TY - JOUR

T1 - Simultaneous confidence intervals for ratios with applications to the comparison of several treatments with a control

AU - Dilba, Gemechis

AU - Bretz, F.

AU - Guiard, V.

AU - Hothorn, L. A.

PY - 2004

Y1 - 2004

N2 - Objectives: In this article, we illustrate and compare exact simultaneous confidence sets with various approximate simultaneous confidence intervals for multiple ratios as applied to many-to-one comparisons. Quite different datasets ore analyzed to clarify the points. Methods: The methods ore based on existing probability inequalities (e.g., Bonferrani, Slepian and Sidàk), estimation of nuisance parameters and re-sampling techniques. Exact simultaneous confidence sets based on the multivariate t-distribution are constructed and compared with approximate simultaneous confidence intervals. Results: It is found that the coverage probabilities associated with the various methods of constructing simultaneous confidence intervals (for ratios) in many-to-one comparisons depend on the ratios of the coefficient of variation for the mean of the control group to the coefficient of variation for the mean of the treatments. If the ratios of the coefficients of variations ore less than one, the Bonferroni corrected Fieller confidence intervals have almost the same coverage probability as the exact simultaneous confidence sets. Otherwise, the use of Bonferroni intervals leads to conservative results. Conclusions: When the ratio of the coefficient of variation for the mean of the control group to the coefficient of variation for the mean of the treatments ore greater than one (e.g., in balanced designs with increasing effects), the Bonferroni simultaneous confidence intervals are too conservative. Therefore, we recommend not using Bonferroni for this kind of data. On the other hand, the plug-in method maintains the intended confidence coefficient quite satisfactorily; therefore, it can serve as the best alternative in any case.

AB - Objectives: In this article, we illustrate and compare exact simultaneous confidence sets with various approximate simultaneous confidence intervals for multiple ratios as applied to many-to-one comparisons. Quite different datasets ore analyzed to clarify the points. Methods: The methods ore based on existing probability inequalities (e.g., Bonferrani, Slepian and Sidàk), estimation of nuisance parameters and re-sampling techniques. Exact simultaneous confidence sets based on the multivariate t-distribution are constructed and compared with approximate simultaneous confidence intervals. Results: It is found that the coverage probabilities associated with the various methods of constructing simultaneous confidence intervals (for ratios) in many-to-one comparisons depend on the ratios of the coefficient of variation for the mean of the control group to the coefficient of variation for the mean of the treatments. If the ratios of the coefficients of variations ore less than one, the Bonferroni corrected Fieller confidence intervals have almost the same coverage probability as the exact simultaneous confidence sets. Otherwise, the use of Bonferroni intervals leads to conservative results. Conclusions: When the ratio of the coefficient of variation for the mean of the control group to the coefficient of variation for the mean of the treatments ore greater than one (e.g., in balanced designs with increasing effects), the Bonferroni simultaneous confidence intervals are too conservative. Therefore, we recommend not using Bonferroni for this kind of data. On the other hand, the plug-in method maintains the intended confidence coefficient quite satisfactorily; therefore, it can serve as the best alternative in any case.

KW - Bonferroni

KW - Fieller's theorem

KW - Many-to-one comparisons

KW - Multivariate t-distribution

KW - Simultaneous confidence sets

UR - http://www.scopus.com/inward/record.url?scp=11144328071&partnerID=8YFLogxK

U2 - 10.1055/s-0038-1633899

DO - 10.1055/s-0038-1633899

M3 - Article

C2 - 15702202

AN - SCOPUS:11144328071

VL - 43

SP - 465

EP - 469

JO - Methods of information in medicine

JF - Methods of information in medicine

SN - 0026-1270

IS - 5

ER -