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The FREQ Procedure |
The odds of a positive response (column 1) in row 1 is n_{11} / n_{12}. Similarly, the odds of a positive response in row 2 is n_{21} / n_{22}. The odds ratio is formed as the ratio of the row 1 odds to the row 2 odds. The odds ratio for 2 ×2 tables is defined as
The odds ratio can be any nonnegative number. When the row and column variables are independent, the true value of the odds ratio equals 1. An odds ratio greater than 1 indicates that the odds of a positive response are higher in row 1 than in row 2. Values less than 1 indicate the odds of positive response are higher in row 2. The strength of association increases with the deviation from 1.
The transformation G = ( OR-1)/( OR+1) transforms the odds ratio to the range (-1,1) with G = 0 when OR = 1; G = -1 when OR = 0; and G approaches 1 as OR approaches infinity. G is the gamma statistic, which PROC FREQ computes when you specify the MEASURES option.
The asymptotic % confidence limits for the odds ratio are
When you specify option OR in the EXACT statement, PROC FREQ computes exact confidence limits for the odds ratio using an iterative algorithm based on that presented by Thomas (1971). Because this is a discrete problem, the confidence coefficient for these exact confidence limits is not exactly but is at least .Thus, these confidence limits are conservative. Refer to Agresti (1992).
The column 1 relative risk is the ratio of the column 1 risks for row 1 to row 2. The column 1 risk for row 1 is the proportion of the row 1 observations classified in column 1,
The asymptotic % confidence limits for the column 1 relative risk are
PROC FREQ computes the column 2 relative risks in a similar manner.
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