A practical approach to a multi-level analysis with a sparse binary outcome within a large surgical trial

Objectives: To assess the potential source of variation that surgeon may add to patient outcome in a clinical trial of surgical procedures. Methods: Two large (n = 1380) parallel multicentre randomized surgical trials were undertaken to compare laparoscopically assisted hysterectomy with conventional methods of abdominal and vaginal hysterectomy; involving 43 surgeons. The primary end point of the trial was the occurrence of at least one major complication. Patients were nested within surgeons giving the data set a hierarchical structure. A total of 10% of patients had at least one major complication, that is, a sparse binary outcome variable. A linear mixed logistic regression model (with logit link function) was used to model the probability of a major complication, with surgeon fitted as a random effect. Models were fitted using the method of maximum likelihood in SAS((R)). Results: There were many convergence problems. These were resolved using a variety of approaches including; treating all effects as fixed for the initial model building; modelling the variance of a parameter on a logarithmic scale and centring of continuous covariates. The initial model building process indicated no significant 'type of operation' across surgeon interaction effect in either trial, the 'type of operation' term was highly significant in the abdominal trial, and the 'surgeon' term was not significant in either trial. Conclusions: The analysis did not find a surgeon effect but it is difficult to conclude that there was not a difference between surgeons. The statistical test may have lacked sufficient power, the variance estimates were small with large standard errors, indicating that the precision of the variance estimates may be questionable.

Solution-free sets for sums of binary forms

In this paper, we obtain quantitative estimates for the asymptotic density of subsets of the integer lattice Z2 that contain only trivial solutions to an additive equation involving binary forms. In the process we develop an analogue of Vinogradov’s mean value theorem applicable to binary forms.

Sample size considerations in active-control non-inferiority trials with binary data based on the odds ratio

This paper presents an approximate closed form sample size formula for determining non-inferiority in active-control trials with binary data. We use the odds-ratio as the measure of the relative treatment effect, derive the sample size formula based on the score test and compare it with a second, well-known formula based on the Wald test. Both closed form formulae are compared with simulations based on the likelihood ratio test. Within the range of parameter values investigated, the score test closed form formula is reasonably accurate when non-inferiority margins are based on odds-ratios of about 0.5 or above and when the magnitude of the odds ratio under the alternative hypothesis lies between about 1 and 2.5. The accuracy generally decreases as the odds ratio under the alternative hypothesis moves upwards from 1. As the non-inferiority margin odds ratio decreases from 0.5, the score test closed form formula increasingly overestimates the sample size irrespective of the magnitude of the odds ratio under the alternative hypothesis. The Wald test closed form formula is also reasonably accurate in the cases where the score test closed form formula works well. Outside these scenarios, the Wald test closed form formula can either underestimate or overestimate the sample size, depending on the magnitude of the non-inferiority margin odds ratio and the odds ratio under the alternative hypothesis. Although neither approximation is accurate for all cases, both approaches lead to satisfactory sample size calculation for non-inferiority trials with binary data where the odds ratio is the parameter of interest.

Predicting sizes of hexagonal and gyroid metal nanostructures from liquid crystal templating

We describe a method to predict and control the lattice parameters of hexagonal and gyroid mesoporous materials formed by liquid crystal templating. In the first part, we describe a geometric model with which the lattice parameters of different liquid crystal mesophases can be predicted as a function of their water/surfactant/oil volume fractions, based on certain geometric parameters relating to the constituent surfactant molecules. We demonstrate the application of this model to the lamellar (LR), hexagonal (H1), and gyroid bicontinuous cubic (V1) mesophases formed by the binary Brij-56 (C16EO10)/water system and the ternary Brij-56/hexadecane/water system. In this way, we demonstrate predictable and independent control over the size of the cylinders (with hexadecane) and their spacing (with water). In the second part, we produce mesoporous platinum using as templates hexagonal and gyroid phases with different compositions and show that in each case the symmetry and lattice parameter of the metal nanostructure faithfully replicate those of the liquid crystal template, which is itself in agreement with the model. This demonstrates a rational control over the geometry, size, and spacing of pores in a mesoporous metal.

Variational data assimilation for parameter estimation: application to a simple morphodynamic model

Data assimilation is a sophisticated mathematical technique for combining observational data with model predictions to produce state and parameter estimates that most accurately approximate the current and future states of the true system. The technique is commonly used in atmospheric and oceanic modelling, combining empirical observations with model predictions to produce more accurate and well-calibrated forecasts. Here, we consider a novel application within a coastal environment and describe how the method can also be used to deliver improved estimates of uncertain morphodynamic model parameters. This is achieved using a technique known as state augmentation. Earlier applications of state augmentation have typically employed the 4D-Var, Kalman filter or ensemble Kalman filter assimilation schemes. Our new method is based on a computationally inexpensive 3D-Var scheme, where the specification of the error covariance matrices is crucial for success. A simple 1D model of bed-form propagation is used to demonstrate the method. The scheme is capable of recovering near-perfect parameter values and, therefore, improves the capability of our model to predict future bathymetry. Such positive results suggest the potential for application to more complex morphodynamic models.

Parameter sensitivity and predictive uncertainty in a new water quality model, Q(2)

A new dynamic model of water quality, Q(2), has recently been developed, capable of simulating large branched river systems. This paper describes the application of a generalized sensitivity analysis (GSA) to Q(2) for single reaches of the River Thames in southern England. Focusing on the simulation of dissolved oxygen (DO) (since this may be regarded as a proxy for the overall health of a river); the GSA is used to identify key parameters controlling model behavior and provide a probabilistic procedure for model calibration. It is shown that, in the River Thames at least, it is more important to obtain high quality forcing functions than to obtain improved parameter estimates once approximate values have been estimated. Furthermore, there is a need to ensure reasonable simulation of a range of water quality determinands, since a focus only on DO increases predictive uncertainty in the DO simulations. The Q(2) model has been applied here to the River Thames, but it has a broad utility for evaluating other systems in Europe and around the world.

MEASUREMENT AND MODELING OF THE TOXICITY OF BINARY MIXTURES IN THE NEMATODE CAENORHABDITIS ELEGANS-A TEST OF INDEPENDENT ACTION

Ecological risk assessments must increasingly consider the effects of chemical mixtures on the environment as anthropogenic pollution continues to grow in complexity. Yet testing every possible mixture combination is impractical and unfeasible; thus, there is an urgent need for models that can accurately predict mixture toxicity from single-compound data. Currently, two models are frequently used to predict mixture toxicity from single-compound data: Concentration addition and independent action (IA). The accuracy of the predictions generated by these models is currently debated and needs to be resolved before their use in risk assessments can be fully justified. The present study addresses this issue by determining whether the IA model adequately described the toxicity of binary mixtures of five pesticides and other environmental contaminants (cadmium, chlorpyrifos, diuron, nickel, and prochloraz) each with dissimilar modes of action on the reproduction of the nematode Caenorhabditis elegans. In three out of 10 cases, the IA model failed to describe mixture toxicity adequately with significant or antagonism being observed. In a further three cases, there was an indication of synergy, antagonism, and effect-level-dependent deviations, respectively, but these were not statistically significant. The extent of the significant deviations that were found varied, but all were such that the predicted percentage effect seen on reproductive output would have been wrong by 18 to 35% (i.e., the effect concentration expected to cause a 50% effect led to an 85% effect). The presence of such a high number and variety of deviations has important implications for the use of existing mixture toxicity models for risk assessments, especially where all or part of the deviation is synergistic.

Thermal expansion of deuterated hopeite, Zn-3(PO4)(2)center dot 4D(2)O

The lattice parameters extracted from Lebail analysis of neutron powder diffraction data collected between 2 and 300 K have been used to calculate the temperature evolution of the thermal expansion tensor for hopeite, Zn-3(PO4)(2)center dot 2H(2)O, Pnma,Z=4with a= 10.6065(4) angstrom, b = 18.2977(4) angstrom, c= 5.0257(2) A at 275 K. The a lattice parameter shows a negative thermal expansion, the b lattice parameter appears to saturate at 275 K while the c lattice parameter has a more typical positive thermal expansion. At 275 K, the magnitudes of the thermal expansion coefficients are alpha(a) = -1. 1(4) x 10(-5) K-1, alpha(b) = 2.4(9) x 10(-6) K-1 and alpha(c) = 3.6(2) x 10(-1) K-1. Under the conditions of these experiments, hopeite begins to dehydrate to the dihydrate between 300 and 325 K, and between 480 and 500 K the monohydrate is formed. The thermal expansion of the dihydrate has been calculated between 335 and 480 and at 480 K the magnitudes of the thermal expansion coefficients are alpha(a) = 1(2) x 10(-5) K-1, alpha(b) = 4(l) x 10(-6) K-1, alpha(c) = 4(2) x 10(-5) K-1, alpha(beta) = 1 (1) x 10(-1) K-1, and alpha(v) = 2(2) x 10(-1) K-1. The thermal expansion of hopeite is described in terms of its crystal structure and possible dehydration mechanisms for the alpha and beta modifications of hopeite are discussed.

Monte Carlo phase diagram for diblock copolymer melts

A partial phase diagram is constructed for diblock copolymer melts using lattice-based Monte Carlo simulations. This is done by locating the order-disorder transition (ODT) with the aid of a recently proposed order parameter and identifying the ordered phase over a wide range of copolymer compositions (0.2 <= f <= 0.8). Consistent with experiments, the disordered phase is found to exhibit direct first-order transitions to each of the ordered morphologies. This includes the spontaneous formation of a perforated-lamellar phase, which presumably forms in place of the gyroid morphology due to finite-size and/or nonequilibrium effects. Also included in our study is a detailed examination of disordered cylinder-forming (f=0.3) diblock copolymers, revealing a substantial degree of pretransitional chain stretching and short-range order that set in well before the ODT, as observed previously in analogous studies on lamellar-forming (f=0.5) molecules. (c) 2006 American Institute of Physics.

Calibrating flood inundation models: methods for assessing model performance

Satellite observed data for flood events have been used to calibrate and validate flood inundation models, providing valuable information on the spatial extent of the flood. Improvements in the resolution of this satellite imagery have enabled indirect remote sensing of water levels by using an underlying LiDAR DEM to extract the water surface elevation at the flood margin. Further to comparison of the spatial extent, this now allows for direct comparison between modelled and observed water surface elevations. Using a 12.5m ERS-1 image of a flood event in 2006 on the River Dee, North Wales, UK, both of these data types are extracted and each assessed for their value in the calibration of flood inundation models. A LiDAR guided snake algorithm is used to extract an outline of the flood from the satellite image. From the extracted outline a binary grid of wet / dry cells is created at the same resolution as the model, using this the spatial extent of the modelled and observed flood can be compared using a measure of fit between the two binary patterns of flooding. Water heights are extracted using points at intervals of approximately 100m along the extracted outline, and the students T-test is used to compare modelled and observed water surface elevations. A LISFLOOD-FP model of the catchment is set up using LiDAR topographic data resampled to the 12.5m resolution of the satellite image, and calibration of the friction parameter in the model is undertaken using each of the two approaches. Comparison between the two approaches highlights the sensitivity of the spatial measure of fit to uncertainty in the observed data and the potential drawbacks of using the spatial extent when parts of the flood are contained by the topography.

Family-based association analysis with ordered categorical phenotypes, covariates and interactions

Genetic association analyses of family-based studies with ordered categorical phenotypes are often conducted using methods either for quantitative or for binary traits, which can lead to suboptimal analyses. Here we present an alternative likelihood-based method of analysis for single nucleotide polymorphism (SNP) genotypes and ordered categorical phenotypes in nuclear families of any size. Our approach, which extends our previous work for binary phenotypes, permits straightforward inclusion of covariate, gene-gene and gene-covariate interaction terms in the likelihood, incorporates a simple model for ascertainment and allows for family-specific effects in the hypothesis test. Additionally, our method produces interpretable parameter estimates and valid confidence intervals. We assess the proposed method using simulated data, and apply it to a polymorphism in the c-reactive protein (CRP) gene typed in families collected to investigate human systemic lupus erythematosus. By including sex interactions in the analysis, we show that the polymorphism is associated with anti-nuclear autoantibody (ANA) production in females, while there appears to be no effect in males.