Optimal design criteria for discrimination and estimation in nonlinear models.

Nonlinear models are common in pharmacokinetics and pharmacodynamics. To date, most work in design in this area has concentrated on parameter estimation. Here, we introduce the idea of optimization of both estimation and model selection. However, experimental designs that provide powerful discrimination between a pair of competing model structures are rarely efficient in terms of estimating the parameters under each model. Conversely, designs which are efficient for parameter estimation may not provide suitable power to discriminate between the models. Several different methods of addressing both of these objectives simultaneously are introduced in this paper and are compared to an existing optimality criterion.

Simultaneous versus sequential optimal design for pharmacokinetic-pharmacodynamic models with FO and FOCE considerations.

We consider nested multiple response models which are used extensively in the area of pharmacometrics. Given the conditional nature of such models, differences in predicted responses are a consequence of different assumptions about how the models interact. As such, sequential versus simultaneous and First Order (FO) versus First Order Conditional Estimation (FOCE) techniques have been explored in the literature where it was found that the sequential and FO approaches can produce biased results. It is therefore of interest to determine any design consequences between the various methods and approximations. As optimal design for nonlinear mixed effects models is dependent upon initial parameter estimates and an approximation to the expected Fisher information matrix, it is necessary to incorporate any influence of nonlinearity (or parameter-effects curvature) into our exploration. Hence, sequential versus simultaneous design with FO and FOCE considerations are compared under low, typical and high degrees of nonlinearity. Additionally, predicted standard errors of parameters are also compared to empirical estimates formed via a simulation/estimation study in NONMEM. Initially, design theory for nested multiple response models is developed and approaches mentioned above are investigated by considering a pharmacokinetic-pharmacodynamic model found in the literature. We consider design for situations where all responses are continuous and extend this methodology to the case where a response may be a discrete random variable. In particular, for a binary response pharmacodynamic model, it is conjectured that such responses will offer little information about all parameters and hence a sequential optimization, in the form of product design optimality, may yield near optimal designs.

Compound optimal design criteria for nonlinear models.

Three approaches for combining parameter estimation with opposing design criteria are proposed for nonlinear models. The first method discussed is the technique found in the literature and as such is the reference method for this paper. The compound crtierion is formed by maximizing a weighted product of efficiencies. The second criterion involves maximizing an opposing criterion while minimizing a defined loss function. The third method simultaneously maximizes both efficiencies with respect to parameter estimation and an opposing criterion with a multiple objective simulated annealing algorithm. The examples presented are based on a PK-model and a generalized linear model found in the literature.

Optimal designs for studying bioimpedance.

D-optimal designs for nonlinear fixed and mixed effects models are explored, and the theory is applied to the measurement and analysis of bioelectrical impedance. Bioimpedance is known to vary more at extreme frequencies than others. D-optimal designs that account for this variation, and also possible mis-specification of initial parameter estimates, are considered in an attempt to find designs that will provide good parameter estimates in practice.

Optimal crossover designs for logistic regression models in pharmacodynamics.

Pharmacodynamics (PD) is the study of the biochemical and physiological effects of drugs. The construction of optimal designs for dose-ranging trials with multiple periods is considered in this paper, where the outcome of the trial (the effect of the drug) is considered to be a binary response: the success or failure of a drug to bring about a particular change in the subject after a given amount of time. The carryover effect of each dose from one period to the next is assumed to be proportional to the direct effect. It is shown for a logistic regression model that the efficiency of optimal parallel (single-period) or crossover (two-period) design is substantially greater than a balanced design. The optimal designs are also shown to be robust to misspecification of the value of the parameters. Finally, the parallel and crossover designs are combined to provide the experimenter with greater flexibility.

Effect of ethylene vinyl acetate (EVA) closed cell foam on transmitted forces in mouthguard material.

OBJECTIVES: To compare transmitted forces through ethylene vinyl acetate (EVA) mouthguard material and the same EVA material with gas inclusions in the form of a closed cell foam. METHOD: EVA mouthguard materials with and without foam gas inclusions and 4 mm thick were impacted with a constant force from an impact pendulum. Various porosity levels in the foam materials were produced by 1%, 5%, and 10% by weight foaming agent. The forces transmitted through the EVA after energy absorption by the test materials were measured with a force sensor and compared. RESULTS: Only minor non-significant differences in transmitted forces through the EVA with and without foam were shown. CONCLUSIONS: The inclusion of gas in the form of a closed cell foam in 4 mm thick EVA mouthguard materials did not improve the impact performance of the EVA mouthguard material.

Beneficial effects of air inclusions on the performance of ethylene vinyl acetate (EVA) mouthguard material.

OBJECTIVE: To investigate the impact characteristics of an ethylene vinyl acetate (EVA) mouthguard material with regulated air inclusions, which included various air cell volumes and wall thickness between air cells. In particular, the aim was to identify the magnitude and direction of forces within the impacts. METHOD: EVA mouthguard material, 4 mm thick and with and without air inclusions, was impacted with a constant force impact pendulum with an energy of 4.4 J and a velocity of 3 m/s. Transmitted forces through the EVA material were measured using an accelerometer, which also allowed the determination of force direction and magnitude within the impacts. RESULTS: Statistically significant reductions in the transmitted forces were observed with all the air inclusion materials when compared with EVA without air inclusions. Maximum transmitted force through one air inclusion material was reduced by 32%. Force rebound was eliminated in one material, and reduced second force impulses were observed in all the air inclusion materials. CONCLUSION: The regulated air inclusions improved the impact characteristics of the EVA mouthguard material, the material most commonly used in mouthguards world wide.

The effect on energy absorption of hard inserts in laminated EVA mouthguards.

One of the suggestions for using laminated mouthguards is the inclusion of hard inserts to improve mouthguard performance. However, there is a paucity of published material on the use of such inserts and this study was designed to investigate this theory. Hard layers of ethylene vinyl acetate (EVA) were included in laminated mouthguard sheets which were then subject to repeated impacts with an impact rig. Hard inserts resulted in reduced energy absorption when compared with a control sheet of the same material and approximate thickness but without the hard inserts. Additionally, the further the hard inserts were located from the impact surface, the least reduction there was on energy absorption.

An improved mouthguard material.

A modified mouthguard material which reduces transmitted forces is described. Tests showed that the inclusion of air cells in a 4 mm thick polyvinyl-acetate-polyethylene (EVA) copolymer reduced the effects of impacts of less than 10 kN when compared with a material of the same EVA composition and thickness. The EVA copolymer with air-inclusions is suitable for the construction of stock mouth-formed and vacuum-formed mouthguards. The improved elastic properties of the modified mouthguard material reduced transmitted forces by 32 per cent when compared with traditional EVA mouthguard polymers of the same thickness.

Forces transmitted through EVA mouthguard materials of different types and thickness.

Previous studies into sporting mouthguards have been mainly attitudinal or epidemiological. The aim of the present study was to build an impact rig to measure the impact absorbed by mouthguard materials of various thicknesses. The acceleration of the pendulum of the rig was measured and used to calculate the force transmitted to the materials. Impact tests were also performed on three commercially available mouthguard materials. Tests showed that the force transmitted through mouthguard materials was inversely related to the material thickness. Mouthguard construction techniques with ethylene vinyl acetate (EVA) plastics should be monitored to avoid occlusal thinning especially on the incisal edges. Thinning results in reduction in the protection offered by the mouthguard.