Chen-Tuo Liao

One- and Two-Sided Tolerance Intervals for General Balanced Mixed Models and Unbalanced One-Way Random Models

In this article we develop procedures for one- and two-sided tolerance intervals for normal general linear models in which there exists a set of independent scaled chi-squared random variables. The proposed procedures are based on the concept of generalized pivotal quantities and are applicable to general mixed models provided that balanced data are available. However, this study focuses on situations involving unbalanced data. Specific attention is given to the unbalanced one-way random model. It is shown that the use of generalized pivotal quantities allows the construction of the tolerance intervals of interest fairly straightforward. Some practical examples are given to illustrate the proposed procedures. Furthermore, detailed statistical simulation studies are conducted to evaluate their performance, showing that the proposed procedures can be recommended for practical use.

Design and Analysis of Two-Level Factorial Experiments With Partial Replication

In a two-level factorial experiment, we consider construction of parallel-flats designs with two identical parallel flats that allow estimation of a set of specified possibly active effects and the pure error variance. A set of sufficient conditions is presented for the designs to be D-optimal for the specified effects, assuming that the other effects are negligible, over the class of competing parallel-flats designs. In addition, an algorithm is developed to generate the D-optimal designs with a choice of flexible degrees of freedom for the pure error variance. Because the proposed partially replicated designs are highly efficient in estimating the possibly active effects and provide a replication-based estimate of the error variance, they provide a practical compromise between the power in identifying truly active effects and the number of runs in experiments. This property is verified through a simulation study.

A β-expectation tolerance interval for general balanced mixed linear models

A @b-expectation tolerance interval procedure is derived from the concept of generalized pivotal quantity, which has been frequently used to obtain confidence intervals in situations where standard procedures do not lead to useful solutions. The proposed procedure can be applied to general balanced mixed linear models. Some practical examples are given to illustrate the proposed procedure. In addition, detailed simulation studies are conducted to evaluate its performance, showing that it can be recommended for use in practical applications.

Tolerance intervals for unbalanced one-way random effects models with covariates and heterogeneous variances

Tolerance intervals are useful in practice to help determine limits for detection monitoring or assessment monitoring of factors that may impact the environment, ecological systems, or other biological processes. This article provides a procedure for construction of one-sided and two-sided tolerance intervals for a normally distributed random variable when the mean and variance of its distribution are estimated using data following an unbalanced one-way random effects model with covariates under heterogeneous error variances. The procedure developed here is based on the concept of a generalized pivotal quantity which has been frequently used to obtain confidence intervals in situations where conventional methods are difficult to apply or fail to provide s satisfactory solutions. For the one-sided case, the generalized pivotal quantity approach yields an exact solution. On the other hand, the method leads to good approximate intervals for the two-sided case. This is confirmed by a detailed simulation study, showing that the method may be recommended for practical use. Two real-data examples are given to illustrate the applicability of the proposed procedures.

Statistical designs for two-color microarray experiments involving technical replication

In a two-color microarray experiment, we consider the issues of determination of which mRNA samples are to be labeled with which fluorescent dye and which mRNA samples are to be hybridized together on the same slide. Specific attention is given to the test-control experiments whose primary interest lies in comparing several test treatments with a control treatment. A statistical linear model is proposed to characterize two major sources of systematic variation: the variation among distinct slides and that between fluorescent dyes. Furthermore, the possible correlation due to technical replication is also incorporated into the model. A series of A-optimal or highly efficient designs are generated from a heuristic algorithm based on the proposed model. It is shown that the obtained designs are robust not only to the variation of the correlation because of technique replication, but also to the loss of one or two slides. In addition, the comparative experiments involving technical replication are also discussed.

Noninferiority tests based on concordance correlation coefficient for assessment of the agreement for gene expression data from microarray experiments.

Microarray is one of the breakthrough technologies in the twenty-first century. Despite of its great potential, transition and realization of microarray technology into the clinically useful commercial products have not been as rapid as the technology could promise. One of the primary reasons is lack of agreement and poor reproducibility of the intensity measurements on gene expression obtained from microarray experiments. Current practices often use the testing the hypothesis of zero Pearson correlation coefficient to assess the agreement of gene expression levels between the technical replicates from microarray experiments. However, Pearson correlation coefficient is to evaluate linear association between two variables and fail to take into account changes in accuracy and precision. Hence, it is not appropriate for evaluation of agreement of gene expression levels between technical replicates. Therefore, we propose to use the concordance correlation coefficient to assess agreement of gene expression levels between technical replicates. We also apply the Generalized Pivotal Quantities to obtain the exact confidence interval for concordance coefficient. In addition, based on the concept of noninferiority test, a one-sided (1 − α) lower confidence limit for concordance correlation coefficient is employed to test the hypothesis that the agreement of expression levels of the same genes between two technical replicates exceeds some minimal requirement of agreement. We conducted a simulation study, under various combinations of mean differences, variability, and sample size, to empirically compare the performance of different methods for assessment of agreement in terms of coverage probability, expected length, size, and power. Numerical data from published papers illustrate the application of the proposed methods.

Identification of dispersion effects from unreplicated 2 n- K fractional factorial designs

Abstract In this article, we present a test for dispersion effects from the unreplicated 2 n − k regular fractional factorial designs. The proposed procedure for the identification of dispersion effects uses the log-likelihood ratio based on normal errors. Some practical examples are given to illustrate the applicability of the test. It is shown that the proposed method is a useful and economical means for the identification of dispersion effects at the screening stage of experiments. Comparing the power of our method with the two methods published in the literature, we suggest that our test might be more sensitive for identifying the dispersion effects.

Optimal 2n-p fractional factorial designs for dispersion effects under a location-diapersion model

We consider main effects models for 2-level experiments that also include. Parameters characterizing potential dispersion effects due to specified factors. One special case is considered. In this case only a single specified factor is responsible for the dispersion effects. We determine the connection between alias relations and Optimality of a design for estimation of dispersion effects in the class of regu!ar fractional Y - P factorial designs of resolution III or higher. This rmectioil heips US identify those designs that are A-optimal for estimating dispersion effects by a suitable choice of defining contrasts. in particuiar, we show that an increase in efficiency with respect to dispersion effects is accompanied by a loss iii efficiency for estimating the location effects. In practice, one mmt thcrcfcre accept a trade& between the efficiencies associated with estirnates of location effects and dispersion effects.

Estimation for Conformance Proportions in a Normal Variance Components Model

Two approaches are proposed for constructing one- and two-sided confidence limits for conformance proportions in a normal variance components model. One approach is based on the concepts of a generalized pivotal quantity, and the other is developed using the modified large-sample method for estimating linear combinations of variance components. The performance of the proposed methods is evaluated through detailed simulation studies. The results reveal that the empirical coverage probabilities for both methods are close to the claimed values and hence their performance is judged to be satisfactory. Nonetheless, the modified large—sample-based method might be recommended in practical applications due to its slightly better performance and computational ease. The framework established in this article can be applied to conformance proportion questions arising in arbitrary balanced mixed linear-model situations. The methods are illustrated using three real datasets. Finally, a bootstrap calibration approach is adopted to have empirical coverage probabilities sufficiently close to the nominal level for the proposed methods.

Statistical Inference for the Within-Device Precision of Quantitative Measurements in Assay Validation

Intermediate precision is one of the most important characteristics for evaluation of precision in assay validation. The current methods for evaluation of within-device precision recommended by the Clinical Laboratory Standard Institute (CLSI) guideline EP5-A2 are based on the point estimator. On the other hand, in addition to point estimators, confidence intervals can provide a range for the within-device precision with a probability statement. Therefore, we suggest a confidence interval approach for assessment of the within-device precision. Furthermore, under the two-stage nested random-effects model recommended by the approved CLSI guideline EP5-A2, in addition to the current Satterthwaites approximation and the modified large sample (MLS) methods, we apply the technique of generalized pivotal quantities (GPQ) to derive the confidence interval for the within-device precision. The data from the approved CLSI guideline EP5-A2 illustrate the applications of the confidence interval approach and comparison of results between the three methods. Results of a simulation study on the coverage probability and expected length of the three methods are reported. The proposed method of the GPQ-based confidence intervals is also extended to consider the between-laboratories variation for precision assessment.