Regression Models for Clinical Trials with Correlated Categorical Responses

Regression models for correlated categorical data are presented in which the covariance is a function of measured effects. The regression and covariance parameters are estimated by extended least square methods. A numerical example of a clinical trial comparing two antiemetic treatment regimes for patients receiving chemotherapy is given to illustrate the approach.     

Effects of competition and shading in planktonic communities

A model for several algal species which compete both for light and for nutrients, and which are also subject to settling and diffusion, is considered. The settling speeds and diffusion coefficients are assumed to be small, in a sense to be made precise later, and a singular perturbation argument is used. In certain cases vertical segregation of the algal species is observed, and the mechanism for this is interpreted biologically.Supported by the Danish Natural Science Research Council (Grant No. 11-8321)     

Vertical structure of Erica umbellata,a representative species of European Ibero-Atlantic dry heaths

The canopy structure of Erica umbellata was studied in order to (a) quantify biomass allocation among several organ types, (b) analyse the possible changes in vertical structure related to season and plant size, and (c) evaluate the effectiveness of non-destructive measures to estimate biomass for a species that is declining in some areas, due to fire and other human disturbances. The study was conducted in NW Spain, sampling E. umbellata plants belonging to three size groups. Destructive (biomass) and non-destructive (frequency, height, diameter) measures were used to characterise the vertical distribution and abundance of photosynthetic, woody, reproductive and dead organs. Allometric equations were calculated to estimate total mass using non-destructive measurements. As E. umbellata increases in size, those organs with a higher renewal rate (leaves, new stems, flowers) increase in the upper strata. Seasonal differences are recorded for the reproductive organs and new stems. A sharp decrease in the green/total phytomass ratio (from 0.51 to 0.17) is observed as plant size increases. Organ biomass can be accurately predicted from total weight and it is also possible to estimate the total weight from non-destructive measures, which provides an easier way of recording data in the field.     

Removing Cancer when it is Correlated with other Causes of Death

This paper presents an identifiability theorem in the theory of dependent competing risks and it applies the result by examining the effect of removing cancer from the United States population when cancer is correlated with the other causes of death. The paper shows how dependence can be modeled with copula functions and it shows that calculating the survival probabilities after cancer is removed is equivalent to solving a system of nonlinear differential equations.     

Three-dimensional Orthotropic Viscoelastic Finite Element Model of a Human Ligament

Ligaments undergo finite strain displaying hyperelastic behaviour as the initially tangled fibrils present straighten out, combined with viscoelastic behaviour (strain rate sensitivity). In the present study the anterior cruciate ligament of the human knee joint is modelled in three dimensions to gain an understanding of the stress distribution over the ligament due to motion imposed on the ends, determined from experimental studies. A three dimensional, finite strain material model of ligaments has recently been proposed by Pioletti in Ref. [2]. It is attractive as it separates out elastic stress from that due to the present strain rate and that due to the past history of deformation. However, it treats the ligament as isotropic and incompressible. While the second assumption is reasonable, the first is clearly untrue. In the present study an alternative model of the elastic behaviour due to Bonet and Burton (Ref. [4]) is generalized. Bonet and Burton consider finite strain with constant modulii for the fibres and for the matrix of a transversely isotropic composite. In the present work, the fibre modulus is first made to increase exponentially from zero with an invariant that provides a measure of the stretch in the fibre direction. At 12% strain in the fibre direction, a new reference state is then adopted, after which the material modulus is made constant, as in Bonet and Burton's model. The strain rate dependence can be added, either using Pioletti's isotropic approximation, or by making the effect depend on the strain rate in the fibre direction only.

A solid model of a ligament is constructed, based on experimentally measured sections, and the deformation predicted using explicit integration in time. This approach simplifies the coding of the material model, but has a limitation due to the detrimental effect on stability of integration of the substantial damping implied by the nonlinear dependence of stress on strain rate. At present, an artificially high density is being used to provide stability, while the dynamics are being removed from the solution using artificial viscosity. The result is a quasi-static solution incorporating the effect of strain rate. Alternate approaches to material modelling and integration are discussed, that may result in a better model.     

Evolution of dispersal and life history interact to drive accelerating spread of an invasive species

Populations on the edge of an expanding range are subject to unique evolutionary pressures acting on their life‐history and dispersal traits. Empirical evidence and theory suggest that traits there can evolve rapidly enough to interact with ecological dynamics, potentially giving rise to accelerating spread. Nevertheless, which of several evolutionary mechanisms drive this interaction between evolution and spread remains an open question. We propose an integrated theoretical framework for partitioning the contributions of different evolutionary mechanisms to accelerating spread, and we apply this model to invasive cane toads in northern Australia. In doing so, we identify a previously unrecognised evolutionary process that involves an interaction between life‐history and dispersal evolution during range shift. In roughly equal parts, life‐history evolution, dispersal evolution and their interaction led to a doubling of distance spread by cane toads in our model, highlighting the potential importance of multiple evolutionary processes in the dynamics of range expansion.     

A Comment on Maximum Likelihood Estimation for Finite Mixtures of Distributions

Iterative numerical methods are necessary to find the maximum likelihood estimates for finite mixture distributions. This paper shows that it will often be possible to analytically reduce the number of equations that must ultimately be solved numerically. Such a reduction in dimensionality has not generally been used, or sought after, for mixture distributions. Yet such results are easily derived when each mixture component is assumed to be from the same parametric model within the exponential family.     

Improved Prediction of Body Fat by Measuring Skinfold Thickness,Circumferences, and Bone Breadths

Objective: To develop improved predictive regression equations for body fat content derived from common anthropometric measurements. Research Methods and Procedures: 117 healthy German subjects, 46 men and 71 women, 26 to 67 years of age, from two different studies were assigned to a validation and a cross‐validation group. Common anthropometric measurements and body composition by DXA were obtained. Equations using anthropometric measurements predicting body fat mass (BFM) with DXA as a reference method were developed using regression models. Results: The final best predictive sex‐specific equations combining skinfold thicknesses (SF), circumferences, and bone breadth measurements were as follows: BFM_New (kg) for men = ?40.750 + [(0.397 × waist circumference) + [6.568 × (log triceps SF + log subscapular SF + log abdominal SF)]] and BFM_New (kg) for women = ?75.231 + [(0.512 × hip circumference) + [8.889 × (log chin SF + log triceps SF + log subscapular SF)] + (1.905 × knee breadth)]. The estimates of BFM from both validation and cross‐validation had an excellent correlation, showed excellent correspondence to the DXA estimates, and showed a negligible tendency to underestimate percent body fat in subjects with higher BFM compared with equations using a two‐compartment (Durnin and Womersley) or a four‐compartment (Peterson) model as the reference method. Discussion: Combining skinfold thicknesses with circumference and/or bone breadth measures provide a more precise prediction of percent body fat in comparison with established SF equations. Our equations are recommended for use in clinical or epidemiological settings in populations with similar ethnic background.