Modified Large Sample Research Articles

Statistical procedures for testing hypotheses of equivalence in the safety evaluation of a genetically modified crop

SUMMARYSafety evaluation of a genetically modified crop entails assessing its equivalence to conventional crops under multi-site randomized block field designs. Despite mounting petitions for regulatory approval, there lack a scientifically sound and powerful statistical method for establishing equivalence. The current paper develops and validates two procedures for testing a recently identified class of equivalence uniquely suited to crop safety. One procedure employs the modified large sample (MLS) method; the other is based on generalized pivotal quantities (GPQs). Because both methods were originally created under balanced designs, common issues associated with incomplete and unbalanced field designs were addressed by first identifying unfulfilled theoretical assumptions and then replacing them with user-friendly approximations. Simulation indicated that the MLS procedure could be very conservative in many occasions irrespective of the balance of the design; the GPQ procedure was mildly liberal with its type I error rate near the nominal level when the design is balanced. Additional pros and cons of these two procedures are also discussed. Their utility is demonstrated in a case study using summary statistics derived from a real-world dataset.

Modified large sample confidence intervals for Poisson distributions: Ratio, weighted average, and product of means

Interval estimation procedures for the ratio of two Poisson means, weighted average of Poisson rates, and product of powers of Poisson means are considered. We propose a confidence interval (CI) based on the modified large sample (MLS) approach, and compare with the Cox CIs and the Wilson-score CIs. Our numerical studies indicate that the MLS CI is comparable with the Cox CI, and offers improvement in some cases. We also provide MLS CI for a weighted sum of Poisson means and compare with the available approximate CIs. The methods are illustrated using two examples.

Sample size methods for constructing confidence intervals for the intra-class correlation coefficient

The intraclass correlation coefficient (ICC) in a two-way analysis of variance is a ratio involving three variance components. Two recently developed methods for constructing confidence intervals (CI’s) for the ICC are the Generalized Confidence Interval (GCI) and Modified Large Sample (MLS) methods. The resulting intervals have been shown to maintain nominal coverage. But methods for determining sample size for GCI and MLS intervals are lacking. Sample size methods that guarantee control of the mean width for GCI and MLS intervals are developed. In the process, two variance reduction methods are employed, called dependent conditioning and inverse Rao-Blackwellization. Asymptotic results provide lower bounds for mean CI widths, and show that MLS and GCI widths are asymptotically equivalent. Simulation studies are used to investigate the new methods. A real data example is used and application issues discussed. The new methods are shown to result in adequate sample size estimates, the asymptotic estimates are accurate, and the variance reduction techniques are effective. A sample size program is developed.11R program can be downloaded at http://dobbinuga.com. Future extensions of these results are discussed.

Sample size determination for individual bioequivalence inference.

Statistical criterion for evaluation of individual bioequivalence (IBE) between generic and innovative products often involves a function of the second moments of normal distributions. Under replicated crossover designs, the aggregate criterion for IBE proposed by the guidance of the U.S. Food and Drug Administration (FDA) contains the squared mean difference, variance of subject-by-formulation interaction, and the difference in within-subject variances between the generic and innovative products. The upper confidence bound for the linearized form of the criterion derived by the modified large sample (MLS) method is proposed in the 2001 U.S. FDA guidance as a testing procedure for evaluation of IBE. Due to the complexity of the power function for the criterion based on the second moments, literature on sample size determination for the inference of IBE is scarce. Under the two-sequence and four-period crossover design, we derive the asymptotic distribution of the upper confidence bound of the linearized criterion. Hence the asymptotic power can be derived for sample size determination for evaluation of IBE. Results of numerical studies are reported. Discussion of sample size determination for evaluation of IBE based on the aggregate criterion of the second moments in practical applications is provided.

A Monte Carlo simulation study of two-sided tolerance intervals in balanced one-way random effects model for non-normal errors

Recently, Ong and Mukerjee [Probability matching priors for two-sided tolerance intervals in balanced one-way and two-way nested random effects models. Statistics. 2011;45:403–411] developed two-sided Bayesian tolerance intervals, with approximate frequentist validity, for a future observation in balanced one-way and two-way nested random effects models. These were obtained using probability matching priors (PMP). On the other hand, Krishnamoorthy and Lian [Closed-form approximate tolerance intervals for some general linear models and comparison studies. J Stat Comput Simul. 2012;82:547–563] studied closed-form approximate tolerance intervals by the modified large-sample (MLS) approach. We compare the performances of these two approaches for normal as well as non-normal error distributions. Monte Carlo simulation methods are used to evaluate the resulting tolerance intervals with regard to achieved confidence levels and expected widths. It turns out that PMP tolerance intervals are less conservative for data with large number of classes and small number of observations per class and the MLS procedure is preferable for smaller sample sizes.

Closed-form approximate tolerance intervals for some general linear models and comparison studies

The problems of constructing tolerance intervals (TIs) in random effects model and in a mixed linear model are considered. The methods based on the generalized variable (GV) approach and the one based on the modified large sample (MLS) procedure are evaluated with respect to coverage probabilities and expected width in various setups using Monte Carlo simulation. Our comparison studies indicate that the TIs based on the MLS procedure are comparable to or better than those based on the GV approach. As the MLS TIs are in closed-form, they are easier to compute than those based on the GV approach. TIs for a two-way nested model are also derived using the MLS method, and their merits are evaluated using simulation. The procedures are illustrated using a practical example.

Statistical evaluation of non‐profile analyses for the in vitro bioequivalence

AbstractFor locally acting drug products such as nasal aerosols and nasal sprays, the 2003 US Food and Drug Administration (FDA) draft guidance suggests that bioequivalence between generic and brand‐name products be established through in vitro tests. In addition, for non‐profile analyses based on spray content uniformity, droplet size distribution, spray pattern, priming, and re‐priming, the draft US FDA guidance recommends that the population bioequivalence (PBE) between generic and innovator's products be demonstrated. However, the linearized criterion recommended in the draft FDA guidance does not take into consideration the variations due to batches, samples, and life stages. Hence, under a two‐stage nested random effects model, we apply the methods of modified large‐sample (MLS) and generalized pivotal quantities (GPQs) to construct the upper 95% confidence limit for in vitro PBE criterion with consideration of variance components as the statistical testing procedures for establishing the in vitro BE. A simulation study was conducted to compare empirical size and empirical power among the three methods. A numerical example illustrates the proposed methods. Copyright © 2010 John Wiley & Sons, Ltd.

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 Satterthwaite's 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.

Confidence Intervals for Linear Function of Variance Components in Two-Fold Nested Random Effects Model

In the article, we consider the unbalanced case of the two-way nested random effects model under partial balance. Using the method of generalized confidence intervals (GCIs) introduced in Weeranhandi (19931995), a new method is proposed for constructing confidence intervals on linear function of variance components. To compare the resulted intervals with the Modified Large Sample (MLS) intervals by Hernandez and Burdick (1993), a simulation study is conducted. The results indicate that the proposed method performs better than the MLS method, especially for very unbalanced designs.

Confidence intervals for the comparison of variability estimates for a mixed model

AbstractIn this paper, we develop methods for generating confidence intervals for the comparison of variability estimates in a mixed‐effects model. A generalized confidence interval (GCI) is developed and contrasted to the modified large sample (MLS) method with an adjustment for a fixed effect. The methods are assessed using a computer simulation. Recommendations are provided for selecting an appropriate method. Copyright © 2007 John Wiley & Sons, Ltd.

Confidence Intervals on Sum of Variance Components in Unbalanced Two-Fold Nested Designs with Equal Subsampling

In the article, we consider the the unbalanced case of the two-way nested designs with equal subsampling. Using the method of generalized confidence intervals introduced in Weeranhandi (19931995), a new method is proposed for constructing confidence intervals on sum of variance components. To compare the resulted intervals with the Modified Large Sample (MLS) intervals by Burdick and Graybill (1985), a simulation study is conducted. The results indicate that the proposed method performs better than the MLS method, especially for very unbalanced designs.

Closed-Form Confidence Intervals on Measures of Precision for An Interlaboratory Study

Within the pharmaceutical industry it is common practice to transfer analytical methods from one laboratory to other laboratories. An experiment or interlaboratory study is performed to estimate the repeatability, the intermediate precision, and the reproducibility of the analytical method. These measures of precision are quantified by appropriate sums of variance components from an analysis of variance model describing the structure of the data. In the literature, several methods have been described for calculating approximate (closed-form) confidence intervals on sums of variance components, i.e., Welch, Satterthwaite, and modified large-sample (MLS). Comparisons between these methods have been performed for one-way and two-way classification analysis of variance models only. Interlaboratory studies though often need higher order classifications. Therefore, these methods for constructing confidence intervals are compared on the measures of precision from a specific three-way classification analysis of variance model that is frequently used for method transfer studies. Using a simulation study, the coverage probability for these methods is evaluated in situations where variance components may be estimated negatively with the standard moment estimates and where either the standard moment estimates are adjusted to zero or remain unadjusted. The MLS method is superior to the other two methods in case the standard moment estimates are used. If the adjusted moment estimates are used, then the method of Satterthwaite performs similar to the MLS method for many settings of the variance components and sample sizes but much better for some particular settings. The method of Satterthwaite performs better than the method of Welch for all the selected settings of variance components and sample sizes, irrespective of the standard or adjusted moment estimates.

분산 성분 모형에 대한 붓스트랩 보정 신뢰구간

분산 성분 모형 하에서 분산 성분들의 함수에 대한 통계적인 추론, 특히 소표본 하에서의 신뢰구간에 대한 방법들은 오랜 기간에 걸쳐서 여러 가지 방법들이 개발되어져 왔다. 그 대표적인 방법이 Graybill and Wang(1980)에 의해 제안된 수정 대표본 방법에 의거한 신뢰구간 추정법이며 현재까지 다양한 실험계획 방법 하에서 분산 성분들의 여러 가지 형태의 함수들에 대하여 확장과 개량이 이루어져 왔다. 본 연구에서는 분산 성분 모형의 균형 실험 가정 하에서 분산 성분들의 선형 결합이 관심있는 모수일 때 분산 분석에 의해 얻어진 수정 대표본 신뢰구간의 실제 포함확률을 툴스트랩 보정을 이용하여 개선하는 방법에 대하여 논의한다. 붓스트랩 보정을 이용함으로서 신뢰구간의 포함 확률의 정도는 점근적 이차 차수까지 개선되며 특히 선형 결합의 계수들이 모두 양수이고 결합의 수가 증가할 경우 수정 대표본 신뢰구간의 포함확률이 주어진 신뢰계수보다 항상 커지게 되는 단점을 개선할 수 있음을 보인다. 제안된 붓스트랩 보정 신뢰구간의 효율을 소표본의 경우에 모의실험을 통하여 평가한다. We consider use of Bootstrap calibration in the problem of setting a confidence interval for a linear combination of variance components. Based on the the modified large sample(MLS) method by Graybill and Wang(1980), Bootstrap Calibration is applied to improve the coverage probability of the MLS confidence bound when the experiment is balanced and coefficients of a linear combination are positive. Performance of the proposed confidence bound in small sample is investigated by simulation studies.

Confidence intervals on intraclass correlation coefficients in a balanced two-factor random design

A modified large-sample (MLS) approach and a generalized confidence interval (GCI) approach are proposed for constructing confidence intervals for intraclass correlation coefficients. Two particular intraclass correlation coefficients are considered in a reliability study. Both subjects and raters are assumed to be random effects in a balanced two-factor design, which includes subject-by-rater interaction. Computer simulation is used to compare the coverage probabilities of the proposed MLS approach (GiTTCH) and GCI approaches with the Leiva and Graybill [1986. Confidence intervals for variance components in the balanced two-way model with interaction. Comm. Statist. Simulation Comput. 15, 301–322] method. The competing approaches are illustrated with data from a gauge repeatability and reproducibility study. The GiTTCH method maintains at least the stated confidence level for interrater reliability. For intrarater reliability, the coverage is accurate in several circumstances but can be liberal in some circumstances. The GCI approach provides reasonable coverage for lower confidence bounds on interrater reliability, but its corresponding upper bounds are too liberal. Regarding intrarater reliability, the GCI approach is not recommended because the lower bound coverage is liberal. Comparing the overall performance of the three methods across a wide array of scenarios, the proposed modified large-sample approach (GiTTCH) provides the most accurate coverage for both interrater and intrarater reliability.

Confidence Intervals on Sum of Variance Components with Unbalanced Designs

ABSTRACT In this article, a new method is proposed for constructing confidence intervals on the response variance in the unbalanced case of the one-way variance component model via generalized inference. It is shown that the generalized pivotal quantity in the method can be derived by the fiducial method directly and easily. To compare the resulted interval with the Modified Large Sample (MLS) interval by Burdick and Graybill (1984) and an approximate generalized confidence interval, a simulation study is conducted. The results indicate that the proposed method performs better than the other two methods, especially for very unbalanced designs.

A new approach for interval estimation and hypothesis testing of a certain intraclass correlation coefficient: the generalized variable method.

We consider the problems of interval estimation and hypothesis testing for the intraclass correlation coefficient in an interrater reliability study when both raters and subjects are assumed to be randomly selected from populations of raters and subjects, respectively. We propose a novel approach for the confidence interval estimation and hypothesis testing using the concepts of generalized confidence interval (GCI) and generalized P-values. A simulation study is conducted to investigate the coverage probabilities of the GCI approach relative to the modified large sample (MLS) approach. Both methods tend to provide somewhat conservative coverage. Relative to the MLS approach, the GCI approach is closer to the correct (nominal) coverage for a two-sided interval, but farther to the correct coverage for a one-sided lower interval. Unlike the MLS approach, the GCI approach can also easily provide P-values. The fact that the GCI approach is suitable for confidence interval estimation and obtaining P-values makes the GCI approach a suitable candidate for making inference about interrater reliability.

Modified Large-Sample Confidence Intervals for Linear Combinations of Variance Components

We consider the problem of setting a confidence interval or bound for a linear combination of variance components related to a multivariate normal distribution, which includes important applications such as comparing variance components and testing the bioequivalence between two drug products. The lack of an exact confidence interval for a general linear combination of variance components spurred the development of a modified large-sample (MLS) method that was shown to be superior to many other approximation methods. But existing MLS method requires the use of independent estimators of variance components. Using a chi-squared representation of a quadratic form of a multivariate normal vector, we extend the MLS method to situations in which estimators of variance components are dependent. Using Edgeworth and Cornish–Fisher expansions, we explicitly derive the second-order asymptotic coverage error of the MLS confidence bound. Our results show that the MLS confidence bound is not second-order accurate in general, but is much better than the confidence bound based on normal approximation and is nearly second-order accurate in some special cases. Our results also show how to construct an MLS confidence bound that is second-order accurate. As an application, we discuss the use of the MLS method in assessing population bioequivalence, with some simulation results and an example.

A MODIFIED LARGE SAMPLE APPROACH IN THE ASSESSMENT OF POPULATION BIOEQUIVALENCE

The U.S. Food and Drug Administration (FDA) requires pharmaceutical companies to show bioequivalence between different formulations or generic companies to show bioequivalence between generic drugs and brand drugs before a9680186roval. In a recent FDA guidance on bioequivalence, new criteria were proposed for assessment of population and individual bioequivalence. In this article, computer simulation is used to compare a modified large sample (MLS) upper bound for the population bioequivalence ratio with the bootstrap upper bound recommended by the FDA. The comparison criteria are the ability to maintain the stated confidence level and the estimated power of tests based on these bounds.

Confidence intervals for variance components from gauge capability studies

Two methods of constructing confidence intervals for variance components in gauge capability studies are presented in this article. Comparisons are made between the restricted maximum likelihood (REML) method and the modified large sample (MLS) method for constructing confidence intervals for components of repeatability, reproducibility, and total (gauge) variability. The examples considered involve a factorial design and a nonstandard nested design. © 1997 John Wiley & Sons, Ltd.