Confidence intervals on linear combinations of variance components that are unrestricted in sign

Ting, Naitee; Burdick, Richard K.; Graybill, Franklin A.; Jeyaratnam, S.; Lu, Tai-Fang C.

doi:10.1080/00949659008811240

Cited by 94 publications

(43 citation statements)

References 5 publications

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“…The conÿdence interval of X − Y is calculated based on (9). A total of 10 000 simulation runs was considered.…”

Section: Parallel Be Trialmentioning

confidence: 99%

“…As indicated in Howe [6], his method can be applied to obtain an approximate upper conÿdence bound for positive linear combination of chi-square random variables. This approach has been generalized to any linear combination of chi-square random variables by Graybill and Wang [8], and Ting et al [9]. Hyslop et al [10] obtained a 95 per cent conÿdence upper bound for the linearized individual bioequivalence (IBE) criteria by applying this approach to a 2 × 4 cross-over design.…”

Section: Introductionmentioning

confidence: 98%

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A practical approach for comparing means of two groups without equal variance assumption

Wang

Chow

2002

Statistics in Medicine

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In this paper we consider two-groups of i.i.d. normally distributed random variables (N(mu(x),sigma(x) (2)) and N(mu(y),sigma(y) (2))) without assuming equal variance (sigma(x) (2) = sigma(y) (2)). We propose a simple method for constructing confidence bounds based on Howe's approximation I. Its applications in parallel clinical trial (testing H(0) : mu(x)-mu(y)=0 versus H(1) : mu(x)-mu(y)<0) and parallel bioequivalence (BE) trial (testing H(0):mid R:mu(x)-mu(y)mid R:delta versus H(1):mid R:mu(x)-mu(y)mid R:

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“…The conÿdence interval of X − Y is calculated based on (9). A total of 10 000 simulation runs was considered.…”

Section: Parallel Be Trialmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

A practical approach for comparing means of two groups without equal variance assumption

Wang

Chow

2002

Statistics in Medicine

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“…In this approach, the confidence limits under large-sample normal theory are modified so that they become exact for small or moderate sample sizes. Later, an extension of the MLS-type approach was proposed 28 on linear combinations of variance components that are unrestricted in sign. The MLS approach was extended 29,30 to ICC, but none of these approaches investigated ICCs for three-way mixed effects models.…”

Section: Introductionmentioning

confidence: 99%

Confidence intervals for intraclass correlation coefficients in variance components models

Demetrashvili

Wit

Heuvel

2016

Stat Methods Med Res

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Confidence intervals for intraclass correlation coefficients in agreement studies with continuous outcomes are model-specific and no generic approach exists. This paper provides two generic approaches for intraclass correlation coefficients of the form P Q q¼12 p Þ. The first approach uses Satterthwaite's approximation and an F-distribution. The second approach uses the first and second moments of the intraclass correlation coefficient estimate in combination with a Beta distribution. Both approaches are based on the restricted maximum likelihood estimates for the variance components involved. Simulation studies are conducted to examine the coverage probabilities of the confidence intervals for agreement studies with a mix of small sample sizes. Two different three-way variance components models and balanced and unbalanced one-way random effects models are investigated. The proposed approaches are compared with other approaches developed for these specific models. The approach based on the F-distribution provides acceptable coverage probabilities, but the approach based on the Beta distribution results in accurate coverages for most settings in both balanced and unbalanced designs. A real agreement study is provided to illustrate the approaches.

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“…Our intervals are based on the methods presented by Howe [12] for the sum of two independent random variables with known distributions. Howe's method was generalized for linear combinations of variance components by Graybill and Wang [13], and Burdick and Graybill [14] and Ting et al [15]. Also, Holder and Hsuan [7] considered these methods in an alternative approach to individual bioequivalence.…”

Section: Introductionmentioning

confidence: 99%

A small sample confidence interval approach to assess individual bioequivalence

2000

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The concept of interchangeable pharmaceutical products has been examined in great detail in the literature. Anderson and Hauck proposed a statistical random coefficient model to study ‘switchability’, and coined the phrase ‘individual bioequivalence’ which they defined with a probability‐based inequality. Since that paper there has been considerable work and discussion. The Food and Drug Administration has recommended the introduction of individual bioequivalence (IBE) and population bioequivalence (PBE) methods in a draft guidance document. The proposal in the draft guidance includes criteria for IBE and PBE and recommends the use of non‐parametric bootstrap 95 per cent upper confidence intervals for the conclusion of either IBE or PBE. However, this method requires intensive computations. We have developed an alternative confidence interval procedure to assess IBE by the FDA recommended criteria. This method utilizes Howe's approximation I to a Cornish–Fisher expansion. Our proposed method is applicable to balanced or unbalanced data in a broad class of extended cross‐over designs, and can be easily programmed using readily available software. Copyright © 2000 John Wiley & Sons, Ltd.

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Confidence intervals on linear combinations of variance components that are unrestricted in sign

Cited by 94 publications

References 5 publications

A practical approach for comparing means of two groups without equal variance assumption

A practical approach for comparing means of two groups without equal variance assumption

Confidence intervals for intraclass correlation coefficients in variance components models

A small sample confidence interval approach to assess individual bioequivalence

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