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).

Optimal sampling strategy for estimation of spatial genetic structure in tree populations

Fine-scale spatial genetic structure (SGS) in natural tree populations is largely a result of restricted pollen and seed dispersal. Understanding the link between limitations to dispersal in gene vectors and SGS is of key interest to biologists and the availability of highly variable molecular markers has facilitated fine-scale analysis of populations. However, estimation of SGS may depend strongly on the type of genetic marker and sampling strategy (of both loci and individuals). To explore sampling limits, we created a model population with simulated distributions of dominant and codominant alleles, resulting from natural regeneration with restricted gene flow. SGS estimates from subsamples (simulating collection and analysis with amplified fragment length polymorphism (AFLP) and microsatellite markers) were correlated with the 'real' estimate (from the full model population). For both marker types, sampling ranges were evident, with lower limits below which estimation was poorly correlated and upper limits above which sampling became inefficient. Lower limits (correlation of 0.9) were 100 individuals, 10 loci for microsatellites and 150 individuals, 100 loci for AFLPs. Upper limits were 200 individuals, five loci for microsatellites and 200 individuals, 100 loci for AFLPs. The limits indicated by simulation were compared with data sets from real species. Instances where sampling effort had been either insufficient or inefficient were identified. The model results should form practical boundaries for studies aiming to detect SGS. However, greater sample sizes will be required in cases where SGS is weaker than for our simulated population, for example, in species with effective pollen/seed dispersal mechanisms.

Prospective evaluation of a D-optimal designed population pharmacokinetic study

Recently, methods for computing D-optimal designs for population pharmacokinetic studies have become available. However there are few publications that have prospectively evaluated the benefits of D-optimality in population or single-subject settings. This study compared a population optimal design with an empirical design for estimating the base pharmacokinetic model for enoxaparin in a stratified randomized setting. The population pharmacokinetic D-optimal design for enoxaparin was estimated using the PFIM function (MATLAB version 6.0.0.88). The optimal design was based on a one-compartment model with lognormal between subject variability and proportional residual variability and consisted of a single design with three sampling windows (0-30 min, 1.5-5 hr and 11 - 12 hr post-dose) for all patients. The empirical design consisted of three sample time windows per patient from a total of nine windows that collectively represented the entire dose interval. Each patient was assigned to have one blood sample taken from three different windows. Windows for blood sampling times were also provided for the optimal design. Ninety six patients were recruited into the study who were currently receiving enoxaparin therapy. Patients were randomly assigned to either the optimal or empirical sampling design, stratified for body mass index. The exact times of blood samples and doses were recorded. Analysis was undertaken using NONMEM (version 5). The empirical design supported a one compartment linear model with additive residual error, while the optimal design supported a two compartment linear model with additive residual error as did the model derived from the full data set. A posterior predictive check was performed where the models arising from the empirical and optimal designs were used to predict into the full data set. This revealed the optimal'' design derived model was superior to the empirical design model in terms of precision and was similar to the model developed from the full dataset. This study suggests optimal design techniques may be useful, even when the optimized design was based on a model that was misspecified in terms of the structural and statistical models and when the implementation of the optimal designed study deviated from the nominal design.

A theory for optimal monitoring of marine reserves

Monitoring of marine reserves has traditionally focused on the task of rejecting the null hypothesis that marine reserves have no impact on the population and community structure of harvested populations. We consider the role of monitoring of marine reserves to gain information needed for management decisions. In particular we use a decision theoretic framework to answer the question: how long should we monitor the recovery of an over-fished stock to determine the fraction of that stock to reserve? This exposes a natural tension between the cost (in terms of time and money) of additional monitoring, and the benefit of more accurately parameterizing a population model for the stock, that in turn leads to a better decision about the optimal size for the reserve with respect to harvesting. We found that the optimal monitoring time frame is rarely more than 5 years. A higher economic discount rate decreased the optimal monitoring time frame, making the expected benefit of more certainty about parameters in the system negligible compared with the expected gain from earlier exploitation.

Optimal design for model discrimination and parameter estimation for itraconazole population pharmacokinetics in cystic fibrosis patients

Optimal sampling times are found for a study in which one of the primary purposes is to develop a model of the pharmacokinetics of itraconazole in patients with cystic fibrosis for both capsule and solution doses. The optimal design is expected to produce reliable estimates of population parameters for two different structural PK models. Data collected at these sampling times are also expected to provide the researchers with sufficient information to reasonably discriminate between the two competing structural models.

Optimal eradication: when to stop looking for an invasive plant

The notion of being sure that you have completely eradicated an invasive species is fanciful because of imperfect detection and persistent seed banks. Eradication is commonly declared either on an ad hoc basis, on notions of seed bank longevity, or on setting arbitrary thresholds of 1% or 5% confidence that the species is not present. Rather than declaring eradication at some arbitrary level of confidence, we take an economic approach in which we stop looking when the expected costs outweigh the expected benefits. We develop theory that determines the number of years of absent surveys required to minimize the net expected cost. Given detection of a species is imperfect, the optimal stopping time is a trade-off between the cost of continued surveying and the cost of escape and damage if eradication is declared too soon. A simple rule of thumb compares well to the exact optimal solution using stochastic dynamic programming. Application of the approach to the eradication programme of Helenium amarum reveals that the actual stopping time was a precautionary one given the ranges for each parameter.

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.

Population pharmacokinetics of perhexiline from very sparse, routine monitoring data

Using NONMEM, the population pharmacokinetics of perhexiline were studied in 88 patients (34 F, 54 M) who were being treated for refractory angina. Their mean +/- SD (range) age was 75 +/- 9.9 years (46-92), and the length of perhexiline treatment was 56 +/- 77 weeks (0.3-416). The sampling time after a dose was 14.1 +/- 21.4 hours (0.5-200), and the perhexiline plasma concentrations were 0.39 +/- 0.32 mg/L (0.03-1.56). A one-compartment model with first-order absorption was fitted to the data using the first-order (FO) approximation. The best model contained 2 subpopulations (obtained via the $MIXTURE subroutine) of 77 subjects (subgroup A) and 11 subjects (subgroup B) that had typical values for clearance (CL/F) of 21.8 L/h and 2.06 L/h, respectively. The volumes of distribution (V/F) were 1470 L and 260 L, respectively, which suggested a reduction in presystemic metabolism in subgroup B. The interindividual variability (CV%) was modeled logarithmically and for CL/F ranged from 69.1% (subgroup A) to 86.3% (subgroup B). The interindividual variability in V/F was 111%. The residual variability unexplained by the population model was 28.2%. These results confirm and extend the existing pharmacokinetic data on perhexiline, especially the bimodal distribution of CL/F manifested via an inherited deficiency in hepatic and extrahepatic CYP2D6 activity.

Design of clinical pharmacology trials

1. There are a variety of methods that could be used to increase the efficiency of the design of experiments. However, it is only recently that such methods have been considered in the design of clinical pharmacology trials. 2. Two such methods, termed data-dependent (e.g. simulation) and data-independent (e.g. analytical evaluation of the information in a particular design), are becoming increasingly used as efficient methods for designing clinical trials. These two design methods have tended to be viewed as competitive, although a complementary role in design is proposed here. 3. The impetus for the use of these two methods has been the need for a more fully integrated approach to the drug development process that specifically allows for sequential development (i.e. where the results of early phase studies influence later-phase studies). 4. The present article briefly presents the background and theory that underpins both the data-dependent and -independent methods with the use of illustrative examples from the literature. In addition, the potential advantages and disadvantages of each method are discussed.

Impact of mycophenolate mofetil loading on drug exposure in the early posttransplant period

Achieving adequate therapeutic levels of immunosuppressive medications is important in rejection prevention. This study examined exposure to mycophenolic acid (MPA) in kidney transplant patients within the first 5 days posttransplantation. Methods. This single-center, nonrandomized study of first solitary kidney allograft recipients receiving cyclosporine (n = 116) or tacrolimus (n = 50) included patients who received either 1 g or 1.5 g of mycophenolate mofetil twice daily starting postoperatively. Exposure to MPA was measured at days 3 and 5 posttransplant using published limited sampling time equations. Results. There were no significant differences in exposure in the cyclosporine-treated patients receiving 3-g (n = 22) compared to 2-g (n = 94) daily doses (AUC([0-12]) 33.8 +/- 10.0 mg*h/L versus 30.1 +/- 9.7 mg*h/L, P =.20, respectively). About half the patients in both groups had AUC([0-12]) < 30 mg*h/L on days 3 and 5 posttransplant. On the other hand, there was significantly greater exposure on day 3 in the tacrolimus-treated patients receiving 3 g (n = 21) compared to 2 g (n = 29) daily (AUC([0-12]) 43.1 +/- 9.0 mg*h/L versus 36.8 +/- 11.1 mg*h/L, P =.016, respectively). On day 3 one (4.8%) patient receiving 3 g had an AUC([0-12]) of < 30 mg*h/L; whereas, eight (27.5%) receiving 2 g were below this level (P =.068). The AUC([0-12]) levels were not different on day 5. Conclusions. Loading with higher doses of mycophenolate mofetil results in greater exposure and a trend toward more patients in the therapeutic window within the first week for tacrolimus- but not for cyclosporine-treated patients.

Do predators aggregate in response to pest density in agroecosystems? Assessing within-field spatial patterns

1. The spatial heterogeneity of predator populations is an important component of ecological theories pertaining to predator-prey dynamics. Most studies within agricultural fields show spatial correlation (positive or negative) between mean predator numbers and prey abundance across a whole field over time but generally ignore the within-field spatial dimension. We used explicit spatial mapping to determine if generalist predators aggregated within a soybean field, the size of these aggregations and if predator aggregation was associated with pest aggregation, plant damage and predation rate. 2. The study was conducted at Gatton in the Lockyer Valley, 90 km west of Brisbane, Australia. Intensive sampling grids were used to investigate within-field spatial patterns. The first row of each grid was located in a lucerne field (10 m from interface) and the remaining rows were in an adjacent soybean field. At each point on the grid the abundance of foliage-dwelling and ground-dwelling pests and predators was measured, predation rates [using sentinel Helicoverpa armigera (Hubner) egg cards] and plant damage were estimated. Eight grids were sampled across two summer cropping seasons (2000/01, 2001/02). 3. Predators exhibited strong spatial patterning with regions of high and low abundance and activity within what are considered to be uniform soybean fields. Ground-dwelling and foliage-dwelling predators were often aggregated in patches approximately 40 m across. 4. Lycosidae (wolf spiders) displayed aggregation and were consistently more abundant within the lucerne, with a decreasing trap catch with distance from the lucrene/soybean interface. This trend was consistent between subsequent grids in a single field and between fields. 5. The large amount of spatial variability in within-field arthropod abundance (pests and predators) and activity (egg predation and plant damage) indicates that whole field averages were misleading. This result has serious implications for sampling of arthropod abundance and pest management decision-making based on scouting data. 6. There was a great deal of temporal change in the significant spatial patterns observed within a field at each sampling time point during a single season. Predator and pest aggregations observed in these fields were generally not stable for the entire season. 7. Predator aggregation did not correlate consistently with pest aggregation, plant damage or predation rate. Spatial patterns in predator abundance were not associated consistently with any single parameter measured. The most consistent positive association was between foliage-dwelling predators and pests (significant in four of seven grids). Inferring associations between predators and prey based on an intensive one-off sampling grid is difficult, due to the temporal variability in the abundance of each group. 8. Synthesis and applications. This study demonstrated that generalist predator populations are rarely distributed randomly and field edges and adjacent crops can have an influence on within-field predator abundance. This must be considered when estimating arthropod (pest and predator) abundance from a set of samples taken at random locations within a field.

Practicality of time-optimal two-qubit Hamiltonian simulation

What is the time-optimal way of using a set of control Hamiltonians to obtain a desired interaction? Vidal, Hammerer, and Cirac [Phys. Rev. Lett. 88, 237902 (2002)] have obtained a set of powerful results characterizing the time-optimal simulation of a two-qubit quantum gate using a fixed interaction Hamiltonian and fast local control over the individual qubits. How practically useful are these results? We prove that there are two-qubit Hamiltonians such that time-optimal simulation requires infinitely many steps of evolution, each infinitesimally small, and thus is physically impractical. A procedure is given to determine which two-qubit Hamiltonians have this property, and we show that almost all Hamiltonians do. Finally, we determine some bounds on the penalty that must be paid in the simulation time if the number of steps is fixed at a finite number, and show that the cost in simulation time is not too great.

Morningness-eveningness orientation, optimal time-of-day and attitude change: Evidence for the systematic processing of a persuasive communication

This study investigates the effects of morningness-eveningness orientation and time-of-day on persuasion. In an attitude change paradigm, 120 female participants read a persuasive message that consisted of six counter-attitudinal arguments (anti-voluntary euthanasia) either in the morning (8:30 a.m.) or in the evening (7:00 p.m.). Attitude change was assessed by measuring attitudes towards the target issue before and after exposure to the message. Message processing was assessed by thought-listing and message recall tasks. Self-reported mood and arousal were monitored throughout. Participants were classified into M- and E-types according to their scores on the Horne and Ostberg (1976) MEQ questionnaire. When tested at their respective optimal time-of-day (i.e., morning for M-types/evening for E-types), M- and E-types reported higher energetic arousal, greater agreement with the message, greater message-congruent thinking, and a propensity for superior message recall compared to M- and E-types tested at their nonoptimal time-of-day (i.e., evening for M-types/morning for E-types). The attitude change in those tested at their optimal time-of-day was mediated by the level of message-congruent thinking. Results are interpreted in terms of the Elaboration Likelihood Model of persuasion. (c) 2005 Elsevier Ltd. All rights reserved.