Designs for generalized linear models with several variables and model uncertainty

Standard factorial designs sometimes may be inadequate for experiments that aim to estimate a generalized linear model, for example, for describing a binary response in terms of several variables. A method is proposed for finding exact designs for such experiments that uses a criterion allowing for uncertainty in the link function, the linear predictor, or the model parameters, together with a design search. Designs are assessed and compared by simulation of the distribution of efficiencies relative to locally optimal designs over a space of possible models. Exact designs are investigated for two applications, and their advantages over factorial and central composite designs are demonstrated.

A flux ratio theorem for multicomponent linear diffusion equations

Ussing [1] considered the steady flux of a single chemical component diffusing through a membrane under the influence of chemical potentials and derived from his linear model, an expression for the ratio of this flux and that of the complementary experiment in which the boundary conditions were interchanged. Here, an extension of Ussing's flux ratio theorem is obtained for n chemically interacting components governed by a linear system of diffusion-migration equations that may also incorporate linear temporary trapping reactions. The determinants of the output flux matrices for complementary experiments are shown to satisfy an Ussing flux ratio formula for steady state conditions of the same form as for the well-known one-component case. (C) 2000 Elsevier Science Ltd. All rights reserved.

The comprehensive osteoarthritis test: a simple index for measurement of treatment effects in clinical trials

Objective. To assess the measurement properties of a simple index of symptom severity in osteoarthritis (OA) of the hips and knees. Methods. Both the Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC) and the proposed new Comprehensive Osteoarthritis Test (COAT) instrument were completed weekly by 125 subjects in the context of a randomized, 12-week, 3 parallel-arm clinical trial. The reliabilities of the various scales were assessed on a weekly basis by use of Cronbach's alpha coefficients. The validity of the COAT total scale was assessed by correlation with the WOMAC total scale on a weekly basis with correlation coefficients, and in terms of the correlations between subject-level intercepts and slopes over time. The relative responsiveness of the WOMAC and COAT total scales was assessed using a multilevel (longitudinal) multivariate (WOMAC, COAT) linear model. Results. The WOMAC and COAT total scales were highly reliable (mean over weeks: WOMAC alpha = 0.98; COAT alpha = 0.97). The correlations between the WOMAC and COAT scales were very high (mean over weeks = 0.92; subject-level intercepts = 0.91, slopes = 0.88). The COAT total scale was significantly more responsive than the WOMAC total scale in the active treatment (34.8% improvement vs 26.8%; p = 0.002). Conclusion. The COAT total scale is simple to administer, reliable, valid, and responsive to treatment effects.

Finite deformation model of simple shear of fault with microrotations: apparent strain localisation and en-echelon fracture pattern

Strain localisation is a widespread phenomenon often observed in shear and compressive loading of geomaterials, for example, the fault gouge. It is believed that the main mechanisms of strain localisation are strain softening and mismatch between dilatancy and pressure sensitivity. Observations show that gouge deformation is accompanied by considerable rotations of grains. In our previous work as a model for gouge material, we proposed a continuum description for an assembly of particles of equal radius in which the particle rotation is treated as an independent degree of freedom. We showed that there exist critical values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-surface layers of the fault, even in the absence of inelasticity. Here, we generalise the model to the case of finite deformations characteristic for the gouge deformation. We derive objective constitutive relationships relating the Jaumann rates of stress and moment stress to the relative strain and curvature rates, respectively. The model suggests that the pattern of localisation remains the same as in the linear case. However, the presence of the Jaumann terms leads to the emergence of non-zero normal stresses acting along and perpendicular to the shear layer (with zero hydrostatic pressure), and localised along the mid-line of the gouge; these stress components are absent in the linear model of simple shear. These additional normal stresses, albeit small, cause a change in the direction in which the maximal normal stresses act and in which en-echelon fracturing is formed.

Norwegian long-distance reflexives: Lectal variation and speaker attitudes

10 lectal variables were examined with respect to Norwegian speakers' acceptance of long-distance reflexives (LDR), using a questionnaire to elicit grammaticality judgements on 50 potential LDR sentences. A sample of 180 speakers completed the questionnaire. The data was analysed using a general linear model univariate model, and Spearman's correlation. In this sample the results showed that dialect and level of education had significant effects on speakers' acceptance of long-distance reflexives, while sex, age, being a native speaker, having both native-speaker parents, living in the city or the country, and the speaker's attitudes to the two Norwegian writing languages had no influence on speakers' acceptance of long-distance reflexives. It is suggested that the influence of Danish on Norwegian writing and on the southern dialects may be the cause of the observed variation with respect to LDR in Norwegian.

Population subdivision in marine environments: the contributions of biogeography, geographic distance, and discontinuous habitat to genetic differentiation in a blennioid

The relative importance of factors that may promote genetic differentiation in marine organisms is largely unknown. Here, contributions to population structure from biogeography, habitat distribution, and isolation by distance were investigated in Axoclinus nigricaudus, a small subtidal rock reef fish, throughout its range in the Gulf of California. A 408 basepair fragment of the mitochondrial control region was sequenced from 105 individuals. Variation was significantly partitioned between many pairs of populations. Phylogenetic analyses, hierarchical analyses of variance, and general linear models substantiated a major break between two putative biogeographic regions. This genetic discontinuity coincides with an abrupt change in ecological characteristics (including temperature and salinity) but does not coincide with known oceanographic circulation patterns. Geographic distance and the nature of habitat separating populations (continuous habitat along a shoreline, discontinuous habitat along a shoreline, and open water) also contributed to population structure in general linear model analyses. To verify that local populations are genetically stable over time, one population was resampled on four occasions over eighteen months; it showed no evidence of a temporal component to diversity. These results indicate that having a planktonic life stage does not preclude geographically partitioned genetic variation over relatively small geographic distances in marine environments. Moreover, levels of genetic differentiation among populations of Axoclinus nigricaudus cannot be explained by a single factor, but are due to the combined influences of a biogeographic boundary, habitat, and geographic distance.

Short-term spatial diffusion in sigma o+ o- optical molasses

We have measured the spatial diffusion of atoms in a three-dimensional sigma(+)-sigma(-) optical molasses over twenty milliseconds timescale, starting from the initial interaction of the atoms with the molasses. We find that the diffusion constants agree well with a linear model for these short time scales and also compare favourably to other studies of diffusion made over longer time scales. These measurements enable us to quantify the detection method known as freezing molasses. We discuss this method, for detecting and measuring the momentum distribution of cold atoms, which relies on the slow diffusion of atoms in optical molasses to produce a freeze-frame of the spatial distribution of the atoms. This method enables a longer interrogation interval, providing a greatly increased signal-to-noise ratio. (C) 1998 Elsevier Science B.V.

Levene tests of homogeneity of variance for general block and treatment designs

This article develops a weighted least squares version of Levene's test of homogeneity of variance for a general design, available both for univariate and multivariate situations. When the design is balanced, the univariate and two common multivariate test statistics turn out to be proportional to the corresponding ordinary least squares test statistics obtained from an analysis of variance of the absolute values of the standardized mean-based residuals from the original analysis of the data. The constant of proportionality is simply a design-dependent multiplier (which does not necessarily tend to unity). Explicit results are presented for randomized block and Latin square designs and are illustrated for factorial treatment designs and split-plot experiments. The distribution of the univariate test statistic is close to a standard F-distribution, although it can be slightly underdispersed. For a complex design, the test assesses homogeneity of variance across blocks, treatments, or treatment factors and offers an objective interpretation of residual plot.

The effect of a triclosan-containing dentifrice on the progression of periodontal disease in an adult population

Objectives: The aim of the present study was to determine the effect of unsupervised, long-term use of a 0.3% triclosan/2% copolymer dentifrice on the progression of periodontal disease in a general adult population. Methods: Five hundred and four volunteers were enrolled in a double-blind, controlled clinical trial. Participants were matched for disease status, plaque index, age and gender. At the baseline examination, probing pocket depths and relative attachment levels were recorded and participants were assigned to either the test or control group. Re-examinations took place after 6, 12, 24, 36, 48 and 60 months. Subgingival plaque samples were collected at each examination and assayed for Porphyromonas gingivalis , Actinobacillus actinomycetemcomitans and Prevotella intermedia . A generalised linear model was used to analyse the data, with a number of covariates thought to influence the responses included as the possible confounding effects. Results: The triclosan/copolymer dentifrice had a significant effect in subjects with interproximal probing depths greater than or equal to3.5 mm, where it significantly reduced the number of sites with probing depths greater than or equal to3.5 mm at the following examination, when compared with the control group (p

Independent contribution of plaque complexity to myocardial ischemia during Dobutamine stress echocardiography

The influence of complex plaque morphology on the extent of demand-induced ischemia in unselected patients is not well defined. We sought to investigate the functional significance of lesion morphology in patients who underwent coronary angiography and dobutamine stress echocardiography (DSE).,Angiography and DSE were performed within a 6-month period (mean 1 +/- 1 month) in 196 patients. Angiographic assessments involved quantification of stenosis severity, assessment of the extent of jeopardized myocardium, and categorization of plaque morphology according to the Ambrose classification. DSE was interpreted by separate investigators with respect to wall motion score index (WMSI) and number of coronary territories involved. A general linear model was constructed to assess,the independent contribution of patient characteristics and angiographic and DSE results with respect to extent of ischemic myocardium. Complex lesion morphology was seen in 62 patients (32%). Patients with complex lesions were more likely to have had prior myocardial infarction (p < 0.001) and be current smokers (p = 0.03). During angiography, they exhibited a trend toward a greater number of diseased vessels, had a greater coronary jeopardy score (p < 0.001) and more frequent collateral flow (p = 0.03). During echocardiography, patients had a higher stress WMSI (p < 0.001) and were more likely to show ischemia in all 3 arterial territories (p < 0.01). On multivariate regression, the coronary artery jeopardy score and the presence of complex plaque morphology were independent predictors of the extent of ischemic myocardium (R 2 = 34%, p < 0.001). Thus, patients with complex plaque morphology are older, more likely to smoke, and more likely to have had prior myocardial. infarction. They exhibit more extensive disease with higher coronary jeopardy scores and a higher resting and peak stress WMSI. Despite these differences, complex plaque morphology remains an independent predictor of the extent of ischemia during stress. (C) 2003 by Excerpta Medica, Inc.

Prospective evaluation of a D-optimal designed population pharmacokinetic study

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

Computational properties of min/max autocorrelation factors

Minimum/maximum autocorrelation factor (MAF) is a suitable algorithm for orthogonalization of a vector random field. Orthogonalization avoids the use of multivariate geostatistics during joint stochastic modeling of geological attributes. This manuscript demonstrates in a practical way that computation of MAF is the same as discriminant analysis of the nested structures. Mathematica software is used to illustrate MAF calculations from a linear model of coregionalization (LMC) model. The limitation of two nested structures in the LMC for MAF is also discussed and linked to the effects of anisotropy and support. The analysis elucidates the matrix properties behind the approach and clarifies relationships that may be useful for model-based approaches. (C) 2003 Elsevier Science Ltd. All rights reserved.

Spatial and ontogenetic variation in growth of nursery-bound juvenile lemon sharks, Negaprion brevirostris: a comparison of two age-assigning techniques

We compared growth rates of the lemon shark, Negaprion brevirostris, from Bimini, Bahamas and the Marquesas Keys (MK), Florida using data obtained in a multi-year annual census. We marked new neonate and juvenile sharks with unique electronic identity tags in Bimini and in the MK we tagged neonate and juvenile sharks. Sharks were tagged with tiny, subcutaneous transponders, a type of tagging thought to cause little, if any disruption to normal growth patterns when compared to conventional external tagging. Within the first 2 years of this project, no age data were recorded for sharks caught for the first time in Bimini. Therefore, we applied and tested two methods of age analysis: ( 1) a modified 'minimum convex polygon' method and ( 2) a new age-assigning method, the 'cut-off technique'. The cut-off technique proved to be the more suitable one, enabling us to identify the age of 134 of the 642 previously unknown aged sharks. This maximised the usable growth data included in our analysis. Annual absolute growth rates of juvenile, nursery-bound lemon sharks were almost constant for the two Bimini nurseries and can be best described by a simple linear model ( growth data was only available for age-0 sharks in the MK). Annual absolute growth for age-0 sharks was much greater in the MK than in either the North Sound (NS) and Shark Land (SL) at Bimini. Growth of SL sharks was significantly faster during the first 2 years of life than of the sharks in the NS population. However, in MK, only growth in the first year was considered to be reliably estimated due to low recapture rates. Analyses indicated no significant differences in growth rates between males and females for any area.

Comparison of virulence gene profiles of Escherichia coli strains isolated from healthy and diarrheic swine

A combination of uni- and multiplex PCR assays targeting 58 virulence genes (VGs) associated with Escherichia coli strains causing intestinal and extraintestinal disease in humans and other mammals was used to analyze the VG repertoire of 23 commensal E. coli isolates from healthy pigs and 52 clinical isolates associated with porcine neonatal diarrhea (ND) and postweaning diarrhea (PWD). The relationship between the presence and absence of VGs was interrogated using three statistical methods. According to the generalized linear model, 17 of 58 VGs were found to be significant (P < 0.05) in distinguishing between commensal and clinical isolates. Nine of the 17 genes represented by iha, hlyA, aidA, east1, aah, fimH, iroN(E).(coli), traT, and saa have not been previously identified as important VGs in clinical porcine isolates in Australia. The remaining eight VGs code for fimbriae (F4, F5, F18, and F41) and toxins (STa, STh, LT, and Stx2), normally associated with porcine enterotoxigenic E. coli. Agglomerative hierarchical algorithm analysis grouped E. coli strains into subclusters based primarily on their serogroup. Multivariate analyses of clonal relationships based on the 17 VGs were collapsed into two-dimensional space by principal coordinate analysis. PWD clones were distributed in two quadrants, separated from ND and commensal clones, which tended to cluster within one quadrant. Clonal subclusters within quadrants were highly correlated with serogroups. These methods of analysis provide different perspectives in our attempts to understand how commensal and clinical porcine enterotoxigenic E. coli strains have evolved and are engaged in the dynamic process of losing or acquiring VGs within the pig population.