Single-valued Criterion Research Articles

Prediction Variance Properties of Third-Order Response Surface Designs in the Hypersphere

The variance dispersion graphs (VDGs) and the fraction of design space (FDS) graphs are two graphical methods that effectively describe and evaluate the points of best and worst prediction capability of a design using the scaled prediction variance properties. These graphs are often utilized as an alternative to the single-value criteria such as D- and E- when they fail to describe the true nature of designs. In this paper, the VDGs and FDS graphs of third-order orthogonal uniform composite designs (OUCD₄) and orthogonal array composite designs (OACD₄) using the scaled-prediction variance properties in the spherical region for 2 to 7 factors are studied throughout the design region and over a fraction of space. Single-valued criteria such as D-, A- and G-optimality are also studied. The results obtained show that the OUCD₄ is more optimal than the OACD₄ in terms of D-, A- and G-optimality. The OUCD₄ was shown to possess a more stable and uniform scaled-prediction variance throughout the design region and over a fraction of design space than the OACD₄ although the stability of both designs slightly deteriorated towards the extremes.

A Monte Carlo study of different LET definitions and calculation parameters for proton beam therapy

The strong in vitro evidence that proton Relative Biological Effectiveness (RBE) varies with Linear Energy Transfer (LET) has led to an interest in applying LET within treatment planning. However, there is a lack of consensus on LET definition, Monte Carlo (MC) parameters or clinical methodology. This work aims to investigate how common variations of LET definition may affect potential clinical applications. MC simulations (GATE/GEANT4) were used to calculate absorbed dose and different types of LET for a simple Spread Out Bragg Peak (SOBP) and for four clinical PBT plans covering a range of tumour sites. Variations in the following LET calculation methods were considered: (i) averaging (dose-averaged LET (LETd) & track-averaged LET); (ii) scoring (LETd to water, to medium and to mass density); (iii) particle inclusion (LETd to all protons, to primary protons and to particles); (iv) MC settings (hit type and Maximum Step Size (MSS)). LET distributions were compared using: qualitative comparison, LET Volume Histograms (LVHs), single value criteria (maximum and mean values) and optimised LET-weighted dose models. Substantial differences were found between LET values in averaging, scoring and particle type. These differences depended on the methodology, but for one patient a difference of ∼100% was observed between the maximum LETd for all particles and maximum LETd for all protons within the brainstem in the high isodose region (4 keV μm−1 and 8 keV μm−1 respectively). An RBE model using LETd including heavier ions was found to predict substantially different LET-weighted dose compared to those using other LET definitions. In conclusion, the selection of LET definition may affect the results of clinical metrics considered in treatment planning and the results of an RBE model. The authors’ advocate for the scoring of dose-averaged LET to water for primary and secondary protons using a random hit type and automated MSS.

Prediction Variance Capabilities of Third-Order Response Surface Designs for Cuboidal Regions

Experimenters often evaluate the steadiness and consistency of designs over the region of interest by means of the prediction variance capabilities using the variance dispersion graph and the fraction of design space graph. The variance dispersion graph and the fraction of design space graph effectively describe the prediction variance capabilities of a design in the region of interest. However, the prediction variance capabilities of third-order response surface designs have not been studied in the literature. In this paper, the prediction variance capabilities of two third-order response surface designs term augmented orthogonal uniform composite designs and orthogonal array composite designs in the cuboidal region for 3≤k≤7 with <img src=image/13424429_01.gif> center points are examined. The prediction variance capabilities are evaluated using the variance dispersion graph and the fraction of design space graph. Also, D-, E-, G-and T-optimality criteria are used in evaluating these designs in terms of single-value criterion. The results obtained show that the augmented orthogonal uniform composite designs have better prediction variance capabilities in the cuboidal region in the terms of the variance dispersion graphs for factors 3 and 4. The augmented orthogonal uniform composite designs also have better prediction variance capabilities for 3≤k≤7 compare to the orthogonal array composite designs in terms of the fraction of design space graph. The augmented orthogonal uniform composite designs are shown to be superior over the orthogonal array composite designs in terms of D-, E-, G-and T-optimality criteria for single-value criterion. This shows that the performances of the prediction variance capabilities of third-order response surface designs can be clearly visualized by means of the variance dispersion graph and fraction of design space and should be consider over the single-value criteria even though the single value-criteria show some degree of design performance. The augmented orthogonal uniform composite design is should often be considered in experimentation over the orthogonal array composite design since the augmented orthogonal uniform composite design performance better.

Graphical evaluation of robust parameter designs based on extended scaled prediction variance and extended spherical average prediction variance

ABSTRACTFor any response surface design, there are locations in the design region where responses are estimated well and locations where estimation is relatively poor. Consequently, graphical evaluation—such as variance dispersion graphs and the fraction of design space—is used as an alternative to a single-valued criterion. Such plots are used to investigate and compare the prediction capabilities of certain response surface designs currently available to the researcher. In this article, we propose the extended scaled prediction variance and extended spherical average prediction variance as prediction methods. We also illustrate how graphical methods can be employed to evaluate robust parameter designs.

Modified Exact Single-Value Criteria for Partial Replications of the Central Composite Design

Replication of the factorial (cube) and/or axial (star) portions of the central composite design (CCD in response surface exploration has gained great attention recently. Some well known metrics (called single-value functions or criteria) and graphical methods are utilized in evaluating the regression based response surface design. The single-value functions considered here are the A-efficiency, and the D-efficiency, , where , k is number of factors, is the kth design measure, is the design’s information matrix, is its inverse and N is the total number of experimental runs. These two functions are very popular in parameter estimation in response surface methodology. The exact measures of these two design criteria will be developed analytically in this work to account for partial replication of the cube and/or star components of the CCD. This will alleviate the burden of manual computation of these metrics when there are partial replications and reduce over reliance on software values which, often, are approximate values and maybe inaccurate.

Evaluation of Orthogonally Blocked Central Composite Designs with Partial Replications

In this work, the orthogonal blocking of the central composite designs is evaluated by considering various equal and unequal replications of the centre point in the factorial (cube) and axial (star) blocks. The A-, D- and G-efficiencies as well as the V-criterion are the single-value design criteria used to examine the prediction performances of the designs. The fraction of design space plot is the graphical method used to display the prediction variance characteristics of these designs throughout the entire design space. The cube and star portions are also replicated to enhance the performance of the designs. The results show that higher and equal replication of the centre points in the blocks as well as more centre points in the star blocks than the cube blocks improve the prediction capabilities of the orthogonally blocked CCD in spherical region.

Measuring the Perceived Importance of Speech Segments for Transmission over IP Networks

SUMMARY This paper presents a way of using a linear regression model to produce a single-valued criterion that indicates the perceived importance of each block in a stream of speech blocks. This method is superior to the conventional approach, voice activity detection (VAD), in that it provides a dynamically changing priority value for speech segments with finer granularity. The approach can be used in conjunction with scalable speech coding techniques in the context of IP QoS services to achieve a flexible form of quality control for speech transmission. A simple linear regression model is used to estimate a mean opinion score (MOS) of the various cases of missing speech segments. The estimated MOS is a continuous value that can be mapped to priority levels with arbitrary granularity. Through subjective evaluation, we show the validity of the calculated priority values.

Using Audiometric Thresholds and Word Recognition in a Treatment Study

First, to examine a possible limit on significant results imposed by a progressive floor effect for hearing threshold improvement in a treatment study. This floor effect for hearing recovery suggests that if inclusion criteria are not set sufficiently high, the superiority of a treatment group may not be detectable. Second, to examine the outcomes when using two different types of criteria for significant change in a subject's word recognition score. Several single-number criteria (e.g., 15 percentage points) are compared with the 95% (p=0.05) criteria from the binomial critical difference table for monosyllables. Critical differences for binomial variables change depending on whether the starting value lies in the middle (near 50% correct) or at either extreme of the range of scores (0 or 100%). Different judgments of significant word recognition improvement (or decrease) using binomial versus single-value criteria are presented. A recent treatment study of sudden sensorineural hearing loss (n=318) is used to illustrate these effects. First, there is a progressive floor effect of presenting severity that co-varies with the outcome measure hearing threshold recovery. In some designs, this may act to constrain the ability to detect a significant difference. Second, in the example data set, the use of single-value criteria for significant within-subject change in word recognition (e.g., 15 percentage points) introduced a miscategorization error rate of approximately 9% when compared with the result of the binomial 95% critical difference table.

Variance Dispersion Properties of Second-Order Response Surface Designs

Often, second-order response surface designs are chosen on the basis of a single-valued criterion such as D- or G-optimality. While such criteria provide a useful basis for selecting designs, they often fail to convey the true nature of the design's support of the fitted model in terms of prediction properties over a region of interest. As an alternative to a single-valued criterion, we propose variance dispersion graphs to compare various second-order response surface designs. This graphical procedure is used to examine the relative strengths and weaknesses of such popular designs as the central composite, Box-Behnken, and small composite. Areas in the region of interest where prediction is relatively good and relatively poor are discussed, and designs which have good overall performance are highlighted. A summary comparison of such saturates or near-saturates designs as the hybrid, Box-Draper, and Notz designs is given together with recommendations concerning the proper choice among these designs. Finally, we show how the use of the D-optimality criterion can lead to misleading results when the user is truly interested in response surface prediction.

Prediction of effects of weather on image quality: preliminary results of model validation

Using the atmospheric modulation transfer function area (MTFA) as a single-valued numerical criterion for image quality horizontally near the ground propagated through the atmosphere, a statistical study of atmospheric imaging data accumulated over a three-year period has led to the determination of regression coefficients with which to quantitatively predict image quality as a function of wavelength, over the 400-1000- nm wavelength region, according to weather forecast. Utilization of this procedure is simple: one plugs in expected values for wind speed, air temperature, and relative humidity in the regression coefficient expression for MTFA. The larger the expected MTFA, the better the expected image quality. Two sets of regression coefficient data have been obtained, one each for desert and nondesert climates, corresponding to summer and winter data here. Preliminary experimentation over a different line of sight indicates that the accuracy of the prediction is fairly reliable.