampling times for the population model were optimized previously using POPT v.2.0.[1] POPT is a series of applications that run under MATLAB and provide an evaluation of the information matrix for a nonlinear mixed effects model given a particular design. In addition it can be used to optimize the design based on evaluation of the determinant of the information matrix. The model details for the design were based on prior information obtained from the literature, which suggested that ITRA may have either linear or non-linear elimination. The optimal sampling times were evaluated to provide information for both competing models for the parent and metabolite and for both capsule and solution simultaneously. Blood samples were assayed by validated HPLC.[2] PopPK modelling was performed using FOCE with interaction under NONMEM, version 5 (level 1.1; GloboMax LLC, Hanover, MD, USA). The PK of ITRA and OH‑ITRA was modelled simultaneously using ADVAN 5. Subsequently three methods were assessed for modelling concentrations less than the LOD (limit of detection). These methods (corresponding to methods 5, 6 & 4 from Beal[3], respectively) were (a) where all values less than LOD were assigned to half of LOD, (b) where the closest missing value that is less than LOD was assigned to half the LOD and all previous (if during absorption) or subsequent (if during elimination) missing samples were deleted, and (c) where the contribution of the expectation of each missing concentration to the likelihood is estimated. The LOD was 0.04 mg/L. The final model evaluation was performed via bootstrap with re-sampling and a visual predictive check. The optimal design and the sampling windows of the study were evaluated for execution errors and for agreement between the observed and predicted standard errors. Dosing regimens were simulated for the capsules and the oral solution to assess their ability to achieve ITRA target trough concentration (Cmin,ss of 0.5-2 mg/L) or a combined Cmin,ss for ITRA and OH-ITRA above 1.5mg/L. Results and Discussion: A total of 241 blood samples were collected and analysed, 94% of them were taken within the defined optimal sampling windows, of which 31% where taken within 5 min of the exact optimal times. Forty six per cent of the ITRA values and 28% of the OH-ITRA values were below LOD. The entire profile after administration of the capsule for five patients was below LOD and therefore the data from this occasion was omitted from estimation. A 2-compartment model with 1st order absorption and elimination best described ITRA PK, with 1st order metabolism of the parent to OH-ITRA. For ITRA the clearance (ClItra/F) was 31.5 L/h; apparent volumes of central and peripheral compartments were 56.7 L and 2090 L, respectively. Absorption rate constants for capsule (kacap) and solution (kasol) were 0.0315 h-1 and 0.125 h-1, respectively. Comparative bioavailability of the capsule was 0.82. There was no evidence of nonlinearity in the popPK of ITRA. No screened covariate significantly improved the fit to the data. The results of the parameter estimates from the final model were comparable between the different methods for accounting for missing data, (M4,5,6)[3] and provided similar parameter estimates. The prospective application of an optimal design was found to be successful. Due to the sampling windows, most of the samples could be collected within the daily hospital routine, but still at times that were near optimal for estimating the popPK parameters. The final model was one of the potential competing models considered in the original design. The asymptotic standard errors provided by NONMEM for the final model and empirical values from bootstrap were similar in magnitude to those predicted from the Fisher Information matrix associated with the D-optimal design. Simulations from the final model showed that the current dosing regimen of 200 mg twice daily (bd) would provide a target Cmin,ss (0.5-2 mg/L) for only 35% of patients when administered as the solution and 31% when administered as capsules. The optimal dosing schedule was 500mg bd for both formulations. The target success for this dosing regimen was 87% for the solution with an NNT=4 compared to capsules. This means, for every 4 patients treated with the solution one additional patient will achieve a target success compared to capsule but at an additional cost of AUD $220 per day. The therapeutic target however is still doubtful and potential risks of these dosing schedules need to be assessed on an individual basis. Conclusion: A model was developed which described the popPK of ITRA and its main active metabolite OH-ITRA in adult CF after administration of both capsule and solution. The relative bioavailability of ITRA from the capsule was 82% that of the solution, but considerably more variable. To incorporate missing data, using the simple Beal method 5 (using half LOD for all samples below LOD) provided comparable results to the more complex but theoretically better Beal method 4 (integration method). The optimal sparse design performed well for estimation of model parameters and provided a good fit to the data.

Toward better outcomes with tacrolimus therapy: Population pharmacokinetics and individualized dosage prediction in adult liver transplantation

Patient outcomes in transplantation would improve if dosing of immunosuppressive agents was individualized. The aim of this study is to develop a population pharmacokinetic model of tacrolimus in adult liver transplant recipients and test this model in individualizing therapy. Population analysis was performed on data from 68 patients. Estimates were sought for apparent clearance (CL/F) and apparent volume of distribution (V/F) using the nonlinear mixed effects model program (NONMEM). Factors screened for influence on these parameters were weight, age, sex, transplant type, biliary reconstructive procedure, postoperative day, days of therapy, liver function test results, creatinine clearance, hematocrit, corticosteroid dose, and interacting drugs. The predictive performance of the developed model was evaluated through Bayesian forecasting in an independent cohort of 36 patients. No linear correlation existed between tacrolimus dosage and trough concentration (r(2) = 0.005). Mean individual Bayesian estimates for CL/F and V/F were 26.5 8.2 (SD) L/hr and 399 +/- 185 L, respectively. CL/F was greater in patients with normal liver function. V/F increased with patient weight. CL/F decreased with increasing hematocrit. Based on the derived model, a 70-kg patient with an aspartate aminotransferase (AST) level less than 70 U/L would require a tacrolimus dose of 4.7 mg twice daily to achieve a steady-state trough concentration of 10 ng/mL. A 50-kg patient with an AST level greater than 70 U/L would require a dose of 2.6 mg. Marked interindividual variability (43% to 93%) and residual random error (3.3 ng/mL) were observed. Predictions made using the final model were reasonably nonbiased (0.56 ng/mL), but imprecise (4.8 ng/mL). Pharmacokinetic information obtained will assist in tacrolimus dosing; however, further investigation into reasons for the pharmacokinetic variability of tacrolimus is required.

Development of a dosage strategy in patients receiving enoxaparin by continuous intravenous infusion using modelling and simulation

Aim To develop an appropriate dosing strategy for continuous intravenous infusions (CII) of enoxaparin by minimizing the percentage of steady-state anti-Xa concentration (C-ss) outside the therapeutic range of 0.5-1.2 IU ml(-1). Methods A nonlinear mixed effects model was developed with NONMEM (R) for 48 adult patients who received CII of enoxaparin with infusion durations that ranged from 8 to 894 h at rates between 100 and 1600 IU h(-1). Three hundred and sixty-three anti-Xa concentration measurements were available from patients who received CII. These were combined with 309 anti-Xa concentrations from 35 patients who received subcutaneous enoxaparin. The effects of age, body size, height, sex, creatinine clearance (CrCL) and patient location [intensive care unit (ICU) or general medical unit] on pharmacokinetic (PK) parameters were evaluated. Monte Carlo simulations were used to (i) evaluate covariate effects on C-ss and (ii) compare the impact of different infusion rates on predicted C-ss. The best dose was selected based on the highest probability that the C-ss achieved would lie within the therapeutic range. Results A two-compartment linear model with additive and proportional residual error for general medical unit patients and only a proportional error for patients in ICU provided the best description of the data. Both CrCL and weight were found to affect significantly clearance and volume of distribution of the central compartment, respectively. Simulations suggested that the best doses for patients in the ICU setting were 50 IU kg(-1) per 12 h (4.2 IU kg(-1) h(-1)) if CrCL < 30 ml min(-1); 60 IU kg(-1) per 12 h (5.0 IU kg(-1) h(-1)) if CrCL was 30-50 ml min(-1); and 70 IU kg(-1) per 12 h (5.8 IU kg(-1) h(-1)) if CrCL > 50 ml min(-1). The best doses for patients in the general medical unit were 60 IU kg(-1) per 12 h (5.0 IU kg(-1) h(-1)) if CrCL < 30 ml min(-1); 70 IU kg(-1) per 12 h (5.8 IU kg(-1) h(-1)) if CrCL was 30-50 ml min(-1); and 100 IU kg(-1) per 12 h (8.3 IU kg(-1) h(-1)) if CrCL > 50 ml min(-1). These best doses were selected based on providing the lowest equal probability of either being above or below the therapeutic range and the highest probability that the C-ss achieved would lie within the therapeutic range. Conclusion The dose of enoxaparin should be individualized to the patients' renal function and weight. There is some evidence to support slightly lower doses of CII enoxaparin in patients in the ICU setting.

On minimal models of process systems

Minimal representations are known to have no redundant elements, and are therefore of great importance. Based on the notions of performance and size indices and measures for process systems, the paper proposes conditions for a process model being minimal in a set of functionally equivalent models with respect to a size norm. Generalized versions of known procedures to obtain minimal process models for a given modelling goal, model reduction based on sensitivity analysis and incremental model building are proposed and discussed. The notions and procedures are illustrated and compared on a simple example, that of a simple nonlinear fermentation process with different modelling goals and on a case study of a heat exchanger modelling. (C) 2004 Elsevier Ltd. All rights reserved.

Population pharmacokinetics of itraconazole and its active metabolite hydroxy-itraconazole in paediatric cystic fibrosis and bone marrow transplant patients

Objective: The objective of the study was to characterise the population pharmacokinetic properties of itraconazole and its active metabolite hydroxyitraconazole in a representative paediatric population of cystic fibrosis and bone marrow transplant (BMT) patients and to identify patient characteristics influencing the pharmacokinetics of itraconazole. The ultimate goals were to determine the relative bioavailability between the two oral formulations (capsules vs oral solution) and to optimise dosing regimens in these patients. Methods: All paediatric patients with cystic fibrosis or patients undergoing BMT at The Royal Children's Hospital, Brisbane, QLD, Australia, who were prescribed oral itraconazole for the treatment of allergic bronchopulmonary aspergillosis (cystic fibrosis patients) or for prophylaxis of any fungal infection (BMT patients) were eligible for the study. Blood samples were taken from the recruited patients as per an empirical sampling design either during hospitalisation or during outpatient clinic visits. ltraconazole and hydroxy-itraconazole plasma concentrations were determined by a validated high-performance liquid chromatography assay with fluorometric detection. A nonlinear mixed-effect modelling approach using the NONMEM software to simultaneously describe the pharmacokinetics of itraconazole and its metabolite. Results: A one-compartment model with first-order absorption described the itraconazole data, and the metabolism of the parent drug to hydroxy-itraconazole was described by a first-order rate constant. The metabolite data also showed one-compartment characteristics with linear elimination. For itraconazole the apparent clearance (CLitraconazole) was 35.5 L/hour, the apparent volume of distribution (V-d(itraconazole)) was 672L, the absorption rate constant for the capsule formulation was 0.0901 h(-1) and for the oral solution formulation was 0.96 h-1. The lag time was estimated to be 19.1 minutes and the relative bioavailability between capsules and oral solution (F-rel) was 0.55. For the metabolite, volume of distribution, V-m/(F (.) f(m)), and clearance, CL/(F (.) fm), were 10.6L and 5.28 L/h, respectively. The influence of total bodyweight was significant, added as a covariate on CLitraconazoie/F and V-d(itraconazole)/F (standardised to a 70kg person) using allometric three-quarter power scaling on CLitraconazole/F, which therefore reflected adult values. The unexplained between-subject variability (coefficient of variation %) was 68.7%, 75.8%, 73.4% and 61.1% for CLitraconazoie/F, Vd(itraconazole)/F, CLm/(F (.) fm) and F-rel, respectively. The correlation between random effects of CLitraconazole and Vd((itraconazole)) was 0.69. Conclusion: The developed population pharmacokinetic model adequately described the pharmacokinetics of itraconazole and its active metabolite, hydroxy-itraconazole, in paediatric patients with either cystic fibrosis or undergoing BMT. More appropriate dosing schedules have been developed for the oral solution and the capsules to secure a minimum therapeutic trough plasma concentration of 0.5 mg/L for these patients.

Sampling times for monitoring tacrolimus in stable adult liver transplant recipients

The aim of this study was to determine the most informative sampling time(s) providing a precise prediction of tacrolimus area under the concentration-time curve (AUC). Fifty-four concentration-time profiles of tacrolimus from 31 adult liver transplant recipients were analyzed. Each profile contained 5 tacrolimus whole-blood concentrations (predose and 1, 2, 4, and 6 or 8 hours postdose), measured using liquid chromatography-tandem mass spectrometry. The concentration at 6 hours was interpolated for each profile, and 54 values of AUC(0-6) were calculated using the trapezoidal rule. The best sampling times were then determined using limited sampling strategies and sensitivity analysis. Linear mixed-effects modeling was performed to estimate regression coefficients of equations incorporating each concentration-time point (C0, C1, C2, C4, interpolated C5, and interpolated C6) as a predictor of AUC(0-6). Predictive performance was evaluated by assessment of the mean error (ME) and root mean square error (RMSE). Limited sampling strategy (LSS) equations with C2, C4, and C5 provided similar results for prediction of AUC(0-6) (R-2 = 0.869, 0.844, and 0.832, respectively). These 3 time points were superior to C0 in the prediction of AUC. The ME was similar for all time points; the RMSE was smallest for C2, C4, and C5. The highest sensitivity index was determined to be 4.9 hours postdose at steady state, suggesting that this time point provides the most information about the AUC(0-12). The results from limited sampling strategies and sensitivity analysis supported the use of a single blood sample at 5 hours postdose as a predictor of both AUC(0-6) and AUC(0-12). A jackknife procedure was used to evaluate the predictive performance of the model, and this demonstrated that collecting a sample at 5 hours after dosing could be considered as the optimal sampling time for predicting AUC(0-6).

Assessing the impacts of grazing levels on bird density in woodland habitat: a Bayesian approach using expert opinion

Many studies on birds focus on the collection of data through an experimental design, suitable for investigation in a classical analysis of variance (ANOVA) framework. Although many findings are confirmed by one or more experts, expert information is rarely used in conjunction with the survey data to enhance the explanatory and predictive power of the model. We explore this neglected aspect of ecological modelling through a study on Australian woodland birds, focusing on the potential impact of different intensities of commercial cattle grazing on bird density in woodland habitat. We examine a number of Bayesian hierarchical random effects models, which cater for overdispersion and a high frequency of zeros in the data using WinBUGS and explore the variation between and within different grazing regimes and species. The impact and value of expert information is investigated through the inclusion of priors that reflect the experience of 20 experts in the field of bird responses to disturbance. Results indicate that expert information moderates the survey data, especially in situations where there are little or no data. When experts agreed, credible intervals for predictions were tightened considerably. When experts failed to agree, results were similar to those evaluated in the absence of expert information. Overall, we found that without expert opinion our knowledge was quite weak. The fact that the survey data is quite consistent, in general, with expert opinion shows that we do know something about birds and grazing and we could learn a lot faster if we used this approach more in ecology, where data are scarce. Copyright (c) 2005 John Wiley & Sons, Ltd.

The return to schooling: Estimates from a sample of young Australian twins

This study uses a sample of young Australian twins to examine whether the findings reported in [Ashenfelter, Orley and Krueger, Alan, (1994). 'Estimates of the Economic Return to Schooling from a New Sample of Twins', American Economic Review, Vol. 84, No. 5, pp.1157-73] and [Miller, P.W., Mulvey, C and Martin, N., (1994). 'What Do Twins Studies Tell Us About the Economic Returns to Education?: A Comparison of Australian and US Findings', Western Australian Labour Market Research Centre Discussion Paper 94/4] are robust to choice of sample and dependent variable. The economic return to schooling in Australia is between 5 and 7 percent when account is taken of genetic and family effects using either fixed-effects models or the selection effects model of Ashenfelter and Krueger. Given the similarity of the findings in this and in related studies, it would appear that the models applied by [Ashenfelter, Orley and Krueger, Alan, (1994). 'Estimates of the Economic Return to Schooling from a New Sample of Twins', American Economic Review, Vol. 84, No. 5, pp. 1157-73] are robust. Moreover, viewing the OLS and IV estimators as lower and upper bounds in the manner of [Black, Dan A., Berger, Mark C., and Scott, Frank C., (2000). 'Bounding Parameter Estimates with Nonclassical Measurement Error', Journal of the American Statistical Association, Vol. 95, No.451, pp.739-748], it is shown that the bounds on the return to schooling in Australia are much tighter than in [Ashenfelter, Orley and Krueger, Alan, (1994). 'Estimates of the Economic Return to Schooling from a New Sample of Twins', American Economic Review, Vol. 84, No. 5, pp. 1157-73], and the return is bounded at a much lower level than in the US. (c) 2005 Elsevier B.V. All rights reserved.

A Score Test for Zero-Inflation in Correlated Count Data

To account for the preponderance of zero counts and simultaneous correlation of observations, a class of zero-inflated Poisson mixed regression models is applicable for accommodating the within-cluster dependence. In this paper, a score test for zero-inflation is developed for assessing correlated count data with excess zeros. The sampling distribution and the power of the test statistic are evaluated by simulation studies. The results show that the test statistic performs satisfactorily under a wide range of conditions. The test procedure is further illustrated using a data set on recurrent urinary tract infections. Copyright (c) 2005 John Wiley & Sons, Ltd.