Fitting models for the joint action of two drugs using SAS(R)

Combinations of drugs are increasingly being used for a wide variety of diseases and conditions. A pre-clinical study may allow the investigation of the response at a large number of dose combinations. In determining the response to a drug combination, interest may lie in seeking evidence of synergism, in which the joint action is greater than the actions of the individual drugs, or of antagonism, in which it is less. Two well-known response surface models representing no interaction are Loewe additivity and Bliss independence, and Loewe or Bliss synergism or antagonism is defined relative to these. We illustrate an approach to fitting these models for the case in which the marginal single drug dose-response relationships are represented by four-parameter logistic curves with common upper and lower limits, and where the response variable is normally distributed with a common variance about the dose-response curve. When the dose-response curves are not parallel, the relative potency of the two drugs varies according to the magnitude of the desired effect and the models for Loewe additivity and synergism/antagonism cannot be explicitly expressed. We present an iterative approach to fitting these models without the assumption of parallel dose-response curves. A goodness-of-fit test based on residuals is also described. Implementation using the SAS NLIN procedure is illustrated using data from a pre-clinical study. Copyright © 2007 John Wiley & Sons, Ltd.

A Generic Deformable Model for Vehicle Recognition

This paper reports the development of a highly parameterised 3-D model able to adopt the shapes of a wide variety of different classes of vehicles (cars, vans, buses, etc), and its subsequent specialisation to a generic car class which accounts for most commonly encountered types of car (includng saloon, hatchback and estate cars). An interactive tool has been developed to obtain sample data for vehicles from video images. A PCA description of the manually sampled data provides a deformable model in which a single instance is described as a 6 parameter vector. Both the pose and the structure of a car can be recovered by fitting the PCA model to an image. The recovered description is sufficiently accurate to discriminate between vehicle sub-classes.

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.

Calibration and sensitivity analysis of a river water quality model under unsteady flow conditions

Water quality models generally require a relatively large number of parameters to define their functional relationships, and since prior information on parameter values is limited, these are commonly defined by fitting the model to observed data. In this paper, the identifiability of water quality parameters and the associated uncertainty in model simulations are investigated. A modification to the water quality model `Quality Simulation Along River Systems' is presented in which an improved flow component is used within the existing water quality model framework. The performance of the model is evaluated in an application to the Bedford Ouse river, UK, using a Monte-Carlo analysis toolbox. The essential framework of the model proved to be sound, and calibration and validation performance was generally good. However some supposedly important water quality parameters associated with algal activity were found to be completely insensitive, and hence non-identifiable, within the model structure, while others (nitrification and sedimentation) had optimum values at or close to zero, indicating that those processes were not detectable from the data set examined. (C) 2003 Elsevier Science B.V. All rights reserved.

Parameter estimation using a particle method: inferring mixing coefficients from sea level observations

This paper presents a first attempt to estimate mixing parameters from sea level observations using a particle method based on importance sampling. The method is applied to an ensemble of 128 members of model simulations with a global ocean general circulation model of high complexity. Idealized twin experiments demonstrate that the method is able to accurately reconstruct mixing parameters from an observed mean sea level field when mixing is assumed to be spatially homogeneous. An experiment with inhomogeneous eddy coefficients fails because of the limited ensemble size. This is overcome by the introduction of local weighting, which is able to capture spatial variations in mixing qualitatively. As the sensitivity of sea level for variations in mixing is higher for low values of mixing coefficients, the method works relatively well in regions of low eddy activity.

The effects of environmental perturbation and measurement error on estimates of the shape parameter in the theta-logistic model of population regulation

The theta-logistic is a widely used generalisation of the logistic model of regulated biological processes which is used in particular to model population regulation. Then the parameter theta gives the shape of the relationship between per-capita population growth rate and population size. Estimation of theta from population counts is however subject to bias, particularly when there are measurement errors. Here we identify factors disposing towards accurate estimation of theta by simulation of populations regulated according to the theta-logistic model. Factors investigated were measurement error, environmental perturbation and length of time series. Large measurement errors bias estimates of theta towards zero. Where estimated theta is close to zero, the estimated annual return rate may help resolve whether this is due to bias. Environmental perturbations help yield unbiased estimates of theta. Where environmental perturbations are large, estimates of theta are likely to be reliable even when measurement errors are also large. By contrast where the environment is relatively constant, unbiased estimates of theta can only be obtained if populations are counted precisely Our results have practical conclusions for the design of long-term population surveys. Estimation of the precision of population counts would be valuable, and could be achieved in practice by repeating counts in at least some years. Increasing the length of time series beyond ten or 20 years yields only small benefits. if populations are measured with appropriate accuracy, given the level of environmental perturbation, unbiased estimates can be obtained from relatively short censuses. These conclusions are optimistic for estimation of theta. (C) 2008 Elsevier B.V All rights reserved.

A swarm pattern transformation method based on macroscopic parameter operations

The work reported in this paper is motivated by biomimetic inspiration - the transformation of patterns. The major issue addressed is the development of feasible methods for transformation based on a macroscopic tool. The general requirement for the feasibility of the transformation method is determined by classifying pattern formation approaches an their characteristics. A formal definition for pattern transformation is provided and four special cases namely, elementary and geometric transformation based on repositioning all and some robotic agents are introduced. A feasible method for transforming patterns geometrically, based on the macroscopic parameter operation of a swarm is considered. The transformation method is applied to a swarm model which lends itself to the transformation technique. Simulation studies are developed to validate the feasibility of the approach, and do indeed confirm the approach.