Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

Approximately Exact Inference for the Common Odds Ration in Several 2 × 2 Tables

Robert L. Strawderman and Martin T. Wells
Journal of the American Statistical Association
Vol. 93, No. 444 (Dec., 1998), pp. 1294-1307
DOI: 10.2307/2670044
Stable URL: http://www.jstor.org/stable/2670044
Page Count: 14
  • Download ($14.00)
  • Cite this Item
Approximately Exact Inference for the Common Odds Ration in Several 2 × 2 Tables
Preview not available

Abstract

The conditional maximum likelihood estimator (MLE) of the common odds ratio in a sequence of independent 2 × 2 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 StatXact, a software package able to solve various aspects of the exact inference problem for a sequence of several 2 × 2 tables in real time. We provide an alternative methodology by developing several useful saddlepoint approximations to the exact distribution of the conditional MLE. The approximations are derived from an interesting representation for hypergeometric random variables as a sum of independent Bernoulli random variables 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 only once for each table. Consequently, the required computational effort is typically minimal; for example, all of the examples herein were done using code written by the authors entirely in S-PLUS.

Page Thumbnails

  • Thumbnail: Page 
1294
    1294
  • Thumbnail: Page 
1295
    1295
  • Thumbnail: Page 
1296
    1296
  • Thumbnail: Page 
1297
    1297
  • Thumbnail: Page 
1298
    1298
  • Thumbnail: Page 
1299
    1299
  • Thumbnail: Page 
1300
    1300
  • Thumbnail: Page 
1301
    1301
  • Thumbnail: Page 
1302
    1302
  • Thumbnail: Page 
1303
    1303
  • Thumbnail: Page 
1304
    1304
  • Thumbnail: Page 
1305
    1305
  • Thumbnail: Page 
1306
    1306
  • Thumbnail: Page 
1307
    1307