Risk Assessment for Toxicity Experiments with Discrete and Continuous Outcomes: A Bayesian Nonparametric Approach

We present a Bayesian nonparametric modeling approach to inference and risk assessment for developmental toxicity studies. The primary objective of these studies is to determine the relationship between the level of exposure to a toxic chemical and the probability of a physiological or biochemical response. We consider a general data setting involving clustered categorical responses on the number of prenatal deaths, the number of live pups, and the number of live malformed pups from each laboratory animal, as well as continuous outcomes (e.g., body weight) on each of the live pups. We utilize mixture modeling to provide flexibility in the functional form of both the multivariate response distribution and the various dose–response curves of interest. The nonparametric model is built from a structured mixture kernel and a dose-dependent Dirichlet process prior for the mixing distribution. The modeling framework enables general inference for the implied dose–response relationships and for dose-dependent correlations between the different endpoints, features which provide practical advances relative to traditional parametric models for developmental toxicology. We use data from a toxicity experiment that investigated the toxic effects of an organic solvent (diethylene glycol dimethyl ether) to demonstrate the range of inferences obtained from the nonparametric mixture model, including comparison with a parametric hierarchical model.Supplementary materials accompanying this paper appear on-line.     

Bayesian Hierarchical Analysis for Multiple Health Endpoints in a Toxicity Study

Bayesian hierarchical models are built to fit multiple health endpoints from a dose-response study of a chemical contaminant, perchlorate. Perchlorate exposure results in iodine uptake inhibition in the thyroid, with health effects manifested by changes in blood hormone concentrations and histopathological effects on the thyroid. We propose empirical models to fit blood hormone concentration and thyroid histopathology data for rats exposed to perchlorate in the 90-day study of Springborn Laboratories Inc. (1998), based upon a mechanistic model derived from the assumed toxicological relationships between dose and the various endpoints. All of the models are fit in a Bayesian framework, and predictions about each endpoint in response to dose are simulated based on the posterior predictive distribution. A hierarchical model tries to exploit possible similarities between different combinations of sex and exposure duration, and it allows us to produce more stable estimates of dose-response curves. We also illustrate how the Bayesian model specification allows us to address additional questions that arise after the analysis.     

An Approximate Method for Population Toxicokinetic Analysis With Aggregated Data

Standard statistical models for analyzing inter-individual variability in clinical pharmacokinetics (nonlinear mixed effects; hierarchical Bayesian) require individual data. However, for environmental or occupational toxicants only aggregated data are usually available, so toxicokinetic analyses typically ignore population variability. We propose a hierarchical Bayesian approach to estimate inter-individual variability from the observed mean and variance at each time point, using a bivariate normal (or lognormal) approximation to their joint likelihood. Through analysis of both simulated data and real toxicokinetic data from 1,3-butadiene exposures, we conclude that given information on the form of the individual-level model, useful information on inter-individual variability may be obtainable from aggregated data, but that additional sensitivity and identifiability checks are recommended.     

The methylmercury to total mercury ratio in selected marine,freshwater, and terrestrial organisms

Total and methylmercury concentrations were determined in muscle and organ tissue from a wide variety of marine and terrestrial organisms spanning several trophic levels. Sediment and water samples from many of the tissue sampling sites were also analyzed to assess the degree of mercury contamination to which the animals were exposed. The methylmercury to total mercury ratios were examined to determine whether this ratio is indicative of elevated exposure to organic or inorganic mercury and how it varies relative to tissue type and position in the food chain. As an ancillary study, a subset of these tissues was analyzed as 1) wet tissue, and 2) freeze-dried, ball-milled tissue to determine whether the form of sample preparation can adversely affect mercury analysis. Results indicate that the methylmercury to total mercury ratios generally approach unity only in muscle tissue of higher food chain carnivorous fish residing in waters that are relatively uncontaminated with respect to inorganic mercury species. Herbivorous terrestrial mammals and low food chain marine organisms tend to have very low methylmercury to total mercury ratios. Marine animals placed higher on the food chain, such as crabs and lobsters, exhibit somewhat higher methylmercury to total mercury ratios and can exhibit a large variation in this ratio between, organ tissue and muscle tissue of the same animal. The samples analyzed as both wet and freeze-dried, ball-milled tissue indicate that freezedrying and ball-milling in no way result in mercury loss or contamination and, in fact, result in better replicate analyses and create a sample sufficiently stable to be archived for several years without refrigeration.     

Estimating Potency for Hierarchical Dichotomous Responses in an Aquatic Toxicology Study

Toxicants in aquatic organisms may impact a variety of responses including hatching, survival, growth, deformity, and reproduction. These responses have a hierarchical relationship since survival is only possible for hatched organisms and deformity is only possible if organisms survive. Linear models and generalized linear models have been widely used to analyze individual responses; however, an analysis that simultaneously considers the structure of all responses would allow a more comprehensive assessment of toxicity. Ignoring the hierarchy of these responses and applying separate modeling approaches could be misleading. Motivated by a study of hatching–survival–deformities in fish, we developed a method to model these responses simultaneously. In the present study, we propose a Bayesian multinomial regression model to analyze the hierarchical toxicity responses simultaneously and estimate the concentrations associated with a specified level of reproductive inhibition (RI _p ) on hatching success, post hatching survival and deformity, respectively. Simulation studies are conducted to compare the estimates from the hierarchical model with those from the response-specific separate models. The proposed model outperforms the separate model by producing more precise point estimates and interval estimates with better coverage probabilities. The proposed method is illustrated with data from a study of hatching–survival–deformities in fish. The proposed model captures the hierarchy in the multiple responses from animals in the toxicity test and hence improves the understanding of concentration–response relationships for these responses. It provides a useful template of modeling hierarchical dichotomous responses in the aquatic toxicity studies.     

Spatial Hierarchical Modeling of Precipitation Extremes From a Regional Climate Model

The goal of this work is to characterize the extreme precipitation simulated by a regional climate model (RCM) over its spatial domain. For this purpose, we develop a Bayesian hierarchical model. Since extreme value analyses typically only use data considered to be extreme, the hierarchical approach is particularly useful as it sensibly pools the limited data from neighboring locations. We simultaneously model the data from both a control and future run of the RCM which allows for easy inference about projected change. Additionally, this hierarchical model is the first to spatially model the shape parameter which characterizes the nature of the distribution’s tail. Our hierarchical model shows that for the winter season, the RCM indicates a general increase in 100-year precipitation return levels for most of the study region. For the summer season, the RCM surprisingly indicates a significant decrease in the 100-year precipitation return level.     

Quantitative exposure assessment for the combustion of meat and bone meal derived from specified risk material in the context of BSE in Ireland

The probability and severity of an adverse event can be analyzed by quantitative exposure assessment (QEA). This methodology was applied to model the human health risks associated with the combustion of specified risk material (SRM) derived meat and bone meal (MBM) in a combustion facility. The identification of MBM and SRM as significant factors in the spread of bovine spongiform encephalopathy (BSE) has resulted in restrictions on their use and movement, and this has led to a requirement for alternative end-uses for these products. A stochastic (Latin Hypercube sampling) simulation model was developed to assess the exposure and hence the risks associated with the use of SRM-derived MBM in a combustion facility. The model simulates the potential infectivity pathways that SRM-derived MBM follows, including its production from animals potentially infected with sub-clinical BSE and subsequent processing of the material with segregation and heat treatments. A failure probability was included to take account of sub-optimal operating conditions. Two scenarios, reflecting the infectivity risk in different animal tissues as defined by the European Commission's scientific steering committee (SSC), were performed with 100,000 iterations of the model. Model results showed that the societal exposure to humans resulting from the combustion of SRM-derived MBM is extremely small (mean values ranging from 7.57 x 10(-6) ID50/year to 8.38 x 10(-5) ID50/year). The resulting societal risks are significantly less than the background societal risk of approximately 2.5 cases of sporadic CJD in Ireland each year. A sensitivity analysis revealed that the species barrier had a large impact on exposure calculations and hence should be the focus of further scientific investigation to reduce our uncertainty about this parameter. The model predicts that material spillage into untreated effluent represents the biggest risk to humans, indicating that efforts for risk mitigation should be focused on reducing the potential for spillage.     

Contaminant Transport Through Initially Dry Soil

We combined dose-response analyses with a probabilistic exposure assessment to estimate the risks to native Canadians who ingest methylmercury via fish consumption from natural lakes and a reservoir in British Columbia. Available dose-response data included multivariate measurements of central nervous system functioning in Iraqi children exposed to methylmercury prenatally. We applied the method of principal components to simplify the data structure. The first principal component described close to 80% of the variability in the data, making it a reasonable choice as an index. The relationship between mercury in maternal hair and the probability of an abnormal neurological effects index was modeled with the logistic and Weibull functions. The goodness-of-fit of the two models is discussed and the results compared to other published dose-response analyses. Exposure distributions were developed to represent methylmercury dose by using observed data on methylmercury contamination in the lakes and reservoir and reasonable assumptions about other key parameters such as fish consumption. We estimated risks to the target population using Monte Carlo simulation. Consumption of reasonable quantities of fish from these bodies of water does not pose a significant risk to the aboriginal population.     

A hierarchical model for compositional data analysis

This article introduces a hierarchical model for compositional analysis. Our approach models both source and mixture data simultaneously, and accounts for several different types of variation: these include measurement error on both the mixture and source data; variability in the sample from the source distributions; and variability in the mixing proportions themselves, generally of main interest. The method is an improvement on some existing methods in that estimates of mixing proportions (including their interval estimates) are sure to lie in the range [0, 1]; in addition, it is shown that our model can help in situations where identification of appropriate source data is difficult, especially when we extend our model to include a covariate. We first study the likelihood surface of a base model for a simple example, and then include prior distributions to create a Bayesian model that allows analysis of more complex situations via Markov chain Monte Carlo sampling from the likelihood. Application of the model is illustrated with two examples using real data: one concerning chemical markers in plants, and another on water chemistry.     

Exposure Patterns and Long Term Sequelae on Adults and Children in Two Canadian Indigenous Communities Exposed to Methylmercury

Health Canada has been collecting data on Inuit and First Nations' methylmercury (MeHg) levels for 25 years. A national overview has been completed and more focussed analyses have now been initiated. This paper deals with two interdependent analytical components: 1) a longitudinal overview of the two most extensively sampled communities in Canada: Grassy Narrows and Whitedog, the residents of which were exposed to ‘point source’ mercury pollution in the 1970's; 2) fetal and post-natal exposure to mercury in these two communities including an outline of the First Nation MeHg child development pilot project in the two communities. A retrospective analysis of Grassy Narrows and Whitedog shows a decreasing MeHg trend in both communities. In Grassy Narrows the average individual annual peak methylmercury level in blood has decreased significantly, from 23.80 ppb (range 1.50–322.90) in 1976 to 7.5 ppb (1.7–46.7) in 1995 (r=-0.65, p<0.001). In Whitedog the average peak has also decreased significantly, from 12.87 ppb (1.50–172.00) in 1976 to 6.1 ppb (1.7–33.3) in 1995 (r=-0.59, p<0.005). However, behind these positive trends is the reality of two communities still suffering the effects of disrupted lifestyles and socio-cultural damage. A number of cord blood samples, maternal blood samples, and samples from women of child-bearing age from these communities have been in the “risk” group (according to the 1990 WHO guidelines). We are therefore now assessing the long term effects of fetal exposure in the communities. Standard clinical examinations in the past failed to prove abnormalities attributable to methylmercury but did not include subtle neuropsychological development tests. Many of the fetally exposed children are now in secondary school. Therefore, we have initiated a pilot project to assess long term effects of methylmercury exposure on the neuropsychological development of these children whose fetal exposure we know. The pilot child development project which was initiated in 1995 in Grassy Narrows and Whitedog, with community support, includes four main components: i) a school records review, looking at attendance, marks, and atypical behaviour; ii) teachers' questionnaires, targeting child behaviour; iii) an in-depth neuropsychological test battery focussing on subtle factors, such as memory, attention, executive functions, perceptual functions and sensory / motor development; and iv) hair sampling, providing current MeHg levels to correlate with results from the previous sampling and findings from the first three components. An overview of progress is given.     

Bayesian multivariate process modeling for prediction of forest attributes

This article investigates multivariate spatial process models suitable for predicting multiple forest attributes using a multisource forest inventory approach. Such data settings involve several spatially dependent response variables arising in each location. Not only does each variable vary across space, they are likely to be correlated among themselves. Traditional approaches have attempted to model such data using simplifying assumptions, such as a common rate of decay in the spatial correlation or simplified cross-covariance structures among the response variables. Our current focus is to produce spatially explicit, tree species specific, prediction of forest biomass per hectare over a region of interest. Modeling such associations presents challenges in terms of validity of probability distributions as well as issues concerning identifiability and estimability of parameters. Our template encompasses several models with different correlation structures. These models represent different hypotheses whose tenability are assessed using formal model comparisons. We adopt a Bayesian hierarchical approach offering a sampling-based inferential framework using efficient Markov chain Monte Carlo methods for estimating model parameters.     

Bayesian Methods for Hierarchical Distance Sampling Models

The few distance sampling studies that use Bayesian methods typically consider only line transect sampling with a half-normal detection function. We present a Bayesian approach to analyse distance sampling data applicable to line and point transects, exact and interval distance data and any detection function possibly including covariates affecting detection probabilities. We use an integrated likelihood which combines the detection and density models. For the latter, densities are related to covariates in a log-linear mixed effect Poisson model which accommodates correlated counts. We use a Metropolis-Hastings algorithm for updating parameters and a reversible jump algorithm to include model selection for both the detection function and density models. The approach is applied to a large-scale experimental design study of northern bobwhite coveys where the interest was to assess the effect of establishing herbaceous buffers around agricultural fields in several states in the US on bird densities. Results were compared with those from an existing maximum likelihood approach that analyses the detection and density models in two stages. Both methods revealed an increase of covey densities on buffered fields. Our approach gave estimates with higher precision even though it does not condition on a known detection function for the density model.     

Predicting the rate of range expansion of an invasive alien bumblebee (Bombus terrestris) using a stochastic spatio-temporal model

To develop effective strategies for managing biological invasions, it is important to understand and be able to predict patterns of invasion and range expansion, and particularly the rate of spread and factors controlling this rate. To predict the spatial dynamics of invasion by an alien bumblebee (Bombus terrestris) in Hokkaido, Japan, we explicitly constructed a stochastic spatio-temporal model that incorporates immigration and establishment processes. Using a Bayesian approach, we parameterized the model based on spatio-temporal presence/absence data collected by citizen volunteers and used the model to predict control of the near-future spread of the bumblebee under several management strategies. The range expansion dynamics of B. terrestris were significantly negatively affected by two aspects of environmental heterogeneity: the land-use pattern (the proportion of woodland) and climate (the snow depth). Of the several spatial management strategies, suppressing the outlying (edge) colonies would be the most efficient strategy to reduce the bumblebee’s spread, irrespective of the level of effort, and would significantly slow the bumblebee’s range expansion during the next 30 years. The modeling approach employed in the present study will be broadly useful for studying real-world biological invasion problems, for which prediction of the progress of an invasion, even in the very near future, is urgently needed to support effective spatial management options and countermeasures. In addition, the model demonstrates that incorporating the dynamics of environmental heterogeneity is a fundamental requirement for prediction and risk assessment during biological invasions, especially in the context of recent rapid changes in the environment at regional and global scales.     

Hierarchical models of animal abundance and occurrence

Much of animal ecology is devoted to studies of abundance and occurrence of species, based on surveys of spatially referenced sample units. These surveys frequently yield sparse counts that are contaminated by imperfect detection, making direct inference about abundance or occurrence based on observational data infeasible. This article describes a flexible hierarchical modeling framework for estimation and inference about animal abundance and occurrence from survey data that are subject to imperfect detection. Within this framework, we specify models of abundance and detectability of animals at the level of the local populations defined by the sample units. Information at the level of the local population is aggregated by specifying models that describe variation in abundance and detection among sites. We describe likelihood-based and Bayesian methods for estimation and inference under the resulting hierarchical model. We provide two examples of the application of hierarchical models to animal survey data, the first based on removal counts of stream fish and the second based on avian quadrat counts. For both examples, we provide a Bayesian analysis of the models using the software WinBUGS.     

A Review of Probabilistic Risk Assessment of Contaminated Land (12 pp)

Background, Aims and Scope   The management and decisions concerning restoration of contaminated land often require in-depth risk analyses. An environmental risk assessment is generally described as proceeding in four separate steps: hazard identification, dose-response assessment, exposure assessment, and risk characterization. The risk assessment should acknowledge and quantify the uncertainty in risk predictions. This can be achieved by applying probabilistic methods which, although they have been available for many years, are still not generally used. Risk assessment of contaminated land is an area where probabilistic methods have proved particularly useful. Many reports have appeared in the literature, mostly by North American researchers. The aim of this review is to summarize the experience gained so far, provide a number of useful examples, and suggest what may be done to promote probabilistic methods in Europe and the rest of the world. Methods   The available literature has been explored through searches in the major scientific and technical databases, WWW resources, textbooks and direct contacts with active researchers. A calculation example was created using standard simulation software. Results and Discussion   Uncertainty and variability are part of every risk assessment. Much work on risks from contaminated soil has focussed on exposure, and choice and structure of the exposure model is then a basic uncertainty factor. Other factors, e.g. parameter uncertainty, are easier to characterize. Variability can be separated into inter-individual, spatial and temporal components. Both uncertainty and variability in the exposure variables can be investigated using Monte Carlo simulation methods. These simulations enable not only the estimation of the probability for a given risk or exposure, but also add information on the sensitivity of the various input variables. This will assist the assessor in further refining the risk analysis. The large number of applications published encompasses soil contamination by lead, arsenic, chromium, uranium, polychlorinated biphenyls (PCB), polycyclic aromatic hydrocarbons (PAH), hexachlorobenzene, pentachlorophenol and chlorinated solvents. Probabilistic risk assessments have been used in widely different settings, such as the metallurgical industry (mining and smelting operations), manufacturing, gas plants, wood impregnation, infrastructure, and waste landfills. Site-specific remediation goals can be specified using probabilistic methods, and a guideline document has been issued within the US Superfund programme. The usability of probabilistic risk assessment is illustrated by a calculation example. The current Swedish generic guideline value for benzo[a]pyrene in contaminated soil, with ingestion of vegetables as the major route of exposure, is compared with a probabilistic estimate. The toxicological reference value corresponds well with the upper 95th percentile of the estimated variability in intake, but does not account for uncertainty in the partition coefficients. Conclusions and Outlook   The probabilistic approach to risk assessment has proved its value in characterizing variability and uncertainty, and thereby contributing to a more informed and transparent decision-making process. The management of contaminated land is a major environmental application for probabilistic risk assessments. A substantial number of studies have been published and the method is now well established in the scientific community. This development has progressed further in the United States than elsewhere, but similar applications are now being reported from Europe and Asia. Probabilistic risk assessment is used to derive soil guideline values in the United Kingdom, and other countries may be anticipated to follow. However, efficient use of probabilistic methods for risk assessment of contaminated land requires certain components. There is a requirement for quality assurance and transparency that can be met by guidelines specifying data requirements and which items to report on. Both federal and state governments in the United States have issued such guidelines, and we see a similar need from a European perspective. A second component, necessary for a successful implementation of probabilistic methods, is education. We have ourselves developed undergraduate curricula, but we also see a need for continuous education of risk assessors and decision makers. The third component required is case studies, showing how probabilistic risk assessment can be implemented successfully in the cleanup of contaminated land. Most published studies originate from the United States, so here too there is a need for the rest of the world to catch up. In addition to the three components mentioned, there is an obvious need to develop and improve methods and practice of risk communication.     

象山港海水养殖区贝叶斯网络水质评价及预测

水质评价是水环境保护与管理的重要环节,传统的评价方法在处理评价中的不确定性、大量信息处理等方面存在局限性。贝叶斯网络可以有效地表达和分析不确定性问题,实现定性分析与定量分析的有机结合。以近10a来象山港海水养殖区的水质监测数据为样本数据,采用贝叶斯网络技术,建立反映各水质指标及水质级别之间相互关系和相互影响强度的贝叶斯网络模型。模型结构表明直接影响水质级别的水质指标为氨氮、化学需氧量、硝酸盐、无机磷和叶绿素a,而其他亚硝酸盐、无机氮等4个水质指标与水质级别存在间接的因果关系。对200条监测数据进行模型精度检验,结果表明,其预测精度达94.8%,Kappa指数为0.892,这说明采用贝叶斯网络技术对水质进行评价及预测是可行的。     

Exposure of Canadian aboriginal peoples to methylmercury

Aboriginal peoples living a traditional lifestyle are potentially exposed to contaminants, such as methylmercury (MeHg), which bioaccumulate in aquatic ecosystems. A preliminary analysis of testing of Canadian indigenous people for MeHg from 1970 to 1992 is outlined. By December 1992,71,842 tests of 38,571 individuals had been carried out in 514 native communities across Canada. Of these, 8,847 individuals (23%) had blood, or blood equivalent, MeHg levels greater than 20 μg/l and 608 (1.6%) had levels over 100 μg/l. Clinical examinations were offered to all with levels greater than 100 μg/l in blood, but were unable to produce a definitive diagnosis. In an attempt to ascertain fetal exposure, 2,405 umbilical cord blood samples were taken. In about half of these cases the samples were paired with maternal levels. Of the cord samples 523 (21.8%) were found to have levels greater than 20 μg/l, and the highest level was 224 μg/l. The highest maternal level found was 86 μg/l. A discussion of the assessment of risk from exposure to MeHg in this population is presented as are the initial results of the 20 year retrospective analysis including seasonal exposure patterns and trends in exposure levels. Probable future intiatives based on this analysis are noted.     

Methylmercury accumulation in rice (Oryza sativa L.) grown at abandoned mercury mines in Guizhou, China

Mercury is a global pollutant that can transform into methylmercury, a highly toxic and bioaccumulative organic form. Previous surveys have shown that fish is the main source of human methylmercury exposure, whereas most other food products have an average value below 20 microg/kg and primarily in the inorganic form. This paper reports that methylmercury in rice (Oryza sativa L.) grown at abandoned mercury mining areas contained levels >100 microg/kg in its edible portion and proved to be 10-100 times higher than other crop plants. The daily adult intake of methylmercury through rice consumption causes abnormally high methylmercury exposure to humans. The results demonstrate that rice is a methylmercury bioaccumulative plant and the main methylmercury source for human exposure in the areas studied.     

A Bayesian Approach to Estimating Agricultural Yield Based on Multiple Repeated Surveys

Forecasting the end-of-year crop yield is critical for agricultural decision-making and inherently difficult. Historically, a panel of commodity specialists known as the Agricultural Statistics Board convene regularly to set estimates based on expert review of a combination of survey data and administrative/auxiliary information. To make this process less subjective and more repeatable, we develop a Bayesian hierarchical model that produces superior yield forecasts/estimates, while quantifying different sources of uncertainty. The proposed hierarchical model naturally combines information from multiple monthly surveys measured on different temporal supports, including a field measurement survey and two farmer interview surveys. The dependence between the monthly updated surveys and the serial dependence of the annual yield are incorporated at different levels of the hierarchy. The effectiveness of our approach is demonstrated through an application from the US Department of Agriculture. Empirical results indicate that the hierarchical model produces superior forecasts to both the panel of experts and the composite estimator developed by Keller and Olkin (Technical Report, National Agricultural Statistics Service, 2002), while providing an accurate measure of uncertainty.     

Strategies for risk assessment of existing chemicals in soil

In the risk assessment of industrial chemicals, an assessment of the risk to soil should be performed whenever relevant inputs occur via the following pathways: application of sewage sludge, wet or dry deposition, application as a pesticide constituent (e.g. solvent or metabolite), irrigation. An evaluation of the results for 34 chemicals from the first EU priority list showed that only 35% of the risk assessments for the terrestrial compartment were performed on the basis of at least 2 valid tests with soil organisms. In the vast majority of cases, the equilibrium partitioning method was used to extrapolate from aquatic to soil toxicity. However, no indications exist for a correlation between aquatic and terrestrial toxicity. Moreover, the exposure routes for soil organisms (uptake via pore water, air included in soil pores, ingestion of soil particles) are much more complex than those for aquatic organisms. As a new approach, it is therefore suggested that, in cases of relevant exposure (e.g. estimated or measured concentrations of >10 μg/kg), an assessment should generally be performed on the basis of valid terrestrial tests rather than on an extrapolation from the aquatic toxicity. It is recommended that prolonged exposure tests should be used already for an initial assessment of substances that have a strong tendency to adsorb on soil particles and thus a long residence time in soil. A decision scheme for the risk assessment of industrial chemicals in soil is presented, trigger values, testing strategies as well as assessment factors for derivation of a Predicted No Effect Concentration (PNEC_soil) are discussed. An example of a terrestrial risk assessment for substances from the first EU priority list is given in order to illustrate current practice.