Negative Difference in Risk Tables

[chrissowden]

I am trying to understand  what a  negative number in the Asym 95% in the  Difference row.

[FreelanceReinh]

Hi @chrissowden,

The risks in the two groups (row 1 and row 2 in the PROC FREQ cross tabulation) seem to be fairly similar: Assuming the true risks were equal to the average empirical risk in your sample (0.08 for column 1, see "Total" row in the upper table), one would expect about 0.08*538≈43 and 0.08*675=54 "cases" in row 1 and row 2, respectively. (I hope I guessed the numbers 538 and 675 correctly.) The slightly different observed numbers, 39 (i.e. 4 less) and 58 (4 more), can be due to chance. This is what I would conclude from the fact that zero is contained in the confidence interval for the risk difference: [-0.0439, 0.0170]. An interval around zero has necessarily a negative lower limit (and a positive upper limit). So, even though the observed relative frequency of "cases" in row 2 was slightly (by 1.34 percentage points) higher than in row 1, it cannot be ruled out that the true (column 1) risk in row 1 is higher. Your data don't provide enough evidence to decide this.

[Ksharp]

That is Confidence Interval for diff of Risk, which contains ZERO , i.e. You can't reject H0: Risk in Row1=Risk in Row2