ASA Journal Session: JASA Theory & Methods
Session Slot: 10:30-12:20 Monday
Estimated Audience Size: xx-xxx
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Session Title: JASA Theory and Methods: Invited Papers
Theme Session: No
Applied Session: Yes/No
Session Organizer: Casella, George Cornell University
Address: Cornell University-Ithaca 434 Warren Hall Ithaca, NY 14853-7801
Phone: 607-255-5488
Fax: 607-255-4698
Email: gc15@cornell.edu
Session Timing: 110 minutes total (Sorry about format):
110 minutes total....however you want Opening Remarks by Chair - 5 minutes First Speaker - 45 minutes Discussant - 15 minutes Discussant - 15 minutes Discussant - 15 minutes Floor Discusion - 15 minutes
Session Chair: Casella, George Cornell University
Address: Cornell University-Ithaca 434 Warren Hall Ithaca, NY 14853-7801
Phone: 607-255-5488
Fax: 607-255-4698
Email: gc15@cornell.edu
1. Approximately Exact Inference for the Common Odds Ratio in Several 2x2 Tables
Strawderman, Robert L., University of Michigan
Address: Department of Biostatistics University of Michigan 1420 Washington Heights Ann Arbor, MI 48109-2029
Phone: (734) 936-1002
Fax: (734) 763-2215
Email: strawder@umich.edu
Wells, Martin T., Cornell University
Abstract: The conditional maximum likelihood estimator of the common odds ratio in a sequence of independent 2X2 tables is known to be superior to the Mantel-Haenszel estimator in terms of asymptotic efficiency and has the further advantage that its exact distribution is known. However, a long-standing barrier to the widespread use of this estimator has been computational intractability; in particular, the calculation of significance levels, confidence sets, and power based on the exact distribution requires fast and efficient algorithms. An important class of such algorithms form the basis of <italic>StatXact</italic> (Cytel, 1992), a software package able to solve various aspects of the exact inference problem for a sequence of several 2X2 tables in real time. In this paper, we provide an alternative methodology by developing several useful saddlepoint approxmiations to the exact distribution of the conditional maximum likelihood estimator. The approximations are derived from an interesting representation for hypergeometric random variables recently developed in Kou and Ying (1996a, b), and provide fast, accurate calculations of power functions, p-values, and confidence sets. The primary computational burden is in determining the roots of a certain polynomial, which need be done numerically but only once for each table. Consequently, the required computational effort is typically minimal; for example, all of the examples in this paper were done using code written by the authors entirely in S-plus.
Discussant: Mehta, Cyrus R. Cytel Software Corporation
Address: Cytel Software Corporation 675 Massachusetts Ave. Cambridge, MA 02139-3309
Phone: (617) 661-4405
Fax: (617) 661-2011
Email: mehta@jimmy.harvard.edu
Discussant: Booth, James University of Florida
Address: Department of Statistics University of Florida Gainesville, FL 32611
Phone: (904) 392-1941
Fax: (904) 392-5175
Email: jbooth@stat.ufl.edu
Butler, Ron, Colorado State University
Address: Department of Statistics Colorado State University Fort Collins, CO 80523
Phone: (303) 491-5269
Fax: (303) 491-7895
Email: walrus@stat.colostate.edu
List of speakers who are nonmembers: None