#### Gail-Simon Test for Qualitative Interactions

The GAILSIMON option in the TABLES statement provides the Gail-Simon test for qualitative interaction for stratified tables. For more information, see Gail and Simon (1985); Silvapulle (2001); Dmitrienko et al. (2005).

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. For more information,
see the section Risks and Risk Differences. By default, PROC FREQ uses column 1 risks to compute the Gail-Simon test. If you specify the GAILSIMON(COLUMN=2) option,
PROC FREQ 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 h, is the standard error of the risk difference, and equals 1 if and 0 otherwise. Similarly, equals 1 if and 0 otherwise. The q tables (strata) are indexed by .

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

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