### Gail-Simon Test for Qualitative Interactions

The GAILSIMON option in the TABLES statement provides the Gail-Simon test for qualitative interaction for stratified tables. See Gail and Simon (1985), Silvapulle (2001), and Dimitrienko et al. (2005) for details.

The Gail-Simon test is based on the risk differences in stratified tables, where the risk difference is defined as the row 1 risk (proportion in column 1) minus the row 2 risk. See the section Risks and Risk Differences for details. By default, the procedure uses column 1 risks to compute the Gail-Simon test. If you specify the GAILSIMON(COLUMN=2) option, the procedure uses column 2 risks.

PROC FREQ computes the Gail-Simon test statistics as described in Gail and Simon (1985),

where is the risk difference in table , is the standard error of the risk difference, and equals 1 if and 0 otherwise. Similarly, equals 1 if and 0 otherwise. The tables (strata) are indexed by .

The -values for the Gail-Simon statistics are computed as

where is the cumulative chi-square distribution function with degrees of freedom and is the binomial probability function with parameters and . The statistic tests the null hypothesis of no qualitative interaction. The statistic tests the null hypothesis of positive risk differences. A small -value for indicates negative differences; similarly, a small -value for indicates positive risk differences.

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