Suggested answer to exercise: Can sutures get wet?, 5

In the Methods section of the paper, we read:

"We calculated sample size on the basis of a pilot study done in February to June 2004 and involving 543 patients, which showed an overall infection rate of 5.7%. On the basis of a projected infection rate of 5%, we decided that an increase in incidence of infection of 5% would be clinically significant."

Hence the view of these authors was that there would be no important difference between the treatments if the proportion experiencing infection rose from 5% for covered sutures to 10% for uncovered sutures. They intended to cary out "a one sided equivalence test of proportions".

These authors wanted to know whether allowing wounds to get wet would be detrimental to the patient, in particular whether it would increase the risk of infection by more than 5 percentage points. 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 5: What argument might be made for a one-tailed test here? Do you think it is sound?

Suggested answer 5

The argument would be that the present practice is to keep wounds covered. The conventional view would be that leaving them uncovered would promote infection. The authors think that if the infection rate is not greatly increased, then leaving wounds uncovered would be the treatment of choice.

If they tested the null hypothesis that there were no difference, this would be irrelevant. They do not mind if the proportion infected increases slightly.

If they tested the null hypothesis that the difference was 0.05 or 5 percentage points, a significant difference showing that the difference was even greater than this would be irrelevant, as even if the difference were 0.05 they would not recommend leaving wounds uncovered.

I think that the whole thing is highly dubious. The null hypothesis value of 0.05 or 5 percentage points in entirely arbitrary and no attempt is made in the paper to justify it.