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In this study, proportional response addition (Prop-RA), a model for predicting response from chemical mixture exposure, is demonstrated and evaluated by statistically analyzing data on all possible binary combinations of the four regulated trihalomethanes (THMs). These THMs were the subject of a multipurpose toxicology study specifically designed to evaluate Prop-RA. The experimental design used a set of doses common to all components and mixtures, providing hepatotoxicity data on the four single THMs and the binary combinations. In Prop-RA, the contribution of each component to mixture toxicity is proportional to its fraction in the mixture based on its response at the total mixture dose. The primary analysis consisted of 160 evaluations. Statistically significant departures from the Prop-RA prediction were found for seven evaluations, with three predications that were greater than and four that were less than the predicted response; interaction magnitudes (n-fold difference in response vs. prediction) ranged from 1.3 to 1.4 for the former and 2.6 to 3.8 for the latter. These predictions support the idea that Prop-RA works best with chemicals where the effective dose ranges overlap. Prop-RA does not assume the similarity of toxic action or independence, but it can be applied to a mixture of components that affect the same organ/system, with perhaps unknown toxic modes of action.

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PURPOSE: The Scheffé's method obtains the difference between pair comparisons with that of the interval scale and can judge the superiority or inferiority of the sample to be compared with no restriction in the observation image by the statistical significant difference. However, the Scheffé's method cannot be judged as a single image quality indicator. Therefore, I examined a method that can evaluate the association of average degree of preference of Scheffé's method and the physical quantities that make up the image. METHODS: This study focuses on the fact that the average degree of preference of the Scheffé's method is quantitative data on the interval scale and that multiple regression analysis is possible. In the multiple regression analysis, the average degree of preference by imaging simulated pulmonary adenocarcinoma with different exposure doses was used as the objective variable and the exposure doses and noise (standard deviation [SD]) were used as the explanatory variables. The Scheffé's method used the Nakaya's modified method. RESULTS: In the multiple regression analysis, SD was P=0.027. By substituting the threshold value of the intersection of the exposure doses and SD into the multiple regression equation (predictive model), the average degree of preference (Y) was calculated. Y(Scheffé;Gy,SD) was -0.147, which was about 1/2 of exposure doses (-0.150). CONCLUSION: The multiple regression analysis of Scheffé's (average degree of preference) and physical quantity factors (exposure doses and noise) has made it possible to design images that can reduce exposure doses while maintaining adequate image quality.

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Beneficial effects of silicon (Si) on growth have been observed in some plant species, reportedly due to stoichiometric changes of C, N, and P. However, little is known about the effects on the stoichiometric relationships between C, N, and P when silicon is supplied via different modes in sorghum and sunflower plants under salt stress conditions. Therefore, the current study was performed to investigate the impact of differing modes of Si supply on shoot biomass production and C:N:P stoichiometry in sorghum and sunflower plants under salt stress. Two experiments were performed in a glass greenhouse using the strong Si-accumulator plant sorghum, as well as the intermediate type Si-accumulator sunflower, both of which were grown in pots filled with washed sand. Plant species were cultivated for 30 days in the absence or presence of salt stress (0 or 100 mM) and supplemented with one of four Si treatments: control plants (without Si), 28.6 mmol Si L-1 via foliar application, 2.0 mmol Si L-1 via nutrient solution, and combined application of foliar and nutrient solution, each group with five replications. The results revealed that supplied Si modified the C, N, and P concentrations, thereby enhancing the C:N:P stoichiometry and shoot dry matter of sorghum and sunflower plants under salt stress. Both application of Si via nutrient solution, as well as combined application via foliar and nutrient solution, increased the C:N ratio in both plant species under salt stress, but in sorghum plants decreased the C:P and N:P ratios and increased the shoot biomass production by 39%, while in sunflower plants increased the C:P and N:P ratios and increased the shoot biomass production by 24%. Our findings suggest that salt stress alleviation by Si impacts C:N:P stoichiometric relationships in a variable manner depending on the ability of the species to accumulate Si, as well as the route of Si administration.

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Multiple comparisons tests (MCTs) include the statistical tests used to compare groups (treatments) often following a significant effect reported in one of many types of linear models. Due to a variety of data and statistical considerations, several dozen MCTs have been developed over the decades, with tests ranging from very similar to each other to very different from each other. Many scientific disciplines use MCTs, including >40,000 reports of their use in ecological journals in the last 60 years. Despite the ubiquity and utility of MCTs, several issues remain in terms of their correct use and reporting. In this study, we evaluated 17 different MCTs. We first reviewed the published literature for recommendations on their correct use. Second, we created a simulation that evaluated the performance of nine common MCTs. The tests examined in the simulation were those that often overlapped in usage, meaning the selection of the test based on fit to the data is not unique and that the simulations could inform the selection of one or more tests when a researcher has choices. Based on the literature review and recommendations: planned comparisons are overwhelmingly recommended over unplanned comparisons, for planned non-parametric comparisons the Mann-Whitney-Wilcoxon U test is recommended, Scheffé's S test is recommended for any linear combination of (unplanned) means, Tukey's HSD and the Bonferroni or the Dunn-Sidak tests are recommended for pairwise comparisons of groups, and that many other tests exist for particular types of data. All code and data used to generate this paper are available at: https://github.com/stevemidway/MultipleComparisons.

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In observational studies of treatment effects, it is common to have several outcomes, perhaps of uncertain quality and relevance, each purporting to measure the effect of the treatment. A single planned combination of several outcomes may increase both power and insensitivity to unmeasured bias when the plan is wisely chosen, but it may miss opportunities in other cases. A method is proposed that uses one planned combination with only a mild correction for multiple testing and exhaustive consideration of all possible combinations fully correcting for multiple testing. The method works with the joint distribution of $\kappa^{T}\left( \mathbf{T}-\boldsymbol{\mu}\right) /\sqrt {\boldsymbol{\kappa}^{T}\boldsymbol{\Sigma\boldsymbol{\kappa}}}$ and $max_{\boldsymbol{\lambda}\neq\mathbf{0}}$$\,\lambda^{T}\left( \mathbf{T} -\boldsymbol{\mu}\right) /$$\sqrt{\boldsymbol{\lambda}^{T}\boldsymbol{\Sigma \lambda}}$ where $\kappa$ is chosen a priori and the test statistic $\mathbf{T}$ is asymptotically $N_{L}\left( \boldsymbol{\mu},\boldsymbol{\Sigma}\right) $. The correction for multiple testing has a smaller effect on the power of $\kappa^{T}\left( \mathbf{T}-\boldsymbol{\mu }\right) /\sqrt{\boldsymbol{\kappa}^{T}\boldsymbol{\Sigma\boldsymbol{\kappa} }}$ than does switching to a two-tailed test, even though the opposite tail does receive consideration when $\lambda=-\kappa$. In the application, there are three measures of cognitive decline, and the a priori comparison $\kappa$ is their first principal component, computed without reference to treatment assignments. The method is implemented in an R package sensitivitymult.

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Multiple comparisons tests (MCTs) are performed several times on the mean of experimental conditions. When the null hypothesis is rejected in a validation, MCTs are performed when certain experimental conditions have a statistically significant mean difference or there is a specific aspect between the group means. A problem occurs if the error rate increases while multiple hypothesis tests are performed simultaneously. Consequently, in an MCT, it is necessary to control the error rate to an appropriate level. In this paper, we discuss how to test multiple hypotheses simultaneously while limiting type I error rate, which is caused by α inflation. To choose the appropriate test, we must maintain the balance between statistical power and type I error rate. If the test is too conservative, a type I error is not likely to occur. However, concurrently, the test may have insufficient power resulted in increased probability of type II error occurrence. Most researchers may hope to find the best way of adjusting the type I error rate to discriminate the real differences between observed data without wasting too much statistical power. It is expected that this paper will help researchers understand the differences between MCTs and apply them appropriately.

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Multiple comparisons tests (MCTs) are performed several times on the mean of experimental conditions. When the null hypothesis is rejected in a validation, MCTs are performed when certain experimental conditions have a statistically significant mean difference or there is a specific aspect between the group means. A problem occurs if the error rate increases while multiple hypothesis tests are performed simultaneously. Consequently, in an MCT, it is necessary to control the error rate to an appropriate level. In this paper, we discuss how to test multiple hypotheses simultaneously while limiting type I error rate, which is caused by α inflation. To choose the appropriate test, we must maintain the balance between statistical power and type I error rate. If the test is too conservative, a type I error is not likely to occur. However, concurrently, the test may have insufficient power resulted in increased probability of type II error occurrence. Most researchers may hope to find the best way of adjusting the type I error rate to discriminate the real differences between observed data without wasting too much statistical power. It is expected that this paper will help researchers understand the differences between MCTs and apply them appropriately.

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It is important to optimize imaging parameters in 3D-double inversion recovery (DIR) magnetic resonance imaging (MRI) for detecting cortical micro lesions. However, inadequate parameters markedly raise blurring in 3DDIR MRI. The purpose of this study was to evaluate the relationship between the blurring and refocus flip angle (RFA) in 3D-DIR MRI. White matter attenuated inversion recovery (WAIR) images as a test sample were obtained by 1.5T MRI with various RFA settings (30°, 40°, 60°, 100°, 140°, 180°, and variable refocus flip angle (VRFA)). Optimal RFA was evaluated using Scheffé's method (Nakaya changing method) by five observers. The results of average preferences indicated that RFA settings of under the 60° of RFA or VRFA suppressed the blurring in 3DDIR MRI. The yard sticks of RFAs of 30° and 40° were significantly higher than the yard sticks of other RFAs (p<0.01). For detecting cortical microlesions, it is very important to obtain WAIR images with no blurring. Using low RFA or VRFA didn't cause significant differences of signal intensity between high-frequency region and low-frequency region in k-space of 3D-DIR MRI. Therefore, it is recommended to set lower RFA (under 60° or VRFA) for suppressing blur in 3D-DIR MRI.

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OBJECTIVE: Lopinavir (LPV), an antiretroviral protease inhibitor shows poor bioavailability because of poor aqueous solubility and extensive hepatic first-pass metabolism. The aim of the present work was to investigate the potential of the solid self-nanoemulsifying drug delivery system (S-SNEDDS) in improving dissolution rate and oral bioavailability of LPV. MATERIALS AND METHODS: Liquid SNEDDS (L-SNEDDS) of LPV were prepared using Capmul MCM C8, Cremophor RH 40 and propylene glycol and their amounts were optimized by Scheffe's mixture design. L-SNEDDS formulations were evaluated for different physicochemical and in vitro drug release parameters. S-SNEDDS were prepared by adsorbing L-SNEDDS on Neusilin US2 and characterized for solid-state properties. In vivo bioavailability of S-SNEDDS, marketed Lopinavir + Ritonavir (LPV/RTV) formulation and pure LPV was studied in Wistar rats. Stability study of S-SNEDDS was performed as per ICH guidelines. RESULTS AND DISCUSSION: Optimized L-SNEDDS obtained by Scheffe design had drug loading 160 ± 1.15 mg, globule size 32.9 ± 1.45 nm and drug release >95% within 15 min. Solid state studies suggested the transformation of the crystalline drug to amorphous drug. The size and zeta potential of globules obtained on dilution S-SNEDDS remained similar to L-SNEEDS. In vivo bioavailability study revealed that S-SNEDDS has 2.97 and 1.54-folds higher bioavailability than pure LPV and LPV/RTV formulation, respectively. The optimized S-SNEDDS was found to be stable and had a shelf life of 2.85 years. CONCLUSION: The significant increase in drug dissolution and bioavailability by prepared SNEDDS suggest that the developed S-SNEDDS is a useful solid platform for improving oral bioavailability of poorly soluble LPV.

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We propose a new class of models providing a powerful unification and extension of existing statistical methodology for analysis of data obtained in mixture experiments. These models, which integrate models proposed by Scheffé and Becker, extend considerably the range of mixture component effects that may be described. They become complex when the studied phenomenon requires it, but remain simple whenever possible. This article has supplementary material online.

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A large number of unconfounded media variations were used with a Scheffe Mix Model to examine in an unambiguous fashion the effects of variations in six important ions; NH4(+), NO3(-), Na(+), K(+), PO4(-), and Cl(-), on the growth of Chlorella vulgaris. This allows several novel observations on media components, for example, the inhibitory effects of chloride, to be made. Using a side by side comparison, it is shown that two strains of Chlorella show significant physiological and functional differences brought out by this approach. Testing selected formulations with a diverse set of algae demonstrated different effects on both growth and cellular lipid content, in some cases driving significant lipid production. This suggests that future work using a larger portion of media composition space could lead to the development of novel media supporting maximal biomass production and lipid production.

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Under a random effects linear additive risk model, we compare two experimental treatments with a placebo in continuous data under an incomplete block crossover trial. We develop three test procedures for simultaneously testing equality between two experimental treatments and a placebo, as well as interval estimators for the mean difference between treatments. We apply Monte Carlo simulations to evaluate the performance of these test procedures and interval estimators in a variety of situations. We note that the bivariate test procedure accounting for the dependence structure based on the F-test is preferable to the other two procedures when there is only one of the two experimental treatments has a non-zero effect vs. the placebo. We note further that when the effects of the two experimental treatments vs. a placebo are in the same relative directions and are approximately of equal magnitude, the summary test procedure based on a simple average of two weighted-least-squares (WLS) estimators can outperform the other two procedures with respect to power. When one of the two experimental treatments has a relatively large effect vs. the placebo, the univariate test procedure with using Bonferroni's equality can be still of use. Finally, we use the data about the forced expiratory volume in 1 s (FEV1) readings taken from a double-blind crossover trial comparing two different doses of formoterol with a placebo to illustrate the use of test procedures and interval estimators proposed here.

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PURPOSE: The purpose of this study was to develop evidence-based guidelines on postoperative pain management via the web and to examine the effects in terms of pain level of patients undergoing abdominal surgery and nurses' knowledge of postoperative pain management. METHODS: First, evidence-based pain guidelines were developed via the web in a tertiary hospital. Second, a special educational program on evidence-based pain guidelines for nurses was developed after validation of content by experts. Third, diverse strategies were adopted in order to facilitate incorporation of evidence-based pain guidelines in practice. Fourth, nurses in the study units were educated on evidence-based guidelines using the developed educational program for 3 weeks before their implementation of evidence-based pain guidelines to patients. Patients were assigned to the control group (from July 29 to August 20, 2011) and the experimental group (from September 24 to October 25, 2011) according to interrupted time interval. The data were analyzed using chi-square test, analysis of variance test with Scheffé's test as a post hoc and repeated measure of analysis of variance. RESULTS: Patients in the experimental group showed a significantly lower level of pain. Nurses' knowledge of management of postoperative pain showed a significant increase after installation of evidence-based guidelines. CONCLUSION: Evidence-based pain guidelines were effective in reducing the pain level of patients as well as improving nurses' knowledge of pain management.

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PURPOSE: Nanoparticle size is important in drug delivery. Clearance of nanoparticles by cells of the reticuloendothelial system has been reported to increase with increase in particle size. Further, nanoparticles should be small enough to avoid lung or spleen filtering effects. Endocytosis and accumulation in tumor tissue by the enhanced permeability and retention effect are also processes that are influenced by particle size. We present the results of studies designed to optimize cross-linked biodegradable stealth polymeric nanoparticles fabricated by dispersion polymerization. METHODS: Nanoparticles were fabricated using different amounts of macromonomer, initiators, crosslinking agent and stabilizer in a dioxane/DMSO/water solvent system. Confirmation of nanoparticle formation was by scanning electron microscopy (SEM). Particle size was measured by dynamic light scattering (DLS). D-optimal mixture statistical experimental design was used for the experimental runs, followed by model generation (Scheffe polynomial) and optimization with the aid of a computer software. Model verification was done by comparing particle size data of some suggested solutions to the predicted particle sizes. RESULTS AND CONCLUSION: Data showed that average particle sizes follow the same trend as predicted by the model. Negative terms in the model corresponding to the cross-linking agent and stabilizer indicate the important factors for minimizing particle size.

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When interactions are identified in analysis of covariance models it becomes important to identify values of the covariates for which there are significant differences or, more generally, significant contrasts among the group mean responses. Inferential procedures that incorporate a priori order restrictions among the group mean responses would be expected to be superior to those that ignore this information. In this paper we focus on analysis of covariance models with pre-specified order restrictions on the mean response across the levels of a grouping variable when the grouping variable may interact with model covariates. In order for the restrictions to hold in the presence of interactions, it is necessary to impose the requirement that the restrictions hold over all levels of interacting categorical covariates and across pre-specified ranges of interacting continuous covariates. The parameter estimation procedure involves solving a quadratic programming minimization problem with a carefully specified constraint matrix. Simultaneous confidence intervals for treatment group contrasts and tests for equality of the ordered group mean responses are determined by exploiting previously unconnected literature. The proposed methods are motivated by a clinical trial of the dopamine agonist pramipexole for the treatment of early-stage Parkinson's disease.

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Chara australis (R. Br.) is a macrophytic alga that can grow in and accumulate Cd from artificially contaminated sediments. We investigated the effects of Zn independently and in combination with Cd on C. australis growth, metal tolerance, and uptake. Plant growth was reduced at concentrations ≥ 75 mg Zn (kg soil)⁻¹. Zn also increased the concentration of glutathione in the plant, suggesting alleviation of stress. Phytotoxic effects were observed at ≥ 250 mg added Zn (kg soil)⁻¹. At 1.5mg Zn (kg soil)⁻¹, the rhizoid bioconcentration factor (BCF) was >1.0 for both Cd and Zn. This is a criterion for hyperaccumulator status, a commonly used benchmark for utility in remediation of contaminated soils by phytoextraction. There was no significant interaction between Cd and Zn on accumulation, indicating that Chara should be effective at phytoextraction of mixed heavy metal contamination in sediments. The effects of the chelator, ethylenediaminetetraacetic acid (EDTA), were also tested. Moderate levels of EDTA increased Cd and Zn accumulation in rhizoids and Cd BCF of shoots, enhancing Chara's potential in phytoremediation. This study demonstrates for the first time the potential of macroalgae to remove metals from sediments in aquatic systems that are contaminated with a mixture of metals.

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The measurement process uncertainty is propagated through the use of a calibration curve. The magnitude and direction of this uncertainty depends on the choice of the controllable variable in producing the calibration curve; in other words, the design of the calibration experiment. In this paper this design is discussed in the context of Scheffé's approach to the uncertainties of a calibration curve and in particular for the case in which the calibration curve is a linear spline. A class of appropriate designs is given, which depend on the location of the knots and the slopes of the segments. One of these designs is quickly calculable and can be found without a computer. Based on these results, a design approach is suggested for the case in which the knots are not known exactly.