Construction of nested space-filling designs using difference matrices

Experiments that study complex real world systems in business, engineering and sciences can be conducted at different levels of accuracy or sophistication. Nested space-filling designs are suitable for such multi-fidelity experiments. In this paper, we propose a systematic method to construct nested space-filling designs for experiments with two levels of accuracy. The method that makes use of nested difference matrices can be easily performed, many nested space-filling designs for experiments with two levels of accuracy can thus be constructed, and the resulting designs achieve stratification in low dimensions. In addition, the proposed method can also be used to obtain sliced space-filling designs for conducting computer experiments with both qualitative and quantitative factors.     

Generation of space-filling uniform designs in unit hypercubes

In this paper a new discrepancy measure of uniformity for uniform designs (UDs) in a unit cube is presented. Alternative measures of uniformity based on distance criteria which can be applied to higher dimensions are also discussed. The good lattice point (glp) method was used to construct the uniform designs. Two approaches (generator equivalence and projection) of reducing the computational cost of the glp method are proposed and discussed. Two examples are presented in this paper.     

Cluster designs to assess the prevalence of acute malnutrition by lot quality assurance sampling: a validation study by computer simulation

Summary.  Traditional lot quality assurance sampling (LQAS) methods require simple random sampling to guarantee valid results. However, cluster sampling has been proposed to reduce the number of random starting points. This study uses simulations to examine the classification error of two such designs, a 67×3 (67 clusters of three observations) and a 33×6 (33 clusters of six observations) sampling scheme to assess the prevalence of global acute malnutrition (GAM). Further, we explore the use of a 67×3 sequential sampling scheme for LQAS classification of GAM prevalence. Results indicate that, for independent clusters with moderate intracluster correlation for the GAM outcome, the three sampling designs maintain approximate validity for LQAS analysis. Sequential sampling can substantially reduce the average sample size that is required for data collection. The presence of intercluster correlation can impact dramatically the classification error that is associated with LQAS analysis.     

Fitting bivariate multilevel models to assess long-term changes in body mass index and cigarette smoking

Using data from the National Health interview Survey from 1997 to 2006, we present a multilevel analysis of change in body mass index (BMI) and number of cigarettes smoked per day in the USA. Smoking and obesity are the leading causes of preventable mortality and morbidity in the USA and most parts of the developed world. A two-stage bivariate model of changes in obesity and number of cigarette smoked per day is proposed. At the within subject stage, an individual's BMI status and the number of cigarette smoked per day are jointly modeled as a function of an individual growth trajectory plus a random error. At the between-subject stage, the parameters of the individual growth trajectories are allowed to vary as a function of differences between subjects with respect to demographic and behavioral characteristics and with respect to the four regions of the USA (Northeast, West, South and North central). Our two-stage modeling techniques are more informative than standard regression because they characterize both group-level (nomothetic) and individual-level (idiographic) effects, yielding a more complete understanding of the phenomena under study.     

A unified approach to regression analysis under double-sampling designs

We propose a unified approach to the estimation of regression parameters under double-sampling designs, in which a primary sample consisting of data on the rough or proxy measures for the response and/or explanatory variables as well as a validation subsample consisting of data on the exact measurements are available. We assume that the validation sample is a simple random subsample from the primary sample. Our proposal utilizes a specific parametric model to extract the partial information contained in the primary sample. The resulting estimator is consistent even if such a model is misspecified, and it achieves higher asymptotic efficiency than the estimator based only on the validation data. Specific cases are discussed to illustrate the application of the estimator proposed.     

A simple method to obtain minimum aberration split-plot designs

ABSTRACT

Split-plot designs have been utilized in factorial experiments with some factors applied to larger units and others to smaller units. Such designs with low aberration are preferred when the experimental size and the number of factors considered in both whole plot and subplot are determined. The minimum aberration split-plot designs can be obtained using either computer algorithms or the exhausted search. In this article, we propose a simple, easy-to-operate approach by using two ordered sequences of columns from two orthogonal arrays in obtaining minimum aberration split-plot designs for experiments of sizes 16 and 32.     

A survey of nested designs

A nest with parameters (r,k,λ)→(r′,k′,λ′) is a BIBD on (b,v,r,k,λ) where each block has a distinguished sublock of cardinality k, the sublocks forming a (b,v,r,k,λ)-design.These designs are ‘nested’ in the sense of W.T. Federer (1972), who recommended the use of these designs for the sequential addition of periods in marketing experiments in order to retain Youden design properties as rows are added. Note that for a Youden design, the b columns and v treatments are in an SBIBD arrangement with parameters v=b, k=r, and λ.     

A graphical method for evaluating mixture designs with respect to the slope

Good estimation of the slopes of the mixture response function may be important as well as estimation of mean mixture response. It is possible to evaluate and compare several mixture designs with respect to the slope. A graphical method is proposed that allows us to evaluate a given design's support for the fitted model in terms of slope variance. We can plot variances of slopes along Cox direction or axial direction according to existence of restriction of simplex region or not when comparing several different mixture designs.     

Bayesian adaptive bandit-based designs using the Gittins index for multi-armed trials with normally distributed endpoints

Adaptive designs for multi-armed clinical trials have become increasingly popular recently because of their potential to shorten development times and to increase patient response. However, developing response-adaptive designs that offer patient-benefit while ensuring the resulting trial provides a statistically rigorous and unbiased comparison of the different treatments included is highly challenging. In this paper, the theory of Multi-Armed Bandit Problems is used to define near optimal adaptive designs in the context of a clinical trial with a normally distributed endpoint with known variance. We report the operating characteristics (type I error, power, bias) and patient-benefit of these approaches and alternative designs using simulation studies based on an ongoing trial. These results are then compared to those recently published in the context of Bernoulli endpoints. Many limitations and advantages are similar in both cases but there are also important differences, specially with respect to type I error control. This paper proposes a simulation-based testing procedure to correct for the observed type I error inflation that bandit-based and adaptive rules can induce.     

A review of uniform cross-over designs

Uniform cross-over designs form an important family of experimental designs. They have been applied in many scientific disciplines including clinical trials, agricultural studies and psychological experiments. In this paper we consider the four types of uniform cross-over design, as given by Williams [1949. Experimental designs balanced for the estimation of residual effects of treatments. Aust. J. Sci. Res. 2, 149–168], Cheng and Wu [1980. Balanced repeated measurements designs. Ann. Statist. 8, 1272–1283. Corrigendum 11 (1983) 349], Bate and Jones [2006. The construction of nearly balanced and nearly strongly balanced uniform cross-over designs. J. Statist. Plann. Inference 136, 3248–3267] and Kunert [1983. Optimal design and refinement of the linear model with applications to repeated measurements designs. Ann. Statist. 11, 247–257]. The efficiency of these designs, existence criteria and methods of construction are described.     

A series of group divisible designs

Bose and Shrikhande C19763 proved that if D(m, k, ?) is a Baer subdesign of another SBIBD D₁ (v₁, k₁ ?), k₁>k, then it also contains a complementary subdesign D^* which is symmetric GDD, D^* (v^*, k^*; ?-1, ?; m, n). Utilising this, we give a necessary condition for a SBIBD D to be a Baer subdesign of D₁ and also give the parameters. Some GD designs are constructed.     

A class of new pbib designs

Two series of PBIB designs, one with three associate classes and theother with four associate classes ars developed. Efficiency factors for two designs are computed.     

A construction of group divisible designs

Given any affine design with parameters v, b, r, k, λ and μ = k²/v and any design with parameters v′, b′, r′, k′, λ′ where r′ = tr for some natural number `t and k′?r, we construct a group divisible design with parameters v′' = vv′, m = v′, n = v, b′' = vb′, k′' = kk′, r′'= kr′, λ₁ = tkλ and λ₂ = μλ′. This is applied to some series of designs. As a lemma, we also show that any 0-1-matrix with row sums tr and column sums ?r may be written as the sum of r 0-1-matrices with row sums t and column sums ?1.     

Using the studentized range to assess kurtosis

Because it is easy to compute from three common statistics (minimum, maximum, standard deviation) the studentized range is a useful test for non-normality when the original data are unavailable. For samples from symmetric populations, the studentized range allows an assessment of kurtosis with Type I and II error rates similar to those obtained from the moment coefficients.     

Nonconformance probability of an air quality index

Air pollution is one of the most important global environmental issues. Taiwan Environmental Protection Agency (EPA) is currently using an Air Quality Index (AQI) to measure and monitor its national air quality. The main objective of this study is to assess the air quality per hour every month in Taichung City of Taiwan from 2014 to 2016 based on the nonconformance probability of the AQI index. The nonconformance probability is defined as the probability that a characteristic of interest falls outside of an acceptance region. A lower confidence bound for the nonconformance probability is applied to test whether the AQI index value exceeds a warning threshold, and then the government could issue warnings according to the decision made by such statistical inference. An unbalanced two-way random effects model is presented for fitting the AQI index values. We evaluate three different lower confidence bound construction methods, including a t-based, an adjusted t-based and a generalized pivotal quantity (GPQ) based methods, through a detailed simulation study. Finally, a hybrid method of the t-based and the adjusted t-based estimators is recommended for practical use.KEYWORDS: Conformance proportion, generalized confidence interval, generalized pivotal quantity, non-inferiority test, Student’s t-test     

A note on the connectivity of generalized cyclic designs

A necessary and sufficient condition is given to ensure that a generating blook of a generalized cyclic design will give rise to a connected design. The use of disconnected designs is briefly discussed.     

A theoretical analysis of the power of biased coin designs

Outlining some recently obtained results of Hu and Rosenberger [2003. Optimality, variability, power: evaluating response-adaptive randomization procedures for treatment comparisons. J. Amer. Statist. Assoc. 98, 671–678] and Chen [2006. The power of Efron's biased coin design. J. Statist. Plann. Inference 136, 1824–1835] on the relationship between sequential randomized designs and the power of the usual statistical procedures for testing the equivalence of two competing treatments, the aim of this paper is to provide theoretical proofs of the numerical results of Chen [2006. The power of Efron's biased coin design. J. Statist. Plann. Inference 136, 1824–1835]. Furthermore, we prove that the Adjustable Biased Coin Design [Baldi Antognini A., Giovagnoli, A., 2004. A new “biased coin design” for the sequential allocation of two treatments. J. Roy. Statist. Soc. Ser. C 53, 651–664] is uniformly more powerful than the other “coin” designs proposed in the literature for any sample size.     

A new special class of peb designs

A new class of partially efficiency-balanced designs is introduced from a practical point of view. This new design includes all equireplicated incomplete block designs available in literature as special cases. The fundamental properties of the design are clarified with relation to other block designs.     

A class of resolvable incomplete block designs

A class of resolvable incomplete block designs with three and four replications is obtained here starting from an additive Abelian group.