The RISKDIFF option in the TABLES statement provides estimates
of risks (or binomial proportions) and risk differences
for 2 ×2 tables. This analysis may be appropriate when
comparing the proportion of some characteristic for two groups,
where row 1 and row 2 correspond to the two groups, and the
columns correspond to two possible characteristics or outcomes.
For example, the row variable might be a treatment or dose,
and the column variable might be the response. Refer to
Collett (1991), Fleiss (1981), and Stokes, Davis, and Koch (1995).
Let the frequencies of the 2 ×2 table be represented
as follows.

Column 1

Column 2

Total

Row 1  n_{11}  n_{12}  n_{1 ·} 
Row 2  n_{21}  n_{22}  n_{2 ·} 
Total  n_{·1}  n_{·2}  n 
The column 1 risk for row 1 is the proportion of row 1
observations classified in column 1,
This estimates the conditional probability of the column
1 response, given the first level of the row variable.
The column 1 risk for row 2 is the proportion of row 2
observations classified in column 1,
and the overall column 1 risk is the proportion of all
observations classified in column 1,

p_{·1} = n_{·1} / n
The column 1 risk difference compares the risks for the two
rows, and it is computed as the column 1 risk for row 1 minus
the column 1 risk for row 2,
The risks and risk difference are defined similarly for column 2.
The standard error of the column 1 risk estimate
for row i is computed as
The standard error of the overall
column 1 risk estimate is computed as
If the two rows represent independent binomial samples, the
standard error for the column 1 risk difference is computed as
The standard errors are computed in a similar manner for the column 2
risks and risk difference.
Using the normal approximation to the binomial distribution,
PROC FREQ constructs asymptotic confidence limits for the
risks and risk differences according to
where est is the estimate, is the
percentile of the standard normal distribution, and
se(est) is the standard error of the estimate.
The confidence level is determined from the value
of the ALPHA= option, which, by default, equals 0.05 and produces
95% confidence limits.
PROC FREQ computes exact confidence limits for the
column 1, column 2, and overall risks using the F distribution
method given in Collett (1991) and also described by
Leemis and Trivedi (1996). PROC FREQ does not provide
exact confidence limits for the risk differences. Refer to
Agresti (1992) for a discussion of issues involved in constructing
exact confidence limits for differences of proportions.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.