# Chapter 10. Combining Evidence from Fourfold Tables

1. Joseph L. Fleiss,
2. Bruce Levin,
3. Myunghee Cho Paik

Published Online: 5 JAN 2004

DOI: 10.1002/0471445428.ch10

## Statistical Methods for Rates and Proportions, Third Edition

#### How to Cite

Fleiss, J. L., Levin, B. and Paik, M. C. (2004) Combining Evidence from Fourfold Tables, in Statistical Methods for Rates and Proportions, Third Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471445428.ch10

#### Author Information

1. Department of Biostatistics, Mailman School of Public Health, Columbia University, USA

#### Publication History

1. Published Online: 5 JAN 2004
2. Published Print: 5 SEP 2003

#### Book Series:

1. Wiley Series in Probability and Statistics

#### Book Series Editors:

1. Walter A. Shewart,
2. Samuel S. Wilks

#### ISBN Information

Print ISBN: 9780471526292

Online ISBN: 9780471445425

## SEARCH

### Keywords:

• fourfold tables;
• construction;
• interpretation;
• chi-squared tests;
• logarithms;
• odds ratios;
• exact inference;
• common odds ratio;
• approximate inference;
• Mantel-Haenszel method;
• stratification versus matching

### Summary

The methods reviewed in this chapter are special cases of those available for the analysis of complex cross-classification tables. We describe how to use method with the logarithm of the odds ratio and then give the foundations of exact inference about a common odds ratio. Next, we describe approximate methods based on results of Cornfield and Gart. The Mantel-Haenszel method is described and presented. These methods are compared for different kinds of study designs, and we then indicate how they can be used as alternatives to matching in the control of confounding factors. We describe some popular but generally invalid methods for comparing and combining data from several fourfold tables. The chapter concludes with comments and results on matters related to confounding, meta-analysis, and tests for homogeneity of odds ratios in the large-sparse case. A problem solving section appears at the end of the chapter.