Measures of Location for Confidence Intervals for Proportions

Newcombe, Robert G.

doi:10.1080/03610921003646406

Cited by 52 publications

(48 citation statements)

References 33 publications

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“…As a result, the ECWs are computed as the average widths between the log of upper and lower limits of the 10,000 confidence intervals. In addition to CPs and ECWs, Newcombe [27] also suggested assessing location from overall coverage, that is, to check whether the CI is completely above or below the true value of the parameter of interest. This can be measured by an index MNCP/(DNCP+MNCP), which ranges on the interval [0,1].…”

Section: Simulationsmentioning

confidence: 99%

“…To overcome this issue, we also develop confidence interval procedures for the MR using the logarithmic transformation suggested by Katz et al [26]. In Section 3, we conduct a simulation study to investigate the performance of various confidence interval procedures, with respect their coverage probabilities, expected confidence widths and interval locations based on the approach suggested by Newcombe [27]. In Section 4, we include two examples from toxicology and epidemiology studies to illustrate the use of the proposed methods.…”

Section: Introductionmentioning

confidence: 99%

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Estimating the Treatment Effect in the Analysis of Extra-Dispersed Count Response Data from Clinical Trials

Saha¹

2013

J Biomet Biostat

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Responses in the form of counts arise in many clinical trials and epidemiological studies, and are usually extradispersed. When one wishes to estimate the treatment effect in comparison with a placebo in clinical trials, confidence intervals are frequently used. It is of common interest in many clinical trials and epidemiological studies, to obtain the confidence interval for one of the two quantities, mean difference and mean ratio. The preference of one measure over the other depends on the design of the study. In many situations, the mean ratio is more relevant than the difference of means. Confidence interval procedures for the mean difference between treatment and control groups in the analysis of such extra-dispersed counts have been studied recently, but no attention has been paid to investigating the problem of confidence interval construction for the mean ratio. In this article, we develop several asymptotic confidence interval procedures for the mean ratio, by using the delta method, to extend the variance of a single mean estimate to the variance of the mean ratio estimate. The simulation studies indicate that all procedures perform reasonably well in terms of coverage. However, the interval based on the generalized estimating equation approach, using the logarithmic transformation, performs uniformly best in terms of coverage, expected width and location, and is preferable to the other intervals, in most of the situations considered here. Finally, three real-life examples from clinical trials are analyzed to illustrate the proposed confidence interval procedures.

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Section: Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Estimating the Treatment Effect in the Analysis of Extra-Dispersed Count Response Data from Clinical Trials

Saha¹

2013

J Biomet Biostat

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“…According to [15], the interval location of the CIs can be characterized by the ratio Q = MNR 1 − R = MNR MNR + DNR This ratio expresses the balance condition between MNR and DNR. Based on a partition of the range of values of Q (see Fig.…”

Section: Coverage and Directional Non-coveragesmentioning

confidence: 99%

“…Based on a partition of the range of values of Q (see Fig. 2, on the top), [15] and, more recently, [13] established a classification criterion for the location of CIs for linear combinations of independent binomial proportions. Concretely, values of Q between 0.375 and 0.625 correspond to satisfactorily located CIs, less than 0.375 to CIs located too mesially to include the true value of L, and greater than 0.625 to CIs located too distally to include L. Hence, when (see Fig.…”

Section: Coverage and Directional Non-coveragesmentioning

confidence: 99%

“…Such evaluations are usually based on the exact coverage probabilities of each method. More recently ( [13,15,16]), the expected interval location of the CIs, which is based on the mesial and distal non-coverage probabilities, has also been considered as an important performance measure. In the present work we discuss a graphical representation of the two directional non-coverage probabilities, aimed at facilitating the characterization of interval location.…”

Section: Introductionmentioning

confidence: 99%

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A Simple Graphical Way of Evaluating Coverage and Directional Non-coverages

Freitas

Escudeiro

Afreixo

2017

Computational Science and Its Applications – ICCSA 2017

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Evaluation of the coverage probability and, more recently, of the intervalar location of confidence intervals, is a useful procedure if exact and asymptotic methods for constructing confidence intervals are used for some populacional parameter. In this paper, a simple graphical procedure is presented to execute this kind of evaluation in confidence methods for linear combinations of k independent binomial proportions. Our proposal is based on the representation of the mesial and distal non-coverage probabilities on a plane. We carry out a simulation study to show how this graphical representation can be interpreted and used as a basis for the evaluation of intervalar location of confidence interval methods.

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Interval estimation of the mean difference in the analysis of over‐dispersed count data

Saha

2012

Biometrical J

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This paper focuses on the development and study of the confidence interval procedures for mean difference between two treatments in the analysis of over-dispersed count data in order to measure the efficacy of the experimental treatment over the standard treatment in clinical trials. In this study, two simple methods are proposed. One is based on a sandwich estimator of the variance of the regression estimator using the generalized estimating equations (GEEs) approach of Zeger and Liang (1986) and the other is based on an estimator of the variance of a ratio estimator (1977). We also develop three other procedures following the procedures studied by Newcombe (1998) and the procedure studied by Beal (1987). As assessed by Monte Carlo simulations, all the procedures have reasonably well coverage properties. Moreover, the interval procedure based on GEEs outperforms other interval procedures in the sense that it maintains the coverage very close to the nominal coverage level and that it has the shortest interval length, a satisfactory location property, and a very simple form, which can be easily implemented in the applied fields. Illustrative applications in the biological studies for these confidence interval procedures are also presented.

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Measures of Location for Confidence Intervals for Proportions

Cited by 52 publications

References 33 publications

Estimating the Treatment Effect in the Analysis of Extra-Dispersed Count Response Data from Clinical Trials

Estimating the Treatment Effect in the Analysis of Extra-Dispersed Count Response Data from Clinical Trials

A Simple Graphical Way of Evaluating Coverage and Directional Non-coverages

Interval estimation of the mean difference in the analysis of over‐dispersed count data

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