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REGRESSION TO THE MEAN: WHAT DOES IT MEAN?

JOHN A. CUNNINGHAM
DOI: http://dx.doi.org/10.1093/alcalc/agl039 580 First published online: 2 June 2006

To the Editor

Johnsson and Berglund's recent article evaluating two interventions for high-risk drinking in university freshman could be regarded as a model of appropriately conservative interpretation of experimental results (Johnsson and Berglund, 2006). The authors found statistically significant reductions in drinking from baseline to one-year follow-up but little evidence of differences between the two, randomly assigned intervention conditions. Given these findings they make the point that the results could be due to regression to the mean, an admission that is rare in the clinical trials literature. However, some benefit might be derived from considering alternate explanations for this pattern of results. One explanation is provided by the authors—that the results can be explained by regression to the mean. This is a statistical concept which is used to describe the phenomenon that a group of people pre-selected for scoring above the mean on a measure are likely to score lower on average, purely by chance, if the measurement is repeated (Morton and Torgerson, 2003). So, to use the present example, people display variation over time in the amount they drink. If a group of drinkers is pre-selected on the basis that their drinking scores above the mean of the general population of drinkers, then, just by chance, the average amount of drinking reported by these respondents will likely be less than at baseline when the measurement is repeated at a later date.

What other explanations are possible to explain this pattern of results? The first is that both interventions might have worked and caused reductions in drinking. This explanation is alluded to at the beginning of the discussion in the Johnsson and Berglund article but the authors appropriately do not try to make the claim that this is necessarily what is happening in their study (Johnsson and Berglund, 2006). The second explanation has to do with the natural history of drinking patterns. University students show a trend towards drinking less as they progress through their college years (Baer et al., 2001). This reduction is not due to chance, as would be the case with regression to the mean, but reflects a real change in the amount students drink as time passes. So, the students in Johnsson and Berglund's study could have been reporting reductions in drinking solely as a reflection of the downward trend that student drinkers display as they progress through college.

Finally, the pattern of results could reflect the fact that heavy drinkers are more likely to be concerned about their drinking than moderate drinkers (Wild et al., 2001). As many problem drinkers reduce their alcohol consumption without ever seeking treatment (Cunningham, 1999), the reduction in drinking observed in the Johnsson and Berglund study could be a result of these heavy drinkers having concern about their drinking and deciding to change. Thus, the sample might include many people who would have reduced their drinking anyway without exposure to any intervention. These alternate explanations underline the importance of randomized controlled trials as a means of establishing the effectiveness of any treatment and are the reason why the cautious presentation of experimental results, as Johnsson and Berglund have done, should be encouraged.

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