TY - JOUR
T1 - A note on confidence bounds after fixed-sequence multiple tests
AU - Tu, Yi Hsuan
AU - Cheng, Bin
AU - Cheung, Ying Kuen
N1 - Funding Information:
We thank the Editor, Associated Editor, and two referees for helpful comments. Dr. Cheung's work was partially supported by NIH Grant R01 NS055809 . Dr. Tu's work was partially supported by National Science Council under Grant NSC 96-2118-M-006-008 .
PY - 2012/11
Y1 - 2012/11
N2 - We are concerned with the problem of estimating the treatment effects at the effective doses in a dose-finding study. Under monotone dose-response, the effective doses can be identified through the estimation of the minimum effective dose, for which there is an extensive set of statistical tools. In particular, when a fixed-sequence multiple testing procedure is used to estimate the minimum effective dose, Hsu and Berger (1999) show that the confidence lower bounds for the treatment effects can be constructed without the need to adjust for multiplicity. Their method, called the dose-response method, is simple to use, but does not account for the magnitude of the observed treatment effects. As a result, the dose-response method will estimate the treatment effects at effective doses with confidence bounds invariably identical to the hypothesized value. In this paper, we propose an error-splitting method as a variant of the dose-response method to construct confidence bounds at the identified effective doses after a fixed-sequence multiple testing procedure. Our proposed method has the virtue of simplicity as in the dose-response method, preserves the nominal coverage probability, and provides sharper bounds than the dose-response method in most cases.
AB - We are concerned with the problem of estimating the treatment effects at the effective doses in a dose-finding study. Under monotone dose-response, the effective doses can be identified through the estimation of the minimum effective dose, for which there is an extensive set of statistical tools. In particular, when a fixed-sequence multiple testing procedure is used to estimate the minimum effective dose, Hsu and Berger (1999) show that the confidence lower bounds for the treatment effects can be constructed without the need to adjust for multiplicity. Their method, called the dose-response method, is simple to use, but does not account for the magnitude of the observed treatment effects. As a result, the dose-response method will estimate the treatment effects at effective doses with confidence bounds invariably identical to the hypothesized value. In this paper, we propose an error-splitting method as a variant of the dose-response method to construct confidence bounds at the identified effective doses after a fixed-sequence multiple testing procedure. Our proposed method has the virtue of simplicity as in the dose-response method, preserves the nominal coverage probability, and provides sharper bounds than the dose-response method in most cases.
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U2 - 10.1016/j.jspi.2012.05.002
DO - 10.1016/j.jspi.2012.05.002
M3 - Article
AN - SCOPUS:84863005110
SN - 0378-3758
VL - 142
SP - 2993
EP - 2998
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
IS - 11
ER -