scholarly journals Testing parallelism for the four-parameter logistic model with D-optimal design

2020 ◽  
Vol 15 (3) ◽  
pp. 273-284
Author(s):  
Lin Ying ◽  
Hyun Seung Won
Keyword(s):  
Optimal Design ◽  
Logistic Model ◽  
Test Preparation ◽  
Test Sample ◽  
Optimal Designs ◽  
Model Parameters ◽  
Reference Standard ◽  
Response Curves ◽  
Classical Design ◽  
Intersection Union Test

In order to determine the potency of the test preparation relative to the standard preparation, it is often important to test parallelism between a pair of dose-response curves of reference standard and test sample. Optimal designs are known to be more powerful in testing parallelism as compared to classical designs. In this study, D-optimal design was implemented to study the parallelism and compare+ its performance with a classical design. We modified D-optimal design to test the parallelism in the four-parameter logistic (4PL) model using Intersection-Union Test (IUT). IUT method is appropriate when the null hypothesis is expressed as a union of sets, and by using this method complicated tests involving several parameters are easily constructed. Since D-optimal design minimizes the variances of model parameters, it can bring more power to the IUT test. A simulation study will be presented to compare the empirical properties of the two different designs.

scholarly journals Optimal designs for asymmetric sigmoidal response curves in bioassays and immunoassays

2019 ◽  
Vol 29 (2) ◽  
pp. 421-436
Author(s):  
Seung Won Hyun ◽  
Weng Kee Wong ◽  
Yarong Yang
Keyword(s):  
Statistical Inference ◽  
Software Package ◽  
Logistic Models ◽  
Experimental Designs ◽  
Optimal Designs ◽  
Model Parameters ◽  
Response Curves ◽  
Different Types ◽  
User Friendly

The 5-parameter logistic (5PL) model is frequently used to model and analyze responses from bioassays and immunoassays which can be skewed. Various types of optimal experimental designs for 2, 3 and 4-parameter logistic models have been reported but not for the more complicated 5PL model. We construct different types of optimal designs for studying various features of the 5PL model and show that commonly used designs in bioassays and immunoassays are generally inefficient for statistical inference. To facilitate use of such designs in practice, we create a user-friendly software package to generate various tailor-made optimal designs for the 5PL model and evaluate robustness properties of a design under a variation of criteria, model forms and misspecification in the nominal values of the model parameters.

Optimal Design of Biaxial Tests for Structural Material Characterization of Flat Tissues

1996 ◽  
Vol 118 (1) ◽  
pp. 41-47 ◽  
Author(s):  
Y. Lanir ◽  
O. Lichtenstein ◽  
O. Imanuel
Keyword(s):  
Optimal Design ◽  
Material Characterization ◽  
Structural Model ◽  
Optimal Designs ◽  
Model Parameters ◽  
Optimal Sampling ◽  
Material Symmetry ◽  
Wide Range ◽  
Biaxial Tests

A rational methodology is developed for optimal design of biaxial stretch tests intended for estimating material parameters of flat tissues. It is applied to a structural model with a variety of constitutive equations and test protocols, and for a wide range of parameter levels. The results show nearly identical optimal designs under all circumstances. Optimality is obtained with two uniaxial stretch tests at mutually normal directions inclined by 22.5 deg to the axes of material symmetry. Protocols which include additional equibiaxial tests provide superior estimation with lower variance of estimates. Tests performed at angles 0, 45, and 90 deg to the axes of material symmetry provide unreliable estimates. The optimal sampling is variable and depends on the protocols and model parameters. In conclusion, the results indicate that biaxial tests can be improved over presently common procedures and show that this conclusion applies for a variety of circumstances.

Q-optimal experimental designs and close to them experimental designs for polynomial regression on the interval

2020 ◽  
Vol 86 (5) ◽  
pp. 65-72
Author(s):  
Yu. D. Grigoriev
Keyword(s):  
Optimal Design ◽  
Polynomial Regression ◽  
Direct Consequence ◽  
Experimental Designs ◽  
Optimal Designs ◽  
Software Systems ◽  
General Character ◽  
Support Points ◽  
Optimal Weights ◽  
Universal Expression

The problem of constructing Q-optimal experimental designs for polynomial regression on the interval [–1, 1] is considered. It is shown that well-known Malyutov – Fedorov designs using D-optimal designs (so-called Legendre spectrum) are other than Q-optimal designs. This statement is a direct consequence of Shabados remark which disproved the Erdős hypothesis that the spectrum (support points) of saturated D-optimal designs for polynomial regression on a segment appeared to be support points of saturated Q-optimal designs. We present a saturated exact Q-optimal design for polynomial regression with s = 3 which proves the Shabados notion and then extend this statement to approximate designs. It is shown that when s = 3, 4 the Malyutov – Fedorov theorem on approximate Q-optimal design is also incorrect, though it still stands for s = 1, 2. The Malyutov – Fedorov designs with Legendre spectrum are considered from the standpoint of their proximity to Q-optimal designs. Case studies revealed that they are close enough for small degrees s of polynomial regression. A universal expression for Q-optimal distribution of the weights pi for support points xi for an arbitrary spectrum is derived. The expression is used to tabulate the distribution of weights for Malyutov – Fedorov designs at s = 3, ..., 6. The general character of the obtained expression is noted for Q-optimal weights with A-optimal weight distribution (Pukelsheim distribution) for the same problem statement. In conclusion a brief recommendation on the numerical construction of Q-optimal designs is given. It is noted that in this case in addition to conventional numerical methods some software systems of symbolic computations using methods of resultants and elimination theory can be successfully applied. The examples of Q-optimal designs considered in the paper are constructed using precisely these methods.

Optimized blood sampling protocols and sequential design of kinetic experiments

1981 ◽  
Vol 240 (5) ◽  
pp. R259-R265 ◽  
Author(s):  
J. J. DiStefano
Keyword(s):  
Endocrine System ◽  
Primary Objective ◽  
Blood Sampling ◽  
Optimal Designs ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Reverse T3 ◽  
Model Parameter ◽  
Maximum Accuracy ◽  
Sampling Protocols

Design of optimal blood sampling protocols for kinetic experiments is discussed and evaluated, with the aid of several examples--including an endocrine system case study. The criterion of optimality is maximum accuracy of kinetic model parameter estimates. A simple example illustrates why a sequential experiment approach is required; optimal designs depend on the true model parameter values, knowledge of which is usually a primary objective of the experiment, as well as the structure of the model and the measurement error (e.g., assay) variance. The methodology is evaluated from the results of a series of experiments designed to quantify the dynamics of distribution and metabolism of three iodothyronines, T3, T4, and reverse-T3. This analysis indicates that 1) the sequential optimal experiment approach can be effective and efficient in the laboratory, 2) it works in the presence of reasonably controlled biological variation, producing sufficiently robust sampling protocols, and 3) optimal designs can be highly efficient designs in practice, requiring for maximum accuracy a number of blood samples equal to the number of independently adjustable model parameters, no more or less.

scholarly journals BAYESIAN APPROACH TO THE D-OPTIMAL FOR MIXTURE EXPERIMENTAL DESIGN

2019 ◽  
Vol 3 (2) ◽  
pp. 109
Author(s):  
Uqwatul Alma Wizsa
Keyword(s):  
Optimal Design ◽  
Quadratic Model ◽  
Model Parameters ◽  
Potential Term ◽  
Lattice Design ◽  
Simplex Lattice Design ◽  
Simplex Lattice ◽  
Mixture Experimental Design ◽  
Special Case ◽  
Experimental Region

A mixture experiment is a special case of response surface methodology in which the value of the components are proportions. In case there are constraints on the proportions, the experimental region can be not a simplex. The classical designs such as a simplex-lattice design or a simplex-centroid design, in some cases, cannot fit to the problem. In this case, optimal design come up as a solution. A D-optimal design is seeking a design in which minimizing the covariance of the model parameter.  Some model parameters are important and some of them are less important. As the priority of the parameters, the prior information of parameters is needed in advance. This brings to a Bayesian D-optimal design. This research was focus on a baking experiment in which consisted of three ingredients with lower bounds on the proportion of the ingredients. The assumption model was a quadratic model. Due to the priority of the model parameters, the Bayesian D-optimal design was used to solve the problem. A point-exchange algorithm was developed to find the optimal design. Nineteen candidates is used to choose twelve design points. It found that the potential term is feasible to the actual model and design points represent overall points in the design area.

scholarly journals A Highly D‑efficient Spring Balance Weighing Design for an Even Number of Objects

2019 ◽  
Vol 5 (344) ◽  
pp. 17-27
Author(s):  
Małgorzata Graczyk ◽  
Bronisław Ceranka
Keyword(s):  
Optimal Design ◽  
Sufficient Conditions ◽  
Optimality Criteria ◽  
Point Of View ◽  
Necessary And Sufficient Conditions ◽  
Optimal Designs ◽  
Efficient Design ◽  
Spring Balance ◽  
Experimental Errors ◽  
Necessary And Sufficient

The problem of determining unknown measurements of objects in the model of spring balance weighing designs is presented. These designs are considered under the assumption that experimental errors are uncorrelated and that they have the same variances. The relations between the parameters of weighing designs are deliberated from the point of view of optimality criteria. In the paper, designs in which the product of the variances of estimators is possibly the smallest one, i.e. D‑optimal designs, are studied. A highly D‑efficient design in classes in which a D‑optimal design does not exist are determined. The necessary and sufficient conditions under which a highly efficient design exists and methods of its construction, along with relevant examples, are introduced.

Optimal Design of Plastic Structures for Fixed and Shakedown Loadings

1973 ◽  
Vol 40 (2) ◽  
pp. 595-599 ◽  
Author(s):  
M. Z. Cohn ◽  
S. R. Parimi
Keyword(s):  
Optimal Design ◽  
Loading Condition ◽  
Minimum Weight ◽  
Optimal Solution ◽  
Failure Criteria ◽  
Optimal Designs ◽  
Design Solution ◽  
Variable Loading ◽  
Framed Structures ◽  
A Value

Optimal (minimum weight) solutions for plastic framed structures under shakedown conditions are found by linear programming. Designs that are optimal for two failure criteria (collapse under fixed loads and collapse under variable repeated loads) are then investigated. It is found that these designs are governed by the ratio of the specified factors defining the two failure criteria, i.e., for shakedown, λs and for collapse under fixed loading, λ. Below a certain value (λs/λ)min the optimal solution under fixed loading is also optimal for fixed and shakedown loading. Above a value (λs/λ)max the optimal design for variable loading is also optimal under the two loading conditions. For intermediate values of λs/λ the optimal design that simultaneously satisfies the two criteria is different from the optimal designs for each independent loading condition. An example illustrates the effect of λs/λ on the nature of the design solution.

Log-Logistic Analysis of Herbicide Dose-Response Relationships

1995 ◽  
Vol 9 (2) ◽  
pp. 218-227 ◽  
Author(s):  
Steven S. Seefeldt ◽  
Jens Erik Jensen ◽  
E. Patrick Fuerst
Keyword(s):  
Dose Response ◽  
Logistic Model ◽  
Response Analysis ◽  
Analysis Method ◽  
Weed Science ◽  
Response Curves ◽  
Herbicide Resistant ◽  
Logistic Analysis ◽  
Analysis Methods ◽  
The Difference

Dose-response studies are an important tool in weed science. The use of such studies has become especially prevalent following the widespread development of herbicide resistant weeds. In the past, analyses of dose-response studies have utilized various types of transformations and equations which can be validated with several statistical techniques. Most dose-response analysis methods 1) do not accurately describe data at the extremes of doses and 2) do not provide a proper statistical test for the difference(s) between two or more dose-response curves. Consequently, results of dose-response studies are analyzed and reported in a great variety of ways, and comparison of results among various researchers is not possible. The objective of this paper is to review the principles involved in dose-response research and explain the log-logistic analysis of herbicide dose-response relationships. In this paper the log-logistic model is illustrated using a nonlinear computer analysis of experimental data. The log-logistic model is an appropriate method for analyzing most dose-response studies. This model has been used widely and successfully in weed science for many years in Europe. The log-logistic model possesses several clear advantages over other analysis methods and the authors suggest that it should be widely adopted as a standard herbicide dose-response analysis method.

Investigations on Optimal Design of a U-Tube Steam Generator

2010 ◽  
Author(s):  
Hui-min Qin ◽  
Chang-qi Yan ◽  
Meng Wang ◽  
Shi-jing He
Keyword(s):  
Optimal Design ◽  
Steam Generator ◽  
Optimization Techniques ◽  
Point Of View ◽  
Geometric Constraints ◽  
Optimal Designs ◽  
Optimal Method ◽  
Obvious Effect ◽  
Pressurized Water ◽  
Performance Point

Steam generator is one of the key equipments in the pressurized water reactor, from the performance point of view, it is necessary to apply optimization techniques to the design of the steam generator. In this work, the optimal designs of a U-tube steam generator (UTSG), taking minimization of the total volume and net weight as objective respectively, are carried out by considering thermohydraulic and geometric constraints using a complex-genetic algorithm (CGA). And the sensitivities of some parameters which influence the total volume and net weight of UTSG are also analyzed. Under the condition of constant secondary thermalhydraulic parameters of the steam generator, the optimal design indicates an obvious effect taking either the overall volume or the total weight of the steam generator as the objective. The optimization results show that the proposed optimal method is feasible and effective. And the results of optimal designs and sensitivity analysis would provide guidance in the engineering design of UTSG.

scholarly journals Optimal designs for group randomized trials and group administered treatments with outcomes at the subject and group level

2019 ◽  
Vol 29 (3) ◽  
pp. 797-810
Author(s):  
Mirjam Moerbeek
Keyword(s):  
Optimal Design ◽  
Randomized Trials ◽  
Smoking Prevention ◽  
Optimal Designs ◽  
Multiple Objective ◽  
Group Level ◽  
Group Randomized Trials ◽  
Treatment Conditions ◽  
The Subject ◽  
And Control

With group randomized trials complete groups of subject are randomized to treatment conditions. Such grouping also occurs in individually randomized trials where treatment is administered in groups. Outcomes may be measured at the level of the subject, but also at the level of the group. The optimal design determines the number of groups and the number of subjects per group in the intervention and control conditions. It is found by taking a budgetary constraint into account, where costs are associated with implementing the intervention and control, and with taking measurements on subject and groups. The optimal design is found such that the effect of treatment is estimated with highest efficiency, and the total costs do not exceed the budget that is available. The design that is optimal for the outcome at the subject level is not necessarily optimal for the outcome at the group level. Multiple-objective optimal designs consider both outcomes simultaneously. Their aim is to find a design that has high efficiencies for both outcome measures. An Internet application for finding the multiple-objective optimal design is demonstrated on the basis of an example from smoking prevention in primary education, and another example on consultation time in primary care.

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