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Problems With Odds Ratios

To the Editor: Gregory B. Bovasso, Ph.D. (1), compared 15 individuals who met DSM-III-R criteria for cannabis abuse with 834 individuals who did not and concluded that for those who met the criteria, the risk of onset of depressive symptoms was 4.49 times greater or, after adjusting for covariates, 4.00 times greater. Neither statement is correct. The 4.49 figure and the 4.00 figure are odds ratios, which have a well-known propensity to exaggerate relative risk (2, 3). In this case, the odds ratios are at least a twofold exaggeration of the relative risk, which I calculate to be 2.16—(10/15)/(257/834).

Odds ratios may be useful in retrospective case-control studies (in which the incident rate of meeting the criteria is unknown) (4); however, this study had a longitudinal cohort design. Odds ratios are also useful in logistic regression, but when estimates from a logistic regression are reported, they should be clearly identified as odds ratios. In this article, the abstract stated only that depressive symptoms were "four times more likely" (p. 2033); there was no mention of odds ratios or logistic regression. Even when logistic regression is used, there is a method for converting the odds-ratio estimates to relative risks (5). For this study, the method yielded a covariate-adjusted relative risk of 2.08, with a 95% confidence interval of 1.15–2.77.

None of this will be apparent to readers who see only the abstract. Additionally, since the abstract mentioned Ns of 1,920 (the entire group), 849 (the subjects with no depressive symptoms at baseline), and 1,837 (the subjects with no cannabis abuse at baseline), readers who see only the abstract will be unaware that the N for the group of interest—the group for which the article was named—is 15. The work described in the article is interesting, and the findings may be important. However, they merit more careful reporting.

References

1. Bovasso GB: Cannabis abuse as a risk factor for depressive symptoms. Am J Psychiatry 2001; 158:2033-2037[Abstract/Free Full Text]
2. Sackett DL, Deeks JJ, Altman DG: Down with odds ratios! Evidence-Based Medicine 1996; 1(9/10):164-166
3. Davies HT, Crombie IK, Tavakoli M: When can odds ratios mislead? Br Med J 1998; 316:989-991[Free Full Text]
4. Deeks J: When can odds ratios mislead? odds ratios should be used only in case-control studies and logistic regression analyses (letter). Br Med J 1998; 317:1155-1157[Free Full Text]
5. Zhang J, Yu KF: What’s the relative risk? a method of correcting the odds ratio in cohort studies of common outcomes. JAMA 1998; 280:1690-1691[Abstract/Free Full Text]

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