On the comparison of effects.

Abstract

In a recent communication,' Poole has proposed epidemiologists draw an occasional p-value function in order to help them avoid misinterpreting confidence intervals (CIs). Such an exercise might well have some value, and certainly p-value function does impart more information than a single CI. However, I doubt such functions are appreciably less subject to misinterpretation than are CIs, and I take strong exception to suggestion by Poole my perspective on CIs2 leads to fallacious conclusions would be averted by a consideration of p-value functions. Poole offers two examples of insights might be provided by plotting of p-value functions. First, he plots such functions for two examples given in Figures 1 and 2 ofmy paper.2 From plots he concludes the two point estimates are virtually identical, but one estimate is much more precise than other. ' Even most cursory inspection of my figures would lead to exactly same conclusion, and I would hope even without benefit of a picture most readers are able to make similar sense out of reported point estimates and CIs of 2.3 (95 per cent CI = 0.4-17.3) versus 2.5 (95 per cent CI = 1.3-4.7). The second of Poole's examples concerns a study of spermicides and Down's syndrome in which Rothman compared cases to each oftwo control groups.3 In study, odds ratio for comparison between cases and random controls was 3.6 (90 per cent CI = 1.2-9.0), as opposed to 2.8 (90 per cent CI = 0.9-7.3) for comparison involving controls with congenital heart disease. Although Poole claims full utility of p-value functions comes when one result is compared with another, I fail to see how in this example inspection of such functions would provide any special insight. It is clear from examination of point estimates themselves and from considerable overlap of CIs comparison of cases with control group would presumably be subject to a corresponding recall bias yields a result is not strikingly different from for comparison with random controls. Consequently, it is difficult to agree with Mills, et al, who have claimed results suggest that recall bias may have caused higher rate of spermicide use reported in Down's group. 4 Poole maintains an erroneous conclusion such as of Mills, et al, follows almost to letter my perspective on interpretation of CIs. This claim is patently false. In fact, I warned explicitly against very type of fallacious reasoning of which Mills, et al, were guilty. In my discussion of interaction,2 I described pitfalls of