Suggested answer to exercise: Can sutures get wet?, 6

In the Results section, Heal et al. (2006) report that:

"The intervention group had an infection rate of 8.4% compared with 8.9% in the control group. The one sided 95% confidence interval of the difference of the two proportions was infinity to 0.028, so the non-inferiority side was lower than 0.05, the maximum allowable difference. We therefore concluded that the intervention group was not inferior to the control group with respect to the resulting infection rates (P < 0.05)."

Question 6: How could we interpret the confidence interval infinity to 0.028? Why must it be wrong?

Suggested answer 6

A confidence interval is a range of values which we estimate to contain the population value. The population value in this case is the difference, uncovered wounds minus covered wounds, in the proportion experiencing infection.

First, it should not include 0.05 or 5 percentage points, because the difference is stated to be significantly below 0.05. Should it therefore be minus infinity to 0.028? Was a minus sign omitted?

Second, the difference between two proportions has to lie between -1.0 and +1.0, because each proportion has to be between zero and one. It cannot be larger than 1.0 or less than -1.0. The one-sided confidence interval should be -1.000 to +0.028.