Proposed Test Procedure Research Articles

Comparison Between Two Experimental Procedures for Cyclic Plastic Characterization of High Strength Steel Sheets

In finite element analysis of sheet metal forming the use of combined isotropic-kinematic hardening models is advisable to improve stamping simulation and springback prediction. This choice becomes compulsory to model recent materials such as high strength steels. Cyclic tests are strictly required to evaluate the parameters of these constitutive models. However, for sheet metal specimens, in case of simple axial tension-compression tests, buckling occurrence during compression represents a serious drawback. This is the reason why alternative set-ups have been devised. In this paper, two experimental arrangements (a cyclic laterally constrained tension-compression test and a three-point fully reversed bending test) are compared so as to point out the advantages and the disadvantages of their application in tuning the well-known Chaboche’s hardening model. In particular, for tension-compression tests, a new clamping device was specifically designed to inhibit compressive instability. Four high strength steel grades were tested: two dual phases (DP), one transformation induced plasticity (TRIP) and one high strength low alloy material (HSLA). Then, the Chaboche’s model was calibrated through inverse identification methods or by means of analytical expressions when possible. The proposed testing procedure proved to be successful in all investigated materials. The achieved constitutive parameters, obtained independently from the two experimental techniques, were found to be consistent. Their accuracy was also been assessed by applying the parameter set obtained from one test to simulate the other one, and vice versa. Clues on what method provides the better transferability are given.

Mixed Effects Designs: The Symmetry Assumption and Missing Data

The classical F test for the hypothesis of no main fixed effects in the two-way crossed mixed effects design is derived under model assumptions that include normality, variance homogeneity, and symmetry. The symmetry assumption specifies that the random main and interaction effects are independent. While it is known that the F test is robust against violations of the normality assumption and/or the homoscedasticity assumption in the balanced case, the effects of the symmetry assumption have not been investigated. Our simulations demonstrate that the F test becomes very liberal under violations of the symmetry assumption. A new test procedure is developed under a more flexible model, which does not require the restrictive assumptions of the classical model. By considering the cell sample sizes to be random, the procedure applies equally well to unbalanced designs and to designs with empty cells, provided the missingness is completely at random. The asymptotic theory of the test statistic pertains to designs where the number of levels of both the fixed and random effects is large. The limiting distribution of the proposed test statistic is an infinite weighted sum of independent χ2 1 random variables. An approximation to this limiting distribution is proposed. Extensive simulations indicate that the proposed test procedure achieves levels reasonably close to the nominal ones under violations of the symmetry and other classical assumptions, and under different patterns of missingness. An analysis of a dataset from the Mussel Watch Project is presented. The supplementary materials for this article are available online and contain the proofs pertaining to the asymptotic distribution of the proposed statistic, as well as the results of simulations with nonnormal errors and random effects.

Information ratio test for model misspecification on parametric structures in stochastic diffusion models

We develop a hypothesis testing approach to checking model misspecification on parametric structures in continuous-time stochastic diffusion models. The key idea behind the development of our test statistic is rooted in a ratio of two types of information matrices, the negative sensitivity matrix and the variability matrix, in the context of martingale estimating equations. We propose a bootstrap resampling method to implement numerically the proposed diagnostic procedure. Through intensive simulation studies, we compare the proposed approach with several currently popular methods and show that our approach is advantageous in the aspects of type I error control, power improvement as well as computational efficiency. Two real-world data examples are included to illustrate the practical use of our proposed testing procedure.

False discovery rate control in two-stage designs

BackgroundFor gene expression or gene association studies with a large number of hypotheses the number of measurements per marker in a conventional single-stage design is often low due to limited resources. Two-stage designs have been proposed where in a first stage promising hypotheses are identified and further investigated in the second stage with larger sample sizes. For two types of two-stage designs proposed in the literature we derive multiple testing procedures controlling the False Discovery Rate (FDR) demonstrating FDR control by simulations: designs where a fixed number of top-ranked hypotheses are selected and designs where the selection in the interim analysis is based on an FDR threshold. In contrast to earlier approaches which use only the second-stage data in the hypothesis tests (pilot approach), the proposed testing procedures are based on the pooled data from both stages (integrated approach).ResultsFor both selection rules the multiple testing procedures control the FDR in the considered simulation scenarios. This holds for the case of independent observations across hypotheses as well as for certain correlation structures. Additionally, we show that in scenarios with small effect sizes the testing procedures based on the pooled data from both stages can give a considerable improvement in power compared to tests based on the second-stage data only.ConclusionThe proposed hypothesis tests provide a tool for FDR control for the considered two-stage designs. Comparing the integrated approaches for both selection rules with the corresponding pilot approaches showed an advantage of the integrated approach in many simulation scenarios.

Technique for Undrained Triaxial Tests on Unsaturated Soils Using Active Control of Pore-Air Pressure

Abstract Triaxial testing apparatus and procedures for unsaturated soils have become common along with the development of equipment and sensors. Although many drainage conditions are related to the pore-air and pore-water phase, the drained pore-air condition is usually adopted for tests of unsaturated soils. The main reason is that it is difficult to keep the pore-air undrained because the air diffuses easily through a rubber membrane. However, pore-air and pore-water are sometimes not allowed to drain under ground deformation problems. Therefore, undrained conditions in which pore-air and pore-water are not allowed to flow in and out of the soil are achieved in the experiments described herein. First, problems of a conventional triaxial apparatus for unsaturated soils were investigated to produce the undrained conditions. Then, triaxial testing methods under the undrained conditions were developed for overcoming the problems. Finally, the performance of the proposed testing procedure was demonstrated in comparison with results obtained using conventional testing.

Gene-environment interactions on growth trajectories.

It has been suggested that children with larger brains tend to perform better on IQ tests or cognitive function tests. Prenatal head growth and head growth in infancy are two crucial periods for subsequent intelligence. Studies have shown that environmental exposure to air pollutants during pregnancy is associated with fetal growth reduction, developmental delay, and reduced IQ. Meanwhile, genetic polymorphisms may modify the effect of environment on head growth. However, studies on gene-environment or gene-gene interactions on growth trajectories have been quite limited partly due to the difficulty to quantitatively measure interactions on growth trajectories. Moreover, it is known that assessing the significance of gene-environment or gene-gene interactions on cross-sectional outcomes empirically using the permutation procedures may bring substantial errors in the tests. We proposed a score that quantitatively measures interactions on growth trajectories and developed an algorithm with a parametric bootstrap procedure to empirically assess the significance of the interactions on growth trajectories under the likelihood framework. We also derived a Wald statistic to test for interactions on growth trajectories and compared it to the proposed parametric bootstrap procedure. Through extensive simulation studies, we demonstrated the feasibility and power of the proposed testing procedures. We applied our method to a real dataset with head circumference measures from birth to age 7 on a cohort currently being conducted by the Columbia Center for Children's Environmental Health (CCCEH) in Krakow, Poland, and identified several significant gene-environment interactions on head circumference growth trajectories.

$f$-Divergence Estimation and Two-Sample Homogeneity Test Under Semiparametric Density-Ratio Models

A density ratio is defined by the ratio of two probability densities. We study the inference problem of density ratios and apply a semiparametric density-ratio estimator to the two-sample homogeneity test. In the proposed test procedure, the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$f$</tex></formula> -divergence between two probability densities is estimated using a density-ratio estimator. The <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$f$</tex> </formula> -divergence estimator is then exploited for the two-sample homogeneity test. We derive an optimal estimator of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$f$</tex></formula> -divergence in the sense of the asymptotic variance in a semiparametric setting, and provide a statistic for two-sample homogeneity test based on the optimal estimator. We prove that the proposed test dominates the existing empirical likelihood score test. Through numerical studies, we illustrate the adequacy of the asymptotic theory for finite-sample inference.

A jackknife-based versatile test for two-sample problems with right-censored data

For testing the equality of two survival functions, the weighted logrank test and the weighted Kaplan–Meier test are the two most widely used methods. Actually, each of these tests has advantages and defects against various alternatives, while we cannot specify in advance the possible types of the survival differences. Hence, how to choose a single test or combine a number of competitive tests for indicating the diversities of two survival functions without suffering a substantial loss in power is an important issue. Instead of directly using a particular test which generally performs well in some situations and poorly in others, we further consider a class of tests indexed by a weighted parameter for testing the equality of two survival functions in this paper. A delete-1 jackknife method is implemented for selecting weights such that the variance of the test is minimized. Some numerical experiments are performed under various alternatives for illustrating the superiority of the proposed method. Finally, the proposed testing procedure is applied to two real-data examples as well.

A Note on Testing Homogeneity of Several Exponential Location Parameters

In this article, the problems of testing homogeneity of several exponential location parameters against simple and tree ordered alternatives are considered separately. Test procedures for both the alternatives are proposed using restricted maximum likelihood estimators (RMLE) of exponential location parameters under the respective orderings. Critical constants for the implementation of the proposed procedures are tabulated. Power comparison of the proposed test procedure under the simple ordered alternative with the procedure of Chen (1982) and of Dhawan and Gill (1999) is carried out using Monte-Carlo simulation.

Compact tension test for fracture characterization of thin bonded asphalt overlay systems at low temperature

Asphalt overlays provide an economical means for treating deteriorated pavements. Thin bonded overlay (TBO) systems have become popular options for pavement rehabilitation. In addition to functional improvements, these systems ensure a high degree of waterproofing benefits. Conventional asphalt concrete fracture tests were developed for pavements with homogeneous asphalt concrete mixtures, and typically their thicknesses exceed 50 mm (2 inch). The use of spray paver technology for construction of TBO leads to continuously varying asphalt binder content, up to approximately one-third of the layer thickness. Commonly utilized fracture test geometries for asphalt concrete include the single-edge notched beam, SEN[B], the disk-shaped compact tension, DC[T], and the semi-circular bend, SC[B]. The SEN[B] test geometry is not preferable for use in pavement systems due to difficulties in procuring beam samples from the field. Applications of the other established test geometries, the DC[T] and SC[B] tests, are limited because of the material nonhomogeneity caused by nonuniform distribution of asphalt binder and smaller as-constructed thicknesses of TBO, which are usually less than 25 mm (1 inch) for gap-graded and 50 mm (2 inch) for dense-graded hot mix asphalt (HMA) mixtures. Both the DC[T] and SC[B] tests simulate movement of the crack fronts in transverse or longitudinal directions in the pavement. Use of these tests on field-procured samples of TBO yields a crack front that encounters nonhomogeneous material through the specimen thickness. The crack moves perpendicular to the axis of material nonhomogeneity, which makes data interpretation and fundamental material fracture characterization challenging. In addition, the crack in the specimen is correlated to a crack channeling across the pavement width rather than a bottom-up or top-down direction, which is more desirable from the standpoint of coupling experimental results with currently available simulation models. This paper proposes a test procedure for fracture characterization of graded asphalt pavement systems that have significant material property gradients through their thicknesses. Suitable specimen geometry and testing procedures were developed using ASTM E399 and ASTM D7313-07b as a starting point. Laboratory tests were performed using an optimized compact tension, or C[T], test geometry for field cores as well as laboratory-fabricated composite specimens. Laboratory testing using the proposed procedure clearly showed distinction in the fracture characteristics for specimens prepared with varying material compositions. The capability of distinguishing different materials combined with stable crack growth makes the proposed testing procedure ideal for fracture characterization of thin and graded pavement systems. Statistical analysis of test data revealed that the proposed C[T] test procedure is capable of detecting differences in fracture energy results across a wide range of pavement systems and yields a low test variability. Finite element simulations of the test procedure further indicate the suitability of the test procedure as well as demonstrating a procedure for extraction of fundamental material properties.

Semiparametric Bayesian Testing Procedure for Noninferiority Trials with Binary Endpoints

A semiparametric testing approach based on the Bayes factor is developed for non-inferiority trials with binary endpoints. The proposed method is shown to work for a broad class of hypotheses by accommodating a variety of dissimilarity measures between two binomial parameters. Two of the unique features of the proposed testing procedure include: (i) construction of a flexible class of conjugate priors using a mixture of beta densities to maintain approximate equality of prior probabilities of the competing hypotheses; and (ii) automatic determination of the cutoff value of the Bayes factor to facilitate the decision making process. In contrast to the use of Jeffreys's rule of thumb, two forms of total weighted average error criteria are used to determine the cutoff value. Through several simulation studies it is demonstrated that the proposed Bayesian procedure has competitive frequentist properties of controlling type I error as compared to the default frequentist test and meanwhile the proposed criterion improves the statistical power, especially in small samples. The method is further illustrated using the data from a streptococcal pharyngitis clinical trial.

Heteroskedasticity and Spatiotemporal Dependence Robust Inference for Linear Panel Models with Fixed Effects

This paper studies robust inference for linear panel models with fixed effects in the presence of heteroskedasticity and spatiotemporal dependence of unknown forms. We propose a bivariate kernel covariance estimator that is flexible to nest existing estimators as special cases with certain choices of bandwidths. For distributional approximations, we embed the level of smoothing and the sample size in two different limiting sequences. In the first case where the level of smoothing increases with the sample size, the proposed covariance estimator is consistent and the associated Wald statistic converges to a χ² distribution. We show that our covariance estimator improves upon existing estimators in terms of robustness and efficiency. In the second case where the level of smoothing is fixed, the covariance estimator has a random limit and we show by asymptotic expansion that the limiting distribution of the Wald statistic depends on the bandwidth parameters, the kernel function, and the number of restrictions being tested. As this distribution is nonstandard, we establish the validity of a convenient F-approximation to this distribution. For bandwidth selection, we employ and optimize a modified asymptotic mean square error criterion. The flexibility of our estimator and the proposed bandwidth selection procedure make our estimator adaptive to the dependence structure. This adaptiveness effectively automates the selection of covariance estimators. Simulation results show that our proposed testing procedure works reasonably well in finite samples.

Two-Stage Designs with Additional Futility Tests for Phase II Clinical Trials with Heterogeneous Patient Populations

The patient population for a phase II clinical trial sometimes consists of multiple subgroups categorized by different prognostic factors such as age, disease stage, etc. Response rates across such subgroups often are heterogeneous; that is, the therapy under study may be inefficacious in some groups but efficacious in others. In this article, we propose a two-stage testing procedure consisting of futility tests and efficacy tests. The futility test is performed first within each subgroup. If there is strong evidence that the therapy is inefficacious in some subgroups, these subgroups are excluded from further consideration. The test then is performed across only the remaining subgroups. We carefully define and compute the Type I error rate and powers under various alternative hypotheses. Our numerical studies show that with proper designs, the addition of futility tests causes little loss of power under the alternative hypothesis that the study therapy is efficacious in all subgroups. Simultaneously, the proposed testing procedure detects inefficacious subgroups with a moderate or high probability when true response rates in these subgroups are low. Finally, we present an application to a Children's Oncology Group phase II clinical trial in relapsed neuroblastoma patients.

Procedure to Perform a Validated Incremental Hole Drilling Measurement: Application to Shot Peening Residual Stresses

Abstract: The paper describes a test rig designed to check and assess the accuracy of the incremental hole drilling (IHD) method. An external load produces a controlled linearly through thickness variable uniaxial stress field (reference bending stress), known with good accuracy, that can be applied and removed at each hole increment. After the separation between the bending relaxed strain from the residual stress relaxed strain, it is possible to reproduce the bending stress distribution in order to have complete confidence of the residual stress measurement. The bending verification of the IHD method was already proposed by other investigators before, but residual stress measurements were then performed on independent configurations. The proposed testing procedure gives a ‘real time’ verification of the residual stress measurement. Any experimental malfunctioning due to the operator inexperience, or any error during the stress calculation from the relaxed strain would produce an evident difference between the expected reference bending stress and the IHD bending stress output. Moreover, the reference bending stress helped for understanding that the not perfect hole cylindrical shape causes an underestimate of the predicted stress near the surface. A zero depth offset correction was proposed. This correction was tested on the reference bending stress, and then applied to the residual stress prediction. Three shot peening residual stresses IHD measurements were successfully validated by means of the bending stress; moreover, they were in good agreement with independent X‐ray diffraction measures also proposed in the paper.

Identification of the minimum effective dose based on weighted Kaplan–Meier statistics

Testing procedures are considered for identifying the minimum effective dose (MED) in a dose–response study with randomly right-censored survival data, where the MED is defined to be the smallest dose level under study that has survival advantage over the zero dose control. The proposed testing procedures are implemented in a step-down manner together with three different types of weighted Kaplan–Meier statistics. Comparative results of a Monte Carlo error rate and power/bias study for a variety of survival and censoring distributions are then presented and discussed. The application of the proposed procedures is finally illustrated for identifying the MED of the diethylstilbestrol in the treatment of prostate cancer.

Logistic Regression Models for Higher Order Transition Probabilities of Markov Chain for Analyzing the Occurrences of Daily Rainfall Data

Logistic regression models for transition probabilities of higher order Markov models are developed for the sequence of chain dependent repeated observations. To identify the significance of these models and their parameters a test procedure for a likelihood ratio criterion is developed. A method of model selection is suggested on the basis of AIC and BIC procedures. The proposed models and test procedures are applied to analyze the occurrences of daily rainfall data for selected stations in Bangladesh. Based on results from these models, the transition probabilities of first order Markov model for temperature and humidity provided the most suitable option to model forecasts for daily rainfall occurrences for five selected stations in Bangladesh.

Testing for Interaction in Two-Way Random and Mixed Effects Models: The Fully Nonparametric Approach

In a recent paper, Gaugler and Akritas (unpublished manuscript) considered testing for no main effect in a two-factor mixed effects design when the traditional assumptions do not hold. Here we extend the nonparametric modeling to the random effects design and consider the problem of testing for no interaction effect. The new models for these designs allow for dependence among the random effects, heteroscedasticity in the error and interaction terms, and do not require normality. At a more systemic level, these models differ from the classical ones in that they do not consider the random interaction term as an additional, extraneous source of variability. The proposed test procedure applies to settings where the random factor in the case of the mixed model or at least one of the random factors in the case of the random effects model has many levels. The number of replications can be small and possibly unbalanced. Moreover, the model and test procedure are general enough to accommodate data missing at random (MAR), provided the missingness mechanism is the same for each level of the random effect. The limiting distribution of the test statistic is normal. Extensive simulations indicate that our test procedure, with or without missing data, maintains the nominal Type I error rate in all simulation settings. On the contrary, the standard procedures (the F-test of PROC GLM in SAS, and the ML and REML methods of PROC MIXED in SAS), as well as the exact F-test of Khuri, Mathew, and Sinha (1998 in Statistical Tests for Mixed Linear Models), are extremely liberal in heteroscedastic settings, while under homoscedasticity and normality, the proposed test procedure is comparable to them. An analysis of a dataset from the Mussel Watch Project is presented.

Modeling of Strain-Stress Relationship for Carbon Steel Deformed at Temperature Exceeding Hot Rolling Range

The subject of the presented paper is the modeling of strain-stress relationship, which is the main mechanical property characteristic of the behavior of steel subjected to plastic deformation. The major challenge of the research is the temperature of the deformation, which significantly exceeds the hot rolling temperature range. This paper presents the results of work leading to the development of a rheological model describing the phenomena accompanying the deformation of 18G2A grade steel at temperature 1420°C and higher. Such temperature is a characteristic of the central parts of steel strands subjected to latest, very high temperature rolling technologies such as integrated rolling and casting processes. Rheological models have crucial influence on the results of the computer simulation of the mentioned processes. The methodology of yield stress curves development requires high accuracy systems of tension and compression test simulation. Hence, the proposed testing procedure is related to dedicated hybrid finite element method system with variable density, which was developed by the authors. The experimental work has been done using the Gleeble® 3800 thermomechanical simulator in the Institute for Ferrous Metallurgy in Gliwice, Poland. The testing machine allows the physical deformation of samples while solidification of their central part is still in progress. The essential goal of the simulation was the computer reconstruction of both temperature changes and strain evolution inside a specimen subjected to simultaneous deformation and solidification. In order to verify the predictive ability of the developed rheological model, a number of compression tests using Gleeble® 3800 simulator have been done, as well. The comparison between the numerical and the experimental results is also a part of the presented paper.

Designing a seamless phase II/III clinical trial using early outcomes for treatment selection: An application in multiple sclerosis

In recent years adaptive seamless phase II/III designs (ASDs) allowing treatment or dose selection at an interim analysis have gained much attention because of their potential to save development costs and to shorten time-to-market of a new compound compared to conventional drug development programmes with separate trials for individual phases. In this paper, we describe an ASD with treatment selection based on early outcome data, specifically considering the situation where no final outcomes are observed at the time of the interim analysis. Bringing together combination tests for adaptive designs and the closure principle for multiple testing, control of the familywise type I error rate in the strong sense is achieved. Furthermore, a simulation model is proposed based on standardized test statistics that allows the generation of virtual trials for a variety of outcomes. We use this simulation model to investigate the actual type I error rate of the proposed testing procedure and find that the familywise type I error rate is controlled as expected. The method is often conservative, with the degree of conservatism depending on the correlation between early and late outcome, the true mean values of the early outcome in the different treatment groups and the selection rule. The investigations are motivated and illustrated by an application of the proposed design and simulation model to progressive multiple sclerosis.

Bayesian and Classical Approaches for Hypotheses Testing in Trisomies

We introduce classical approaches for testing hypotheses on the meiosis I non disjunction fraction in trisomies, such as the likelihood-ratio, bootstrap, and Monte Carlo procedures. To calculate the p-values for the bootstrap and Monte Carlo procedures, different transformations in the data are considered. Bootstrap confidence intervals are also used as a tool to perform hypotheses tests. A Monte Carlo study is carried out to compare the proposed test procedures with two Bayesian ones: Jeffreys and Pereira-Stern tests. The results show that the likelihood-ratio and the Bayesian tests present the best performance. Down syndrome data are analyzed to illustrate the procedures.