Analysis Of Variance Estimates Research Articles

Bayes estimates of variance components in mixed linear model

This paper proves that in mixed linear model, the analysis of variance estimation (ANOVAE), the minimum norm quadratic unbiased estimation (MINQUE), the spectral decomposition estimation (SDE) and the restricted maximum likelihood estimation (RMLE) of variance components are the same under some conditions. Based on this result, we construct a linear Bayes estimation (LBE) for the parameter vector consisting of variance components and establish its superiorities. Numerical computations and an illustration show that the LBE is comparable to Lindley's approximation, Tierney and Kadane's approximation and the usual Bayes estimation (UBE) obtained by the MCMC method and easy to use as well.

Impact of the banking sector reform in the construction sector

Purpose Banking sector reforms can impact the development of the real sector. However, there is very little known about this impact on the construction sector in a developing country context. This study aims to evaluate the impact of the banking sector reform on the construction output (CNS) using the banking sector reform in Nigeria in 2005 (2005 Banking Sector Reform Programme [BSRP]) as a case. Design/methodology/approach This study used econometric methodology comprising unit root test for stationarity, Johansen test for cointegration, analysis of variance (ANOVA) and the analysis of covariance. Time series data covering a period from 1981 to 2017 (37 years) about the banking and construction sector performances are analyzed using ten-time series equations. Findings The ANOVA estimates reveal that the 2005 BSRP positively impacted the CNS and construction sector growth rate. However, the ANOVA estimates reveal that the gross domestic product (GDP) and bank total loan had a positive impact on CNS in the period (1981–2017) before and after the 2005 BSRP, and consequently removing the effect of the 2005 BSRP on CNS. Practical implications This paper concludes that the banking sector reform has a positive impact on CNS in the Nigerian construction industry. The impact is greater and lasting when the reform is directly targeted at improving CNS. Originality/value This study provides empirical evidence of the dependence between banking sector reform and construction sector performance in a developing country context. Also, this study demonstrates the relationship between GDP, banking sector reform and construction sector performance in a developing country context.

1320. Pharmacokinetics of Isavuconazole Administered as Isavuconazonium Sulfate Intravenous Solution via Nasogastric Tube or Orally in Healthy Volunteers

BackgroundNasogastric (NG) tube feeding is most common in the intensive care unit and is also used for cancer patients who are unable to eat (e.g. patients with mucositis) or do not want to eat due to severe nausea1. For such critically ill patients with invasive fungal infections, administration of isavuconazonium sulfate (ISAVUSULF) via NG tube can be an alternate route of drug administration.MethodsThis was a randomized, open-label, 2-period, 2-sequence single dose crossover study in healthy male and female subjects. Each subject participated in 2 treatment periods separated by a washout of at least 30 days between investigational product administrations in each period. Subjects were administered a single dose of 372 mg ISAVUSULF intravenous (IV) solution via NG tube (test formulation) or 372 mg ISAVUSULF capsules for oral (PO) administration (i.e., PO capsules administered to subjects without NG tube) (reference formulation) under fasting conditions on day 1 of each period. Pharmacokinetic (PK) samples were collected predose on day 1 of each period and at multiple time points postdose through day 21. Standard safety and tolerability assessments were conducted in each period.ResultsEighteen subjects were randomized in this study and 13 provided concentrations in both sequences that were PK evaluable. The analysis of variance estimate (Table 1) of the study population suggests that the isavuconazole IV NG tube administration geometric least-square (LS) mean values of the observed maximum concentration (Cmax), area under the plasma concentration-time curve (AUC) to the last measurable concentration (AUClast), AUC to time infinity (AUCinf), and AUC from start of dosing to 72 hours (AUC72) were 105.3%, 97.6%, 99.3% and 97.8%, respectively, of the corresponding oral administration values. The geometric LS mean ratio and 90% Confidence Intervals for the Cmax, AUClast, AUCinf, and AUC72 are completely contained within the prespecified limits of 80% to 125%. There were no deaths or serious adverse events that led to withdrawal of treatment during the conduct of the study.Table 1 ConclusionThe study met its primary endpoint of bioequivalence between the two routes of administration in this population. Both routes of administration are well tolerated.Reference 1 Disclosures Amit Desai, PhD, Astellas Pharma Inc. (Employee, Other Financial or Material Support, This study was initiated and sponsored by Astellas Pharma Global Development Inc) Melanie Helmick, BA, Clinical Research, Astellas Pharma Inc. (Employee, Other Financial or Material Support, This study was initiated and sponsored by Astellas Pharma Global Development Inc) Nakyo Heo, PharmD, MS, Astellas Pharma Inc. (Employee, Other Financial or Material Support, This study was initiated and sponsored by Astellas Pharma Global Development Inc) Selina Moy, BS, Astellas Pharma Inc. (Employee, Other Financial or Material Support, This study was initiated and sponsored by Astellas Pharma Global Development Inc) Stephen Stanhope, PhD, Astellas Pharma Inc. (Employee, Other Financial or Material Support, This study was initiated and sponsored by Astellas Pharma Global Development Inc) Ronald Goldwater, MDCM, Astellas Pharma Inc. (Other Financial or Material Support, This study was initiated and sponsored by Astellas Pharma Global Development Inc. Parexel International received fees for research support from Astellas Pharma Global Development Inc.)Parexel International (Employee, Employee of Parexel International) Nancy Martin, MD, PharmD, Astellas Pharma Inc. (Employee, Other Financial or Material Support, This study was initiated and sponsored by Astellas Pharma Global Development Inc)

A readily available improvement over method of moments for intra-cluster correlation estimation in the context of cluster randomized trials and fitting a GEE-type marginal model for binary outcomes.

Cluster randomized trials are popular in health-related research due to the need or desire to randomize clusters of subjects to different trial arms as opposed to randomizing each subject individually. As outcomes from subjects within the same cluster tend to be more alike than outcomes from subjects within other clusters, an exchangeable correlation arises that is measured via the intra-cluster correlation coefficient. Intra-cluster correlation coefficient estimation is especially important due to the increasing awareness of the need to publish such values from studies in order to help guide the design of future cluster randomized trials. Therefore, numerous methods have been proposed to accurately estimate the intra-cluster correlation coefficient, with much attention given to binary outcomes. As marginal models are often of interest, we focus on intra-cluster correlation coefficient estimation in the context of fitting such a model with binary outcomes using generalized estimating equations. Traditionally, intra-cluster correlation coefficient estimation with generalized estimating equations has been based on the method of moments, although such estimators can be negatively biased. Furthermore, alternative estimators that work well, such as the analysis of variance estimator, are not as readily applicable in the context of practical data analyses with generalized estimating equations. Therefore, in this article we assess, in terms of bias, the readily available residual pseudo-likelihood approach to intra-cluster correlation coefficient estimation with the GLIMMIX procedure of SAS (SAS Institute, Cary, NC). Furthermore, we study a possible corresponding approach to confidence interval construction for the intra-cluster correlation coefficient. We utilize a simulation study and application example to assess bias in intra-cluster correlation coefficient estimates obtained from GLIMMIX using residual pseudo-likelihood. This estimator is contrasted with method of moments and analysis of variance estimators which are standards of comparison. The approach to confidence interval construction is assessed by examining coverage probabilities. Overall, the residual pseudo-likelihood estimator performs very well. It has considerably less bias than moment estimators, which are its competitor for general generalized estimating equation-based analyses, and therefore, it is a major improvement in practice. Furthermore, it works almost as well as analysis of variance estimators when they are applicable. Confidence intervals have near-nominal coverage when the intra-cluster correlation coefficient estimate has negligible bias. Our results show that the residual pseudo-likelihood estimator is a good option for intra-cluster correlation coefficient estimation when conducting a generalized estimating equation-based analysis of binary outcome data arising from cluster randomized trials. The estimator is practical in that it is simply a result from fitting a marginal model with GLIMMIX, and a confidence interval can be easily obtained. An additional advantage is that, unlike most other options for performing generalized estimating equation-based analyses, GLIMMIX provides analysts the option to utilize small-sample adjustments that ensure valid inference.

A Practical ANOVA Approach for Uncertainty Analysis in Population-Based Disease Microsimulation Models.

To provide a practical approach for calculating uncertainty intervals and variance components associated with initial-condition and dynamic-equation parameters in computationally expensive population-based disease microsimulation models. In the proposed uncertainty analysis approach, we calculated the required computational time and the number of runs given a user-defined error bound on the variance of the grand mean. The equations for optimal sample sizes were derived by minimizing the variance of the grand mean using initial estimates for variance components. Finally, analysis of variance estimators were used to calculate unbiased variance estimates. To illustrate the proposed approach, we performed uncertainty analysis to estimate the uncertainty associated with total direct cost of osteoarthritis in Canada from 2010 to 2031 according to a previously published population health microsimulation model of osteoarthritis. We first calculated crude estimates for initial-population sampling and dynamic-equation parameters uncertainty by performing a small number of runs. We then calculated the optimal sample sizes and finally derived 95% uncertainty intervals of the total cost and unbiased estimates for variance components. According to our results, the contribution of dynamic-equation parameter uncertainty to the overall variance was higher than that of initial parameter sampling uncertainty throughout the study period. The proposed analysis of variance approach provides the uncertainty intervals for the mean outcome in addition to unbiased estimates for each source of uncertainty. The contributions of each source of uncertainty can then be compared with each other for validation purposes so as to improve the model accuracy.

An Estimation of Variance Components in Linear Mixed Model

In this paper, a linear mixed model which has two random effects is broken up into two models. This thesis gets the parameter estimation of the original model and an estimation’s statistical qualities based on these two models. Then many important properties are given by comparing this estimation with other general estimations. At the same time, this paper proves the analysis of variance estimate (ANOVAE) about σ of the original model is equal to the least-squares estimation (LSE) about σ of these two models. Finally, it also proves that this estimation is better than ANOVAE under Stein function and special condition in some degree. Keywords—Linear mixed model, Random effects, Parameter estimation, Stein function.

Comparison of the estimators of the intra-cluster correlation for the nested error regression model

ABSTRACTThe intra-cluster correlation is insisted on nested error regression model that, in practice, is rarely known. This article demonstrates the size in generalized least squares (GLS) F-test using Fuller–Battese transformation and modification F-test. For the balanced case, the former using strictly positive, analysis of covariance (ANCOVA) and analysis of variance (ANOVA) estimators of intra-cluster correlation can control the size for moderate intra-cluster correlations. For small intra-cluster correlation, they perform well when the numbers of cluster are large. The latter using the ANOVA estimator performs well except for small numbers of cluster. When intra-cluster correlation is large, it cannot control the size. For the unbalanced case, the GLS F-test using the Fuller–Battese transformation and the modification F-test using the strictly positive, the ANCOVA and the ANOVA estimators maintain the significance level for small total sample size and small intra-cluster correlations when there is a large variation in cluster sizes, but they perform well in controlling the size for large total sample size and small different variation in cluster sizes. Besides, Henderson’s method 3 estimator maintains the significance level for a few situations.

Comparison between ANOVA estimator and SD estimator under balanced data

The analysis of variance (ANOVA) estimator and the spectral decomposition (SD) estimator are very helpful for constructing exact test statistics and generalized <italic>P</italic>-value pivotal variables under linear mixedeffects models. Though two estimators are constructed with completely different methods, they share many similar advantages, such as unbiased and closed form. In this paper, we make some comparison between ANOVA estimator and SD estimator. Based the spectral decomposition of covariance matrix we have obtained, we discover the relationship between ANOVA estimator and SD estimator, and establish necessary and sufficient conditions for the identity of ANOVA estimator and SD estimator for the models with nest-structure covariance matrix and the models with multi-way crossed classification random effects, respectively.

On Estimation of Standard Error of Intra-Class Correlation Coefficient in Unbalanced Nested Designs

In medical research, while reporting the results for cluster randomized trial, intra-class correlation coefficient estimates must be provided along with standard error to account for calculation of sample size to achieve the desired power. In the present article, an attempt is made to derive the standard error of analysis of variance estimates of intra-class correlation coefficient for unbalanced nested design with almost no distributional assumptions. To fulfill the gap of strong need of distributional assumptions, balanced design for ease of calculation, equality of variances between clusters and large sample, there was a need of general formula for standard error of intra-class correlation coefficient which can be deployed in multicentre clinical trials. One simulation study is carried on to assess the behavior of significant constants and validity of formula over varying cluster sizes as well as varying number of clusters.

Comparison of methods for estimating the intraclass correlation coefficient for binary responses in cancer prevention cluster randomized trials

The intraclass correlation coefficient (ICC) is a fundamental parameter of interest in cluster randomized trials as it can greatly affect statistical power. We compare common methods of estimating the ICC in cluster randomized trials with binary outcomes, with a specific focus on their application to community-based cancer prevention trials with primary outcome of self-reported cancer screening. Using three real data sets from cancer screening intervention trials with different numbers and types of clusters and cluster sizes, we obtained point estimates and 95% confidence intervals for the ICC using five methods: the analysis of variance estimator, the Fleiss–Cuzick estimator, the Pearson estimator, an estimator based on generalized estimating equations and an estimator from a random intercept logistic regression model. We compared estimates of the ICC for the overall sample and by study condition. Our results show that ICC estimates from different methods can be quite different, although confidence intervals generally overlap. The ICC varied substantially by study condition in two studies, suggesting that the common practice of assuming a common ICC across all clusters in the trial is questionable. A simulation study confirmed pitfalls of erroneously assuming a common ICC. Investigators should consider using sample size and analysis methods that allow the ICC to vary by study condition.

Assessment of a Measurement System Using Repeat Measurements of Failing Units

ABSTRACT Inspection systems measure every part produced. If the measurement is outside of the inspection limits, then that part is measured again. To assess the quality of these measurement systems, traditionally gauge repeatability and reproducibility (R&R) studies are preformed. Instead of performing a gauge R&R study, we present a method of assessing these measurement systems with operational data from an inspection system. Using the inspection data, we provide a justification for the pooled variance of the measured values for each part that has two measurements. The bias and variance of this analysis of variance (ANOVA) estimator are derived using properties of the truncated normal distribution. We show that the ANOVA estimator has a relatively small bias and high efficiency when compared with the maximum likelihood estimator for most common values of γ or GRR%, which is the measurement system standard deviation divided by total inspection system standard deviation.

Comparison of designs for the three-fold nested random model

The quality of estimation of variance components depends on the design used as well as on the unknown values of the variance components. In this article, three designs are compared, namely, the balanced, staggered, and inverted nested designs for the three-fold nested random model. The comparison is based on the so-called quantile dispersion graphs using analysis of variance (ANOVA) and maximum likelihood (ML) estimates of the variance components. It is demonstrated that the staggered nested design gives more stable estimates of the variance component for the highest nesting factor than the balanced design. The reverse, however, is true in case of lower nested factors. A comparison between ANOVA and ML estimation of the variance components is also made using each of the aforementioned designs.

A new method of spectral decomposition of covariance matrix in mixed effects models and its applications

For the mixed effects models with balanced data, a new ordering of design matrices of random effects is defined, and then a simple formula of the spectral decomposition of covariance matrix is obtained. To compare with the two methods in literature, the decomposition can not only give the actual number of all distinct eigenvalues and their expression, but also show clearly the relationship between the design matrices of random effects and the decomposition. These results can be applied to the problems for testifying the analysis of the variance estimate being a minimum variance unbiased under all random effects models and some mixed effects models with balanced data, for finding the explicit solution of maximum likelihood equations for the general mixed effects model and for showing the relationship between the spectral decomposition estimate and the analysis of variance estimate.

Simultaneous optimal estimates of fixed effects and variance components in the mixed model

For a general linear mixed model with two variance components, a set of simple conditions is obtained, under which, (i) the least squares estimate of the fixed effects and the analysis of variance (ANOVA) estimates of variance components are proved to be uniformly minimum variance unbiased estimates simultaneously; (ii) the exact confidence intervals of the fixed effects and uniformly optimal unbiased tests on variance components are given; (iii) the exact probability expression of ANOVA estimates of variance components taking negative value is obtained.

On the optimum number of levels in the one-way model with random effects

The optimal number of levels is studied for the one-way random model with normally distributed effects. The optimum criteria used are based on the variances of the traditional analysis of variance estimators of the variance components. Exact solutions are compared to earlier results based on lower bounds of the sampling variances. Comparisons are also made to the large-sample variances of the estimates based on restricted maximum likelihood.

Improved non-negative estimation of variance components for exposure assessment.

Hygiene surveys of pollutants exposure data can be analyzed by analysis of variance (ANOVA) model with a random worker effect. Typically, workers are classified into homogeneous exposure groups, so it is very common to obtain a zero or negative ANOVA estimate of the between-worker variance (sigma2B). Negative estimates are not sensible and also pose problems for estimating the probability (theta) that in a job group, a randomly selected worker's mean exposure exceeds the occupational exposure standard. Therefore, it was suggested by Rappaport et al. to replace a non-positive estimate with an approximate one-sided 60% upper confidence bound. This article develops an alternative estimator, based on the upper tolerance interval suggested by Wang and Iyer. We compared the performance of the two methods using real data and simulations with respect to estimating both the between-worker variance and the probability of overexposure in balanced designs. We found that the method of Rappaport et al. has three main disadvantages: (i) the estimated sigma2B remains negative for some data sets; (ii) the estimator performs poorly in estimating sigma2B and theta with two repeated measures per worker and when true sigma2B is quite small, which are quite common situations when studying exposure; (iii) the estimator can be extremely sensitive to small changes in the data. Our alternative estimator offers a solution to these problems.

Modeling the Probability of a Negative ANOVA Estimate of a Variance Component

The usefulness of analysis of variance (ANOVA) estimates of variance components is impaired by the frequent occurrence of negative values. The probability of such an occurrence is therefore of interest. This probability depends on the design used and the true values of the variance components. In the present article, we propose a method for modeling this probability in order to gain a better insight into the effect of data imbalance on the quality of ANOVA estimation. Generalized linear models techniques are used for this purpose. A demonstration of the proposed methodology is made using the unbalanced random one-way model.

General formulae for expectations, variances and covariances of the mean squares for staggered nested designs

Staggered nested experimental designs are the most popular class of unbalanced nested designs. Using a special notation which covers the particular structure of the staggered nested design, this paper systematically derives the canonical form for the arbitrary m-factors. Under the normality assumption for every random variable, a vector comprising m canonical variables from each experimental unit is normally independently and identically distributed. Every sum of squares used in the analysis of variance (ANOVA) can be expressed as the sum of squares of the corresponding canonical variables. Hence, general formulae for the expectations, variances and covariances of the mean squares are directly obtained from the canonical form. Applying the formulae, the explicit forms of the ANOVA estimators of the variance components and unbiased estimators of the ratios of the variance components are introduced in this paper. The formulae are easily applied to obtain the variances and covariances of any linear combinations of the mean squares, especially the ANOVA estimators of the variance components. These results are eff ectively applied for the standardization of measurement methods.

ESTIMATING HIERARCHICAL F-STATISTICS.

This paper presents an analysis of variance (ANOVA) approach by which estimation of F-statistics can be made from data with an arbitrary s-level hierarchical population structure. Assuming a complete random-effect model, a general ANOVA procedure is developed to estimate F-statistics as ratios of different variance components for all levels of population subdivision in the hierarchy. A generalized relationship among F-statistics is also derived to extend the well-known relationship originally found by Sewall Wright. Although not entirely free from the bias particular to small number of subdivisions at each hierarchy and extreme gene frequencies, the ANOVA estimators of F-statistics consider sampling effects at each level of hierarchy, thus removing the bias incurred in the other estimators that are commonly based on direct substitution of unknown gene frequencies by their sample estimates. Therefore, the ANOVA estimation procedure presented here may become increasingly useful in analyzing complex population structure because of increasing use of the estimated hierarchical F-statistics to infer genetic and demographic structures of natural populations within and among species.

Quantile dispersion graphs for analysis of variance estimates of variance components

Summary The exact distribution of an analysis of variance estimator of a variance component is obtained by determining its quantiles on the basis of R. B. Davies' algorithm. A plot of these quantiles provides useful information concerning the efficiency of the estimator, including the extent to which it can be negative. Furthermore, the variability in the values of each quantile is assessed by varying the values of the variance components for the model under consideration. The maximum and minimum of such quantile values can then be determined. A plot of the maxima and minima for various selected quantiles produces the so-called 'quantile dispersion graphs'. These graphs can be used to provide a comprehensive picture of the quality of estimation obtained with a particular design. They also provide an effective graphical tool for comparing designs on the basis of their estimation capabilities.