PROC FREQ: Gail-Simon Test for Qualitative Interactions

Gail-Simon Test for Qualitative Interactions

The GAILSIMON option in the TABLES statement provides the Gail-Simon test for qualitative interaction for stratified $\text{[math]}$ 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 $\text{[math]}$ 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),

$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$

where $\text{[math]}$ is the risk difference in table $\text{[math]}$ , $\text{[math]}$ is the standard error of the risk difference, and $\text{[math]}$ equals 1 if $\text{[math]}$ and 0 otherwise. Similarly, $\text{[math]}$ equals 1 if $\text{[math]}$ and 0 otherwise. The $\text{[math]}$ $\text{[math]}$ tables (strata) are indexed by $\text{[math]}$ .

The $\text{[math]}$ -values for the Gail-Simon statistics are computed as

$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
$\text{[math]}$	$\text{[math]}$	$\text{[math]}$

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

The FREQ Procedure

Gail-Simon Test for Qualitative Interactions