Power to detect reduction in mortality

Rudolf N Cardinal

BMJ, 4 September 2005
http://www.bmj.com/cgi/eletters/331/7515/468#115688

In this interesting article, Crump and colleagues report that "[t]here were significantly fewer deaths in the intervention compounds than in the control compounds (relative risk of death 0.58, P = 0.036)." Tumwine notes in an otherwise excellent editorial: "The authors also report fewer deaths in the intervention group than in the control group. It is not clear, however, whether the study had enough power to detect a significant difference in mortality..." As a statistical matter, the answer to this question is "yes". A significant difference in mortality was detected, albeit between the combined intervention groups (flocculant + hypochlorite groups) and controls. It is relevant to enquire as to the power of a study in advance, and when significant effects are not obtained, but one cannot criticize a study for inadequate power in respect of effects that it found to be significant. Whatever the a priori power to detect an effect (i.e. to declare it significant), if an effect is found (to be significant), the power was sufficient by definition. (A colleague of mine points out that the power to detect a non-existent effect - counterintuitive as this sounds - is defined to be alpha, typically 0.05.) It is, of course, possible that the mortality reduction was due to chance; if there was no genuine reduction in mortality induced by the combined interventions, the probability of finding data as extreme as those obtained by the authors or more so, by chance alone, was P = 0.036. (Unfortunately, we do not know the actual probability that the results obtained were due to chance, for that is a different question entirely.) There was certainly inadequate power to detect a difference in mortality between flocculant and hypochlorite (RR 0.87, P = 0.703 by a simple chi square calculation ignoring family compound). 

Competing interests: None declared