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.

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.

A Mixture model with random-effects components for clustering correlated gene-expression profiles

Motivation: The clustering of gene profiles across some experimental conditions of interest contributes significantly to the elucidation of unknown gene function, the validation of gene discoveries and the interpretation of biological processes. However, this clustering problem is not straightforward as the profiles of the genes are not all independently distributed and the expression levels may have been obtained from an experimental design involving replicated arrays. Ignoring the dependence between the gene profiles and the structure of the replicated data can result in important sources of variability in the experiments being overlooked in the analysis, with the consequent possibility of misleading inferences being made. We propose a random-effects model that provides a unified approach to the clustering of genes with correlated expression levels measured in a wide variety of experimental situations. Our model is an extension of the normal mixture model to account for the correlations between the gene profiles and to enable covariate information to be incorporated into the clustering process. Hence the model is applicable to longitudinal studies with or without replication, for example, time-course experiments by using time as a covariate, and to cross-sectional experiments by using categorical covariates to represent the different experimental classes. Results: We show that our random-effects model can be fitted by maximum likelihood via the EM algorithm for which the E(expectation) and M(maximization) steps can be implemented in closed form. Hence our model can be fitted deterministically without the need for time-consuming Monte Carlo approximations. The effectiveness of our model-based procedure for the clustering of correlated gene profiles is demonstrated on three real datasets, representing typical microarray experimental designs, covering time-course, repeated-measurement and cross-sectional data. In these examples, relevant clusters of the genes are obtained, which are supported by existing gene-function annotation. A synthetic dataset is considered too.

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).

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.

Methods for Categorical Longitudinal Survey Data: Understanding Employment Status of Australian Women

Many variables that are of interest in social science research are nominal variables with two or more categories, such as employment status, occupation, political preference, or self-reported health status. With longitudinal survey data it is possible to analyse the transitions of individuals between different employment states or occupations (for example). In the statistical literature, models for analysing categorical dependent variables with repeated observations belong to the family of models known as generalized linear mixed models (GLMMs). The specific GLMM for a dependent variable with three or more categories is the multinomial logit random effects model. For these models, the marginal distribution of the response does not have a closed form solution and hence numerical integration must be used to obtain maximum likelihood estimates for the model parameters. Techniques for implementing the numerical integration are available but are computationally intensive requiring a large amount of computer processing time that increases with the number of clusters (or individuals) in the data and are not always readily accessible to the practitioner in standard software. For the purposes of analysing categorical response data from a longitudinal social survey, there is clearly a need to evaluate the existing procedures for estimating multinomial logit random effects model in terms of accuracy, efficiency and computing time. The computational time will have significant implications as to the preferred approach by researchers. In this paper we evaluate statistical software procedures that utilise adaptive Gaussian quadrature and MCMC methods, with specific application to modeling employment status of women using a GLMM, over three waves of the HILDA survey.

A Bayesian approach to imposing curvature on distance functions

The estimated parameters of output distance functions frequently violate the monotonicity, quasi-convexity and convexity constraints implied by economic theory, leading to estimated elasticities and shadow prices that are incorrectly signed, and ultimately to perverse conclusions concerning the effects of input and output changes on productivity growth and relative efficiency levels. We show how a Bayesian approach can be used to impose these constraints on the parameters of a translog output distance function. Implementing the approach involves the use of a Gibbs sampler with data augmentation. A Metropolis-Hastings algorithm is also used within the Gibbs to simulate observations from truncated pdfs. Our methods are developed for the case where panel data is available and technical inefficiency effects are assumed to be time-invariant. Two models-a fixed effects model and a random effects model-are developed and applied to panel data on 17 European railways. We observe significant changes in estimated elasticities and shadow price ratios when regularity restrictions are imposed. (c) 2004 Elsevier B.V. All rights reserved.

Characteristics and benefits of professional work - Assessment of their importance over a 30-year career

The Professions in Australia Study is the first longitudinal investigation of the professions in Australia; it spans 33 years. Self-administered questionnaires were distributed on at least eight occasions between 1965 and 1998 to cohorts of students and later practitioners from the professions of engineering, law and medicine. The longitudinal design of this study has allowed for an investigation of individual change over time of three archetypal characteristics of the professions, service, knowledge and autonomy and two of the benefits of professional work, financial rewards and prestige. A cumulative logit random effects model was used to statistically assess changes in the ordinal response scores for measuring importance of the characteristics and benefits through stages of the career path. Individuals were also classified by average trends in response scores over time and hence professions are described through their members' tendency to follow a particular path in attitudes either of change or constancy, in relation to the importance of the five elements (characteristics and benefits). Comparisons in trends are also made between the three professions.

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.

In vitro heterogeneity of osteogenic cell populations at various equine skeletal sites

Bone cell cultures were evaluated to determine if osteogenic cell populations at different skeletal sites in the horse are heterogeneous. Osteogenic cells were isolated from cortical and cancellous bone in vitro by an explant culture method. Subcultured cells were induced to differentiate into bone-forming osteoblasts. The osteoblast phenotype was confirmed by immunohistochemical testing for osteocalcin and substantiated by positive staining of cells for alkaline phosphatase and the matrix materials collagen and glycosaminoglycans. Bone nodules were stained by the von Kossa method and counted. The numbers of nodules produced from osteogenic cells harvested from different skeletal sites were compared with the use of a mixed linear model. On average, cortical bone sites yielded significantly greater numbers of nodules than did cancellous bone sites. Between cortical bone sites, there was no significant difference in nodule numbers. Among cancellous sites, the radial cancellous bone yielded significantly more nodules than did the tibial cancellous bone. Among appendicular skeletal sites, tibial metaphyseal bone yielded significantly fewer nodules than did all other long bone sites. This study detected evidence of heterogeneity of equine osteogenic cell populations at various skeletal sites. Further characterization of the dissimilarities is warranted to determine the potential role heterogeneity plays in differential rates of fracture healing between skeletal sites.

Self-paced reading and sentence comprehension in Parkinson's disease

Parkinson's disease (PD) is associated with disturbances in sentence processing, particularly for noncanonical sentences. The present study aimed to analyse sentence processing in PD patients and healthy control participants, using a word-by-word self-paced reading task and an auditory comprehension task. Both tasks consisted of subject relative (SR) and object relative (OR) sentences, with comprehension accuracy measured for each sentence type. For the self-paced reading task, reading times (RTs) were also recorded for the non-critical and critical processing regions of each sentence. Analysis of RTs using mixed linear model statistics revealed a delayed sensitivity to the critical processing region of OR sentences in the PD group. In addition, only the PD group demonstrated significantly poorer comprehension of OR sentences compared to SR sentences during an auditory comprehension task. These results may be consistent with slower lexical retrieval in PD, and its influence on the processing of noncanonical sentences. (c) 2005 Elsevier Ltd. All rights reserved.

The importance of forest area and configuration relative to local habitat factors for conserving forest mammals: A case study of koalas in Queensland, Australia

The loss and fragmentation of forest habitats by human land use are recognised as important factors influencing the decline of forest-dependent fauna. Mammal species that are dependent upon forest habitats are particularly sensitive to habitat loss and fragmentation because they have highly specific habitat requirements, and in many cases have limited ability to move through and utilise the land use matrix. We addressed this problem using a case study of the koala (Phascolarctos cinereus) surveyed in a fragmented rural-urban landscape in southeast Queensland, Australia. We applied a logistic modelling and hierarchical partitioning analysis to determine the importance of forest area and its configuration relative to site (local) and patch-level habitat variables. After taking into account spatial auto-correlation and the year of survey, we found koala occurrence increased with the area of all forest habitats, habitat patch size and the proportion of primary Eucalyptus tree species; and decreased with mean nearest neighbour distance between forest patches, the density of forest patches, and the density of sealed roads. The difference between the effect of habitat area and configuration was not as strong as theory predicts, with the configuration of remnant forest becoming increasingly important as the area of forest habitat declines. We conclude that the area of forest, its configuration across the landscape, as well as the land use matrix, are important determinants of koala occurrence, and that habitat configuration should not be overlooked in the conservation of forest-dependent mammals, such as the koala. We highlight the implications of these findings for koala conservation. (c) 2006 Elsevier Ltd. All rights reserved.