Analysis of a Pair of Stratified 2x2 Contingency Tables

Anastasia Ivanova	Vance Berger
University of North Carolina at Chapel Hill	National Cancer Institute
aivanova@bios.unc.edu	vb78c@nih.gov

Here we analyze a pair of 2´2 tables, resulting from a study with a single binary endpoint when the analysis calls for stratification. Consider the data from Kurtiz et al. (1988).

	Some initial pain			Lots of initial pain
	5–8 hours	0–4 hours		5–8 hours	0–4 hours
Placebo	4	14	Placebo	11	15
A & B	0	19	A&B	1	25

The software written in Splus implements several tests that can be used to analyze a pair of 2x2 contingency tables

• the Mantel–Haenszel test, a linear rank test that is based on a ratio, with the sum of the upper-left cell counts minus their null expectations as the numerator and the square root of the sum of their variances as the denominator;
• the Smirnov test, a nonlinear rank test that is based on the larger of the two between-group success rates and 0;
• the convex hull test, a nonlinear rank test that is based on directional convex hull peeling of the permutation sample space.

The last two tests had been developed by the authors and have an advantage of being nonlinear rank tests.

Function MH2x2.test plots extreme and rejection regions (one-sided, nominal alpha=0.05), and calculates the p-value.

Function Smirnov2x2.test plots extreme and rejection regions (one-sided, nominal alpha=0.05), and calculates the p-value.

Function chull2x2.test plots extreme and rejection regions (one-sided, nominal alpha=0.05), and calculates the p-value.

Downloads

The programs are developed in S-PLUS 4.0 for Microsoft Windows. The following downloads include the source functions. Create a directory, say CATEGORICAL, for the program. Download and extract the appropriate file there. For example, to install the function MH2x2.test, source the MH2x2.s file into S-PLUS via

source("<path>/ MH2x2.s")

where <path> is the directory in which the program files are located. Or just copy the function and paste it into S-PLUS.

TRY IT

> MH2x2.test(4, 14, 0, 19, 11, 15, 1, 25)

> Smirnov2x2.test(4, 14, 0, 19, 11, 15, 1, 25)

> chull2x2.test(4, 14, 0, 19, 11, 15, 1, 25)