Properties of the full random-effect modeling approach with missing covariate data.

During drug development, a key step is the identification of relevant covariates predicting between-subject variations in drug response. The full random effects model (FREM) is one of the full-covariate approaches used to identify relevant covariates in nonlinear mixed effects models. Here we explore the ability of FREM to handle missing (both missing completely at random (MCAR) and missing at random (MAR)) covariate data and compare it to the full fixed-effects model (FFEM) approach, applied either with complete case analysis or mean imputation. A global health dataset (20 421 children) was used to develop a FREM describing the changes of height for age Z-score (HAZ) over time. Simulated datasets (n = 1000) were generated with variable rates of missing (MCAR) covariate data (0%-90%) and different proportions of missing (MAR) data condition on either observed covariates or predicted HAZ. The three methods were used to re-estimate model and compared in terms of bias and precision which showed that FREM had only minor increases in bias and minor loss of precision at increasing percentages of missing (MCAR) covariate data and performed similarly in the MAR scenarios. Conversely, the FFEM approaches either collapsed at ≥ $$ \ge $$ 70% of missing (MCAR) covariate data (FFEM complete case analysis) or had large bias increases and loss of precision (FFEM with mean imputation). Our results suggest that FREM is an appropriate approach to covariate modeling for datasets with missing (MCAR and MAR) covariate data, such as in global health studies.

3D analysis and grading of calcifications from ex vivo human meniscus.

OBJECTIVE: Meniscal calcifications are associated with the pathogenesis of knee osteoarthritis (OA). We propose a micro-computed tomography (µCT) based 3D analysis of meniscal calcifications ex vivo, including a new grading system. METHOD: Human medial and lateral menisci were obtained from 10 patients having total knee replacement for medial compartment OA and 10 deceased donors without knee OA (healthy references). The samples were fixed; one subsection was imaged with µCT, and the adjacent tissue was processed for histological evaluation. Calcifications were examined from the reconstructed 3D µCT images, and a new grading system was developed. To validate the grading system, meniscal calcification volumes (CVM) were quantitatively analyzed and compared between the calcification grades. Furthermore, we estimated the relationship between histopathological degeneration and the calcification severity. RESULTS: 3D µCT images depict calcifications in every sample, including diminutive calcifications that are not visible in histology. In the new grading system, starting from grade 2, each grade results in a CVM that is 20.3 times higher (95% CI 13.3-30.5) than in the previous grade. However, there was no apparent difference in CVM between grades 1 and 2. The calcification grades appear to increase with the increasing histopathological degeneration, although histopathological degeneration is also observed with small calcification grades. CONCLUSIONS: 3D µCT grading of meniscal calcifications is feasible. Interestingly, it seems that there are two patterns of degeneration in the menisci of our sample set: 1) with diminutive calcifications (calcification grades 1-2), and 2) with large to widespread calcifications (calcification grades 3-5).

Medicines postpartum in Sweden and coverage in Janusmed Breastfeeding.

PURPOSE: The purpose of this article is (1) to investigate which medicines are prescribed and dispensed to women the first 6 months postpartum, (2) to identify medicines dispensed postpartum but not recommended during breastfeeding, and (3) to find medicines commonly dispensed postpartum, but not currently included in Janusmed Breastfeeding. METHODS: In this register-based cohort study covering births between January 2017 and August 2019, the Swedish Medical Birth Register (MBR), the Prescribed Drug Register, and Janusmed Breastfeeding were linked to identify medicines dispensed to women during the first 6 months postpartum, and how they are covered and classified in Janusmed Breastfeeding. RESULTS: During the first 6 months postpartum, 66% of women purchased at least one prescription medicine from the pharmacy. The most common medicines were contraceptive agents, analgesics, antibiotics, and glucocorticoids. A third of the 30 most commonly dispensed medicines have no information available about the safety of use in breastfeeding. The most dispensed medicines, where the database advises against use in breastfeeding, included several antitussive agents, a local anaesthetic, and several gestagens. The most commonly dispensed medicines not covered by the Janusmed Breastfeeding were medicines for dry eyes, for assisted reproduction, and HIV. CONCLUSION: Prescribed medicines compatible with breastfeeding are more common during the first 6 months postpartum than medicines not compatible with breastfeeding, but medicines which lack evidence for safety in breastfeeding are still commonly used.

Cerebellar volume and cerebellocerebral structural covariance in schizophrenia: a multisite mega-analysis of 983 patients and 1349 healthy controls.

Although cerebellar involvement across a wide range of cognitive and neuropsychiatric phenotypes is increasingly being recognized, previous large-scale studies in schizophrenia (SZ) have primarily focused on supratentorial structures. Hence, the across-sample reproducibility, regional distribution, associations with cerebrocortical morphology and effect sizes of cerebellar relative to cerebral morphological differences in SZ are unknown. We addressed these questions in 983 patients with SZ spectrum disorders and 1349 healthy controls (HCs) from 14 international samples, using state-of-the-art image analysis pipelines optimized for both the cerebellum and the cerebrum. Results showed that total cerebellar grey matter volume was robustly reduced in SZ relative to HCs (Cohens's d=-0.35), with the strongest effects in cerebellar regions showing functional connectivity with frontoparietal cortices (d=-0.40). Effect sizes for cerebellar volumes were similar to the most consistently reported cerebral structural changes in SZ (e.g., hippocampus volume and frontotemporal cortical thickness), and were highly consistent across samples. Within groups, we further observed positive correlations between cerebellar volume and cerebral cortical thickness in frontotemporal regions (i.e., overlapping with areas that also showed reductions in SZ). This cerebellocerebral structural covariance was strongest in SZ, suggesting common underlying disease processes jointly affecting the cerebellum and the cerebrum. Finally, cerebellar volume reduction in SZ was highly consistent across the included age span (16-66 years) and present already in the youngest patients, a finding that is more consistent with neurodevelopmental than neurodegenerative etiology. Taken together, these novel findings establish the cerebellum as a key node in the distributed brain networks underlying SZ.

Silica dust and sarcoidosis in Swedish construction workers.

BACKGROUND: The aetiology of sarcoidosis is not well established. In previous studies, smoking has been negatively associated with sarcoidosis and there are some indications of an association between exposure to silica dust and sarcoidosis. AIMS: To study the risk of sarcoidosis in relation to silica dust exposure. METHODS: A longitudinal cohort of construction workers linked with a registry of Swedish inpatient diagnoses. Workers were designated as exposed or unexposed to silica based on job titles in a job-exposure matrix. The relative risk (RR) was analysed with Poisson regression adjusting for age and smoking. RESULTS: We identified 371 cases of sarcoidosis among 297 917 male workers. There was an increased risk of sarcoidosis in the medium- to high-exposure group [RR 1.83 (95% confidence interval {CI} 1.14-2.95)]. A stratified analysis according to smoking showed that ever-smoking workers had an increased risk of sarcoidosis if highly exposed to silica dust [RR 2.44 (95% CI 1.37-4.33)] compared to non-exposed ever-smokers. The risk of non-smokers highly exposed to silica was not significantly increased [RR 1.07 (95% CI 0.72-1.58)] compared to non-exposed non-smokers. CONCLUSION: The study indicates an increased risk of developing sarcoidosis in ever-smoking men exposed to silica.

A health economic simulation model for the clinical management of osteoporosis.

The objective was to estimate the burden of osteoporosis in Sweden based on current clinical practice and the cost-effectiveness of improvements in the management of osteoporosis over the clinical management compared to current clinical practice. Results showed that better compliance to treatment guidelines is associated with better projected outcomes and cost-savings. INTRODUCTION: The purpose of this study is to estimate the burden of osteoporosis in Sweden based on current clinical practice and the cost-effectiveness of improvements in the management of osteoporosis over the clinical management compared to current clinical practice. METHODS: The analysis was carried out using a model that simulates the individual patients considered for pharmacological treatment during 1 year and their projected osteoporosis treatment pathway, quality-adjusted life years (QALYs) and costs over their remaining lifetime. All patients regardless of treatment or no treatment were simulated. Information on current management of osteoporosis in terms of patient characteristics and treatment patterns were derived from a Swedish osteoporosis research database based on national registers and patient records. Current (standard) clinical management was compared with alternative scenarios mirroring Swedish treatment guidelines. RESULTS: The national burden in terms of lost QALYs was estimated at 14,993 QALYs and the total economic cost at €776M. Scenario analyses showed that 382-3864 QALYs could be gained at a cost/QALY ranging from cost-saving to €31368, depending on the scenario. The margin of investment, i.e. the maximum amount that could be invested in the healthcare system to achieve these improvements up to the limit of the willingness to pay/QALY, was estimated at €199M on a population level (€3,634/patient). CONCLUSIONS: The analysis showed that better compliance to treatment guidelines is associated with better projected outcomes and cost-savings. From a cost-effectiveness perspective, there is also considerable room for investment to achieve these improvements in the management of osteoporosis.

Prefrontal cortical thinning links to negative symptoms in schizophrenia via the ENIGMA consortium.

BACKGROUND: Our understanding of the complex relationship between schizophrenia symptomatology and etiological factors can be improved by studying brain-based correlates of schizophrenia. Research showed that impairments in value processing and executive functioning, which have been associated with prefrontal brain areas [particularly the medial orbitofrontal cortex (MOFC)], are linked to negative symptoms. Here we tested the hypothesis that MOFC thickness is associated with negative symptom severity. METHODS: This study included 1985 individuals with schizophrenia from 17 research groups around the world contributing to the ENIGMA Schizophrenia Working Group. Cortical thickness values were obtained from T1-weighted structural brain scans using FreeSurfer. A meta-analysis across sites was conducted over effect sizes from a model predicting cortical thickness by negative symptom score (harmonized Scale for the Assessment of Negative Symptoms or Positive and Negative Syndrome Scale scores). RESULTS: Meta-analytical results showed that left, but not right, MOFC thickness was significantly associated with negative symptom severity (ß std = -0.075; p = 0.019) after accounting for age, gender, and site. This effect remained significant (p = 0.036) in a model including overall illness severity. Covarying for duration of illness, age of onset, antipsychotic medication or handedness weakened the association of negative symptoms with left MOFC thickness. As part of a secondary analysis including 10 other prefrontal regions further associations in the left lateral orbitofrontal gyrus and pars opercularis emerged. CONCLUSIONS: Using an unusually large cohort and a meta-analytical approach, our findings point towards a link between prefrontal thinning and negative symptom severity in schizophrenia. This finding provides further insight into the relationship between structural brain abnormalities and negative symptoms in schizophrenia.

Contribution of non-genetic factors to dopamine and serotonin receptor availability in the adult human brain.

The dopamine (DA) and serotonin (5-HT) neurotransmission systems are of fundamental importance for normal brain function and serve as targets for treatment of major neuropsychiatric disorders. Despite central interest for these neurotransmission systems in psychiatry research, little is known about the regulation of receptor and transporter density levels. This lack of knowledge obscures interpretation of differences in protein availability reported in psychiatric patients. In this study, we used positron emission tomography (PET) in a twin design to estimate the relative contribution of genetic and environmental factors, respectively, on dopaminergic and serotonergic markers in the living human brain. Eleven monozygotic and 10 dizygotic healthy male twin pairs were examined with PET and [(11)C]raclopride binding to the D2- and D3-dopamine receptor and [(11)C]WAY100635 binding to the serotonin 5-HT1A receptor. Heritability, shared environmental effects and individual-specific non-shared effects were estimated for regional D2/3 and 5-HT1A receptor availability in projection areas. We found a major contribution of genetic factors (0.67) on individual variability in striatal D2/3 receptor binding and a major contribution of environmental factors (pairwise shared and unique individual; 0.70-0.75) on neocortical 5-HT1A receptor binding. Our findings indicate that individual variation in neuroreceptor availability in the adult brain is the end point of a nature-nurture interplay, and call for increased efforts to identify not only the genetic but also the environmental factors that influence neurotransmission in health and disease.

Positive symptoms associate with cortical thinning in the superior temporal gyrus via the ENIGMA Schizophrenia consortium.

OBJECTIVE: Based on the role of the superior temporal gyrus (STG) in auditory processing, language comprehension and self-monitoring, this study aimed to investigate the relationship between STG cortical thickness and positive symptom severity in schizophrenia. METHOD: This prospective meta-analysis includes data from 1987 individuals with schizophrenia collected at seventeen centres around the world that contribute to the ENIGMA Schizophrenia Working Group. STG thickness measures were extracted from T1-weighted brain scans using FreeSurfer. The study performed a meta-analysis of effect sizes across sites generated by a model predicting left or right STG thickness with a positive symptom severity score (harmonized SAPS or PANSS-positive scores), while controlling for age, sex and site. Secondary models investigated relationships between antipsychotic medication, duration of illness, overall illness severity, handedness and STG thickness. RESULTS: Positive symptom severity was negatively related to STG thickness in both hemispheres (left: ßstd = -0.052; P = 0.021; right: ßstd = -0.073; P = 0.001) when statistically controlling for age, sex and site. This effect remained stable in models including duration of illness, antipsychotic medication or handedness. CONCLUSION: Our findings further underline the important role of the STG in hallmark symptoms in schizophrenia. These findings can assist in advancing insight into symptom-relevant pathophysiological mechanisms in schizophrenia.

Population pharmacokinetics of tanezumab in phase 3 clinical trials for osteoarthritis pain.

AIMS: The aims were to 1) develop the pharmacokinetics model to describe and predict observed tanezumab concentrations over time, 2) test possible covariate parameter relationships that could influence clearance and distribution and 3) assess the impact of fixed dosing vs. a dosing regimen adjusted by body weight. METHODS: Individual concentration-time data were determined from 1608 patients in four phase 3 studies conducted to assess efficacy and safety of intravenous tanezumab. Patients received two or three intravenous doses (2.5, 5 or 10 mg) every 8 weeks. Blood samples for assessment of tanezumab PK were collected at baseline, 1 h post-dose and at weeks 4, 8, 16 and 24 (or early termination) in all studies. Blood samples were collected at week 32 in two studies. Plasma samples were analyzed using a sensitive, specific, validated enzyme-linked immunosorbent assay. RESULTS: A two compartment model with parallel linear and non-linear elimination processes adequately described the data. Population estimates for clearance (CL), central volume (V1 ), peripheral volume (V2 ), inter-compartmental clearance, maximum elimination capacity (VM) and concentration at half-maximum elimination capacity were 0.135 l day(-1) , 2.71 l, 1.98 l, 0.371 l day(-1) , 8.03 µg day(-1) and 27.7 ng ml(-1) , respectively. Inter-individual variability (IIV) was included on CL, V1 , V2 and VM. A mixture model accounted for the distribution of residual error. While gender, dose and creatinine clearance were significant covariates, only body weight as a covariate of CL, V1 and V2 significantly reduced IIV. CONCLUSIONS: The small increase in variability associated with fixed dosing is consistent with other monoclonal antibodies and does not change risk : benefit.

A Bayesian decision support tool for efficient dose individualization of warfarin in adults and children.

BACKGROUND: Warfarin is the most widely prescribed anticoagulant for the prevention and treatment of thromboembolic events. Although highly effective, the use of warfarin is limited by a narrow therapeutic range combined with a more than ten-fold difference in the dose required for adequate anticoagulation in adults. An optimal dose that leads to a favourable balance between the wanted antithrombotic effect and the risk of bleeding as measured by the prothrombin time International Normalised Ratio (INR) must be found for each patient. A model describing the time-course of the INR response can be used to aid dose selection before starting therapy (a priori dose prediction) and after therapy has been initiated (a posteriori dose revision). RESULTS: In this paper we describe a warfarin decision support tool. It was transferred from a population PKPD-model for warfarin developed in NONMEM to a platform independent tool written in Java. The tool proved capable of solving a system of differential equations that represent the pharmacokinetics and pharmacodynamics of warfarin with a performance comparable to NONMEM. To estimate an a priori dose the user enters information on body weight, age, baseline and target INR, and optionally CYP2C9 and VKORC1 genotype. By adding information about previous doses and INR observations, the tool will suggest a new dose a posteriori through Bayesian forecasting. Results are displayed as the predicted dose per day and per week, and graphically as the predicted INR curve. The tool can also be used to predict INR following any given dose regimen, e.g. a fixed or an individualized loading-dose regimen. CONCLUSIONS: We believe that this type of mechanism-based decision support tool could be useful for initiating and maintaining warfarin therapy in the clinic. It will ensure more consistent dose adjustment practices between prescribers, and provide efficient and truly individualized warfarin dosing in both children and adults.

Characterizing variability in warfarin dose requirements in children using modelling and simulation.

AIMS: Although genetic, clinical and demographic factors have been shown to explain approximately half of the inter-individual variability in warfarin dose requirement in adults, less is known about causes of dose variability in children. This study aimed to identify and quantify major genetic, clinical and demographic sources of warfarin dose variability in children using modelling and simulation. METHODS: Clinical, demographic and genetic data from 163 children with a median age of 6.3 years (range 0.06-18.9 years), covering over 183 years of warfarin therapy and 6445 INR observations were used to update and optimize a published adult pharmacometric warfarin model for use in children. RESULTS: Genotype effects in children were found to be comparable with what has been reported for adults, with CYP2C9 explaining up to a four-fold difference in dose (CYP2C9 *1/*1 vs. *3/*3) and VKORC1 explaining up to a two-fold difference in dose (VKORC1 G/G vs. A/A), respectively. The relationship between bodyweight and warfarin dose was non-linear, with a three-fold difference in dose for a four-fold difference in bodyweight. In addition, age, baseline and target INR, and time since initiation of therapy, but not CYP4F2 genotype, had a significant impact on typical warfarin dose requirements in children. CONCLUSIONS: The updated model provides quantitative estimates of major clinical, demographic and genetic factors impacting on warfarin dose variability in children. With this new knowledge more individualized dosing regimens can be developed and prospectively evaluated in the pursuit of improving both efficacy and safety of warfarin therapy in children.

Plasma growth hormone-binding protein levels in Atlantic salmon Salmo salar during smoltification and seawater transfer.

Specific growth hormone (GH)-binding protein (Ghbp) was purified from Atlantic salmon Salmo salar and rainbow trout Oncorhynchus mykiss plasma with immunoprecipitation and characterized in cross-linking studies using autoradiography and western blots. The size of the Ghbp was estimated to be c. 53 kDa. A radioimmunoassay was established to measure Ghbp in salmonids, using antibodies specific against the extracellular segment of the S. salar growth hormone receptor 1 (grh1; GenBank AY462105). Plasma Ghbp levels were measured in S. salar smolts in fresh water and after transfer to seawater (SW; experiments 1 and 2), and in post-smolts kept at different salinities (0, 12, 22 and 34) for 3 months (experiment 3). A transient increase in plasma Ghbp, which lasted for 1 month or less, was noted in smolts after transfer to SW. Concomitantly, plasma GH and gill Na(+) -K(+) -ATPase activity increased during smoltification (in experiment 2). No difference in plasma Ghbp was evident between post-smolts kept at different salinities, although the fish kept at salinity 34 had higher plasma GH than the group kept at salinity 22 and higher hepatic ghr1 expression than post-smolts kept at salinity 12. This suggests that plasma Ghbp regulation may respond to salinity changes in the short term. The lack of correlation between Ghbp, plasma GH and hepatic ghr1 expression in the long-term post-smolt experiment indicates that Ghbp levels may be regulated independently of other components of the endocrine GH system in salmonids.

Using forest plots to interpret covariate effects in pharmacometric models.

The inclusion of covariates in pharmacometric models is important due to their ability to explain variability in drug exposure and response. Clear communication of the impact of covariates is needed to support informed decision making in clinical practice and in drug development. However, effectively conveying these effects to key stakeholders and decision makers can be challenging. Forest plots have been proposed to meet these communication needs. However, forest plots for the illustration of covariate effects in pharmacometrics are complex combinations of model predictions, uncertainty estimates, tabulated results, and reference lines and intervals. The purpose of this tutorial is to outline the aspects that influence the interpretation of forest plots, recommend best practices, and offer specific guidance for a clear and transparent communication of covariate effects.

Full random effects models (FREM): A practical usage guide.

The full random-effects model (FREM) is an innovative and relatively novel covariate modeling technique. It differs from other covariate modeling approaches in that it treats covariates as observations and captures their impact on model parameters using their covariances. These unique characteristics mean that FREM is insensitive to correlations between covariates and implicitly handles missing covariate data. In practice, this implies that covariates are less likely to be excluded from the modeling scope in light of the observed data. FREM has been shown to be a useful modeling method for small datasets, but its pre-specification properties make it a very compelling modeling choice for late-stage phases of drug development. The present tutorial aims to explain what FREM models are and how they can be used in practice.

Warfarin dose prediction in children using pharmacometric bridging--comparison with published pharmacogenetic dosing algorithms.

PURPOSE: Numerous studies have investigated causes of warfarin dose variability in adults, whereas studies in children are limited both in numbers and size. Mechanism-based population modelling provides an opportunity to condense and propagate prior knowledge from one population to another. The main objectives with this study were to evaluate the predictive performance of a theoretically bridged adult warfarin model in children, and to compare accuracy in dose prediction relative to published warfarin algorithms for children. METHOD: An adult population pharmacokinetic/pharmacodynamic (PK/PD) model for warfarin, with CYP2C9 and VKORC1 genotype, age and target international normalized ratio (INR) as dose predictors, was bridged to children using allometric scaling methods. Its predictive properties were evaluated in an external data set of children 0-18 years old, including comparison of dose prediction accuracy with three pharmacogenetics-based algorithms for children. RESULTS: Overall, the bridged model predicted INR response well in 64 warfarin-treated Swedish children (median age 4.3 years), but with a tendency to overpredict INR in children ≤2 years old. The bridged model predicted 20 of 49 children (41 %) within ± 20 % of actual maintenance dose (median age 7.2 years). In comparison, the published dosing algorithms predicted 33-41 % of the children within ±20 % of actual dose. Dose optimization with the bridged model based on up to three individual INR observations increased the proportion within ±20 % of actual dose to 70 %. CONCLUSION: A mechanism-based population model developed on adult data provides a promising first step towards more individualized warfarin therapy in children.

Cortical folding in Broca's area relates to obstetric complications in schizophrenia patients and healthy controls.

BACKGROUND: The increased occurrence of obstetric complications (OCs) in patients with schizophrenia suggests that alterations in neurodevelopment may be of importance to the aetiology of the illness. Abnormal cortical folding may reflect subtle deviation from normal neurodevelopment during the foetal or neonatal period. In the present study, we hypothesized that OCs would be related to cortical folding abnormalities in schizophrenia patients corresponding to areas where patients with schizophrenia display altered cortical folding when compared with healthy controls. METHOD: In total, 54 schizophrenia patients and 54 healthy control subjects underwent clinical examination and magnetic resonance image scanning on a 1.5 T scanner. Information on OCs was collected from original birth records. An automated algorithm was used to calculate a three-dimensional local gyrification index (lGI) at numerous points across the cortical mantle. RESULTS: In both schizophrenia patients and healthy controls, an increasing number of OCs was significantly related to lower lGI in the left pars triangularis (p<0.0005) in Broca's area. For five other anatomical cortical parcellations in the left hemisphere, a similar trend was demonstrated. No significant relationships between OCs and lGI were found in the right hemisphere and there were no significant case-control differences in lGI. CONCLUSIONS: The reduced cortical folding in the left pars triangularis, associated with OCs in both patients and control subjects suggests that the cortical effect of OCs is caused by factors shared by schizophrenia patients and healthy controls rather than factors related to schizophrenia alone.

Degradation and leaching of fluroxypyr after application to railway tracks.

Fluroxypyr is an auxin-type herbicide used for postemergent control of broad-leaved weeds in agriculture and in nonagricultural environments such as railways. The overall aim of this study was to assess the potential environmental impact from fluroxypyr application to railway tracks and to elucidate some of the factors that control its environmental fate. In laboratory studies, we examined the degradation of fluroxypyr and the formation of its metabolites fluroxypyr-methoxypyridine (F-MP) and fluroxypyr-pyridinol (F-P) in soil from two Swedish railways. We also investigated the degradation and leaching of fluroxypyr in three different railway plots treated with fluroxypyr (360 g ae ha). The half-life of fluroxypyr in soil samples ranged between 28 and 78 d. An estimated mean 48.6 ± 20% of the fluroxypyr was converted into F-P and 8.0 ± 2% into F-MP. The main metabolite, F-P, was rapidly degraded, with an average half-life of 10 ± 5 d. However, F-MP was not degraded to a significant degree in any sample, resulting in slowly increasing concentrations throughout the experiment. This pattern of relatively rapid degradation of F-P and slow accumulation of F-MP was also observed in the field. The persistent nature of F-MP may be of concern if fluroxypyr is used repeatedly at the same location. Fluroxypyr was detected in the groundwater beneath the track at all three locations studied in concentrations exceeding the EU limit of 0.1 µg L for pesticides in drinking water, and F-P was detected in the groundwater at two of three locations. The most important factor controlling fluroxypyr degradation rate in soil was the soil water content, which modulated microbial activity and presumably also fluroxypyr availability to microorganisms. Our findings imply that fluroxypyr may not be a suitable herbicide for weed control on railway tracks.

A quantitative approach to the choice of number of samples for percentile estimation in bootstrap and visual predictive check analyses.

Understanding the uncertainty in parameter estimates or in derived secondary variables is important in all data analysis activities. In pharmacometrics, this is often done based on the standard errors from the variance-covariance matrix of the estimates. Confidence intervals derived in this way are by definition symmetrical, which may lead to implausible outcomes, and will require translation to generate uncertainties in derived variables. An often-used alternative is numerical percentile estimation by, for example, nonparametric bootstraps to circumvent these issues. Visual predictive checks (VPCs), which is a commonly used model diagnostic tool in pharmacometric analyses, also rely on the estimation of percentiles through numerical approaches. Given the cost in terms of run times and processing times for these methods, it is important to consider the trade-off between the number of bootstrap samples or simulated data sets in the VPCs, to the increase in precision related to a large number of bootstrap samples or simulated data sets. The objective with this tutorial is to provide a quantitative framework for assessing the precision in estimated percentile limits in bootstrap and visual predictive checks analyses to facilitate an informed choice of confidence interval width, number of bootstrap samples/simulated data sets, and required level of precision.