Henrik Spliid

Multivariate statistical analysis of organ weights in toxicity studies.

Toxicity studies with drugs in animals are performed to establish the toxicity profile including the no-toxic-effect-level in the animals. One of the responses used in the search for effects is organ weight. Since organ weight is related to body weight of the animal, the analysis of organ weight has to be adjusted. A traditional analysis of covariance with body weight as covariate is not always appropriate since the body weight itself can be affected by the test compound. Hence, a multivariate analysis of variance is suggested, where the correlation between organ weight and body weight is taken into account in testing an overall treatment effect. Two dimensional plots of the contour curves are used to visualize the treatment effect on organ weight and body weight simultaneously. The test procedure suggested for comparing differences between control and treated groups of animals is: start by testing hypotheses of equality of covariance matrices for the different treatment groups and then, depending on the results from the first test, test equality of the mean vectors.

Induction of micronuclei in hemocytes of Mytilus edulis and statistical analysis

A genotoxicity test focusing on micronucleus production in the blood cells (hemocytes) of blue mussel M. edulis has been developed as a possible indicator for marine pollution. A linear dose-response relationship was found when M. edulis was exposed to low concentrations (0, 12.5, and 25 mg/liter) of the alkylating agent ethyl methanesulfonate under laboratory conditions, while higher concentrations (50 and 100 mg/liter) resulted in cytotoxic effects. Furthermore the micronuclei (MN) frequencies in wild mussels from four different field locations have been determined. Mussels collected from two polluted sites showed an elevated MN frequency, indicating the presence of genotoxic pollution. A method to determine the micronuclei background level is suggested and the further implications for applying the method in biomonitoring investigations are discussed. The considered M. edulis exhibits a high biological variation, emphasizing the importance of application of a correct statistical method. A systematic approach to the statistical evaluation of the mussel MN test is outlined. The statistical model includes three different situations: (a) estimation of parameters of a single sample, (b) estimation and comparison of two samples, and (c) estimation of a dose-response relationship. Cases (a) and (b) are especially relevant in biomonitoring investigations while case (c) primarily concerns laboratory experiments.

Selective flow injection analysis of ultra-trace amounts of Cr(VI), preconcentration of it by solvent extraction, and determination by electrothermal atomic absorption spectrometry (ETAAS)

A rapid, robust, sensitive and selective time-based flow injection (FI) on-line solvent extraction system interfaced with electrothermal atomic absorption spectrometry (ETAAS) is described for analyzing ultra-trace amounts of Cr(VI). The sample is initially mixed on-line with isobutyl methyl ketone (IBMK). The Cr(VI) is complexed by reaction with ammonium pyrrolidine dithiocarbamate (APDC), and the non-charged Cr(VI)-PDC chelate formed is extracted into IBMK in a knotted reactor made from PTFE tubing. The organic extractant is separated from the aqueous phase by a gravity phase separator with a small conical cavity and delivered into a collector tube, from which 55 mul organic concentrate is subsequently introduced via an air flow into the graphite tube of the ETAAS instrument. The operations of the FI-system and the ETAAS detector are synchronously coupled. A significant advantage of the approach is that matrix constituents, such as high salt contents, effectively are eliminated. The extraction procedure was optimized by a simplex approach. A central composite design was subsequently employed to verify the estimated operational optimum. An 18-fold enhancement in sensitivity of Cr(VI) was achieved after preconcentration for 99 s at a sample flow rate of 5.5 ml min(-1), as compared to direct introduction of 55 mul of sample, yielding a detection limit (3sigma) of 3.3 ng l(-1). The sampling frequency was 24.2 samples h(-1). The proposed method was successfully evaluated by analyzing a NIST Cr(VI)-reference material, synthetic seawater and waste waters, and waste water samples from an incineration plant and a desulphurization plant, respectively.

Method for fractional solid-waste sampling and chemical analysis

Chemical characterization of solid waste is a demanding task due to the heterogeneity of the waste. This article describes how 45 material fractions hand-sorted from Danish household waste were subsampled and prepared for chemical analysis of 61 substances. All material fractions were subject to repeated particle-size reduction, mixing, and mass reduction until a sufficiently small but representative sample was obtained for digestion prior to chemical analysis. The waste-fraction samples were digested according to their properties for maximum recognition of all the studied substances. By combining four subsampling methods and five digestion methods, paying attention to the heterogeneity and the material characteristics of the waste fractions, it was possible to determine 61 substances with low detection limits, reasonable variance, and high accuracy. For most of the substances of environmental concern, the waste-sample concentrations were above the detection limit (e.g. Cd > 0.001 mg kg−1, Cr > 0.01 mg kg−1, Hg > 0.002 mg kg−1, Pb > 0.005 mg kg−1). The variance was in the range of 5–100%, depending on material fraction and substance as documented by repeated sampling of two highly different material fractions (‘Vegetable food’ and ‘Shoes, leather, etc.’). Statistical analysis showed for the ‘Vegetable food’ that the variance could not be attributed to a single step in the procedure, whereas in the case of ‘Shoes, leather, etc.’, the first coarse shredding was the main source of variance (20–85% of the overall variation). Only by increasing the sample size significantly can this variance be reduced. The accuracy and short-term reproducibility of the chemical characterization were good, as determined by the analysis of several relevant certified reference materials. Typically, six to eight different certified reference materials representing a range of concentrations levels and matrix characteristics were included. Based on the documentation provided, the methods introduced were considered satisfactory for characterization of the chemical composition of waste-material fractions.

Continuous Ecotoxicological Data Evaluated Relative to a Control Response

This article describes a generalized nonlinear regression method that models continuous ecotoxicological response data evaluated relative to a control response. The major improvement and difference from the methods described in the literature is consideration of the covariance between data, which is induced when modeling responses relative to a control response. The capability to estimate ECps (the concentration that corresponds to p % effect), such as ECIo and EC50, and their confidence limits is evaluated through a simulation study. The method is illustrated with real data from growth inhibition tests with freshwater microalgae. Recommendations are given on the choice of regression function, on how to handle initial stimulation and on test designs.

Optimal Drinking Water Composition for Caries Control in Populations

Apart from the well-documented effect of fluoride in drinking water on dental caries, little is known about other chemical effects. Since other ions in drinking water may also theoretically influence caries, as well as binding of fluoride in the oral environment, we hypothesized that the effect of drinking water on caries may not be limited to fluoride only. Among 22 standard chemical variables, including 15 ions and trace elements as well as gases, organic compounds, and physical measures, iterative search and testing identified that calcium and fluoride together explained 45% of the variations in the numbers of decayed, filled, and missing tooth surfaces (DMF-S) among 52,057 15-year-old schoolchildren in 249 Danish municipalities. Both ions had reducing effects on DMF-S independently of each other, and could be used in combination for the design of optimal drinking water for caries control in populations.

An exponentially weighted moving average control chart for Bernoulli data

We consider a production process in which units are produced in a sequential manner. The units can, for example, be man- ufactured items or services, provided to clients.Each unit produced can be a failure with probability p or a success (non-failure) with probability (1−p). A novel exponentially weighted moving average (EWMA) control chart intended for surveillance of the probability of failure, p, is described. The chart is based on counting the number of non-failures produced between failures in combina- tion with a variance-stabilizing transformation. The distribution function of the transformation is given and its limit for small values of p is derived. Control of high yield processes is discussed and the chart is shown to perform very well in comparison with both the most common alternative EWMA chart and the CUSUM chart. The construction and the use of the proposed EWMA chart are described and a practical example is given. It is demonstrated how the method communicates the current failure probability in a direct and interpretable way, which makes it well suited for surveillance of a great variety of activities in industry or in the service sector such as in hospitals, for example. Copyright

Markov Models in Discrete and Continuous Time for Hourly Observations of Cloud Cover

Abstract An analysis of 15 years of hourly observations of cloud cover at an airport location near Copenhagen, Denmark shows that the main part of the variations can be described by first-order homogeneous Markov models. Models in both discrete and continuous time are considered. Special emphasis is laid upon the representation of the variation by a Markov model in continuous time. The physical restrictions for transitions of cloud cover are investigated and it is shown that the natural restrictions imply a very simple structure for the matrix of transition rates corresponding to the embedded Markov process in continuous time. The maximum likelihood estimate of the matrix of transition rates is found by numerical methods and an indication of the estimation error under the model is given.

Estimation in Stochastic Differential Equations with a State Dependent Diffusion Term

Abstract The most widely used methods for estimating parameters in stochastic differential equations, where the discrete time observations are corrupted with white noise, are based on (extended) Kalman filtering techniques for calculating the one-step prediction errors. Such methods cannot be used directly for estimation of parameters in stochastic differential equations (SDE) with a state dependent diffusion term. This paper describes a general transformation for some univariate SDEs that eliminates the state dependent diffusion term using the Ito formula. By employing this transformation the methods based on the Kalman filter techniques may still be used. Using simulation it is demonstrated that the approach leads to practically the same results as if a second order filter was used on the original SDE. As a case study a SDE describing the short term interest rate is studied.

Modelling the growth of methane-oxidizing bacteria in a fixed biofilm

Abstract Methane-oxidizing bacteria were grown in a fixed biofilm reactor in order to study their ability to degrade chlorinated aliphatic hydrocarbons. Focus is on the growth behaviour of the mixed culture. The growth is described by a model that includes methanotrophic bacteria in the active biomass fraction. The inactive biomass fraction consists of exocellular polymers and biodegradable and inert particulate biomass. The model describes the oxygen respiration in detail. Yield coefficients, decay constants and hydrolysis constants are estimated based on the oxygen respiration. An analysis of the observability of the system reveals that several of the coefficients cannot be determined explicitly due to the complexity of the model and the limited amount of variables measured. Estimation procedures based on least squares methods are employed and parameter estimates and confidence intervals are computed. The study forms the basis for setting up a future measuring programme. This work indicates a yield coefficient for methanotrophs of 0.36 mg biomass COD per mg CH 4 . In weight units this corresponds to approx. 1.44 mg biomass per mg CH 4 . This is close to the theoretical maximum growth yield for methanotrophs.