PROC FREQ provides Mantel-Haenszel and summary score estimates for the common risk (proportion) difference for multiway tables.

PROC FREQ computes the Mantel-Haenszel (Mantel and Haenszel, 1959) estimate of the common risk difference as

where is the risk difference in stratum h and

The column 1 risk difference in stratum h is computed as

where is the proportion of row 1 observations that are classified in column 1 and is the proportion or row 2 observations that are classified in column 1. The column 2 risk is computed in the same way. For more information, see Agresti (2013, p. 231).

PROC FREQ computes the variance of (Sato, 1989) as

where

The % confidence limits for the common risk difference are

PROC FREQ computes the summary score estimate of the common risk difference as described in Agresti (2013, p. 231). This estimate is computed from Miettinen-Nurminen (score) confidence limits for the stratum risk differences. For more information, see the section “Miettinen-Nurminen (Score) Confidence Limits.” The score confidence interval for the risk difference in stratum h can be expressed as , where is the midpoint of the score confidence interval and is the width of the confidence interval divided by . The summary score estimate of the common risk difference is computed as

where

The variance of is computed as

The % summary score confidence limits for the common risk difference are