IMS
Session Slot: 8:30-10:20 Thursday
Estimated Audience Size:
AudioVisual Request: Two Overheads
Session Title: Multiple Comparisons
Theme Session: No
Applied Session: No
Session Organizer: Hsu, Jason
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Session Timing: 110 minutes total (Sorry about format):
Session Chair: Spurrier, John University of South Carolina
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1. Semi-Bayesian Approaches to Multiple Pairwise Comparisons of Normal Means
Shaffer, Juliet P., University of California at Berkeley
Address: University of California, Department of Statistics, 367 Evans Hall # 3860, Berkeley, CA 94720-3860
Phone: 510-642-5411
Fax: 510-642-7892
Email: shaffer@stat.berkeley.edu
Abstract: Duncan proposed a Bayesian decision-theoretic approach to pairwise comparisons of normal means under the assumption that the population means are realizations of independent identically- distributed normal random variables; the method has minimum Bayes risk under the additional assumption of additive loss functions. Lewis and Shaffer have proposed pairwise comparison methods retaining the Duncan assumption of normally-distributed population means but using different loss functions. A modification of Lewis' method to control the familywise error rate (fwe), the most commonly-used error control criterion, allows a comparison with Shaffer's method, which controls the fwe for the overall null hypothesis only but is otherwise more compatible with the loss-function approach of Duncan. The comparison allows separate assessment of the increase in power due to (1) the assumption of a normal distribution of the population means over standard methods which do not incorporate this assumption, and (2) the modified criterion for error control.
2. Multiple Test Procedures for Safety Assessment
Tamhane, Ajit, Northwestern University
Address: Department of Statistics, 2006 Sheridan Road, Northwestern University, Evanston, IL 60208
Phone: (847)491-3577
Fax: (847)491-8005
Email: ajit@iems.nwu.edu
Abstract: We consider dose response studies for safety assessment of a compound and offer a new hypothesis testing approach for identifying the maximum dose level that is guaranteed to be safe with preassigned confidence. The conventional approach in which the lack of safety of a dose is demonstrated is also presented for comparison purposes. Both single-step (SS) and step-down (SD) multiple test procedures for identifying a maximum safe dose and a minimum unsafe dose are given in each case. These procedures control the familywise error rates for their respective hypotheses formulations. Their powers are studied via Monte Carlo simulation and sample sizes are provided for meeting specified power requirements. Procedures are illustrated by applying them to crop yield data from an agricultural field trial conducted to assess the safe level of a herbicide.
3. Stepwise Confidence Intervals without Multiplicity Adjustment
Hsu, Jason, The Ohio State University
Address:
Phone: 614-292-7663
Fax: 614-292-2096
Email: jch@stat.ohio-state.edu
Berger, Roger, North Carolina State University
Abstract: Not all simultaneous inferences need multiplicity adjustment. In this talk, we show that if the sequence of individual inferences is predefined, and failure to achieve the desired inference at any step renders subsequent inferences unnecessary, then confidence sets for such inferences can be obtained without multiplicity adjustment. Dose response studies, designed to show superiority of treatments over a placebo (negative control) or a drug known to be efficacious (active control), fit into this setting. Toxicity studies, designed to show equivalence of treated groups with a placebo, also fit into this setting. It is shown that, for these studies, the confidence set approach is more reliable in generating simple methods with meaningful guarantee against incorrect decision than other approaches.
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