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Letters to the Editor   |    
Deficiency of the Odds Ratio for Common Outcomes
Jay S. Kaufman, Ph.D.; Sam Harper, Ph.D.
Am J Psychiatry 2012;169:1118-1118. doi:10.1176/appi.ajp.2012.12060800
View Author and Article Information

The authors report no financial relationships with commercial interests.

Montreal, Quebec

Accepted August , 2012.

To the Editor: The article by Chen et al. (1) in the July issue provides a fascinating account of the interaction by genotype in the context of a smoking cessation trial. Participating smokers were randomly assigned either to placebo (N=132) or to various combinations of active treatments (N=941). The authors then reported the proportion with confirmed 7-day abstinence after 8 weeks, stratified by three common haplotypes (defined by two single-nucleotide polymorphisms on chromosome 15 that have established associations with nicotine and cocaine dependence). Despite clear evidence of statistical interaction between haplotype group and successful smoking cessation, the authors’ stated conclusion that “[s]mokers with the high-risk haplotype were three times as likely to respond to pharmacologic cessation treatments as were smokers with the low-risk haplotype” is not correct. As shown in Figure S4 of the online data supplement that accompanies the Chen et al. article, treatment approximately doubled (not tripled) the 8-week abstinence proportion in the high-risk haplotype group, from about 24% to about 50%. In contrast, there was no treatment effect in the low-risk haplotype group.

The explanation for this large discrepancy is that the authors made the common error of interpreting odds ratios from logistic regression models as relative risks. This interpretation is not valid for outcomes that are not rare. It has been repeatedly noted in the biomedical literature that this is a serious deficiency of the odds ratio (2, 3), and many authors have therefore urged that for cohort analyses such as those used in the Chen et al. study, the odds ratio is not a parameter of interest and should be avoided (4). It is simple in these settings to estimate risk ratios or differences (5), and this also facilitates useful calculations such as the number needed to treat (i.e., the inverse risk difference) (6). For example, manipulation of these absolute risks shows that the number needed to treat in order to prevent one relapse among the high-risk haplotype subpopulation is approximately four. This is an impressive finding that is completely obscured in the published analysis.

Chen  LS;  Baker  TB;  Piper  ME;  Breslau  N;  Cannon  DS;  Doheny  KF;  Gogarten  SM;  Johnson  EO;  Saccone  NL;  Wang  JC;  Weiss  RB;  Goate  AM;  Bierut  LJ:  Interplay of genetic risk factors (CHRNA5-CHRNA3-CHRNB4) and cessation treatments in smoking cessation success.  Am J Psychiatry 2012; 169:735–742
[PubMed]
 
Altman  DG;  Deeks  JJ;  Sackett  DL:  Odds ratios should be avoided when events are common.  BMJ 1998; 317:1318
[CrossRef] | [PubMed]
 
Schwartz  LM;  Woloshin  S;  Welch  HG:  Misunderstandings about the effects of race and sex on physicians’ referrals for cardiac catheterization.  N Engl J Med 1999; 341:279–283; Discussion 286–287
[PubMed]
[CrossRef]
 
Knol  MJ;  Duijnhoven  RG;  Grobbee  DE;  Moons  KG;  Groenwold  RH:  Potential misinterpretation of treatment effects due to use of odds ratios and logistic regression in randomized controlled trials.  PLoS ONE 2011; 6:e21248
[PubMed]
[CrossRef]
 
Austin  PC:  Absolute risk reductions, relative risks, relative risk reductions, and numbers needed to treat can be obtained from a logistic regression model.  J Clin Epidemiol 2010; 63:2–6
[PubMed]
[CrossRef]
 
Bender  R;  Kuss  O;  Hildebrandt  M;  Gehrmann  U:  Estimating adjusted NNT measures in logistic regression analysis.  Stat Med 2007; 26:5586–5595
[PubMed]
[CrossRef]
 
References Container
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References

Chen  LS;  Baker  TB;  Piper  ME;  Breslau  N;  Cannon  DS;  Doheny  KF;  Gogarten  SM;  Johnson  EO;  Saccone  NL;  Wang  JC;  Weiss  RB;  Goate  AM;  Bierut  LJ:  Interplay of genetic risk factors (CHRNA5-CHRNA3-CHRNB4) and cessation treatments in smoking cessation success.  Am J Psychiatry 2012; 169:735–742
[PubMed]
 
Altman  DG;  Deeks  JJ;  Sackett  DL:  Odds ratios should be avoided when events are common.  BMJ 1998; 317:1318
[CrossRef] | [PubMed]
 
Schwartz  LM;  Woloshin  S;  Welch  HG:  Misunderstandings about the effects of race and sex on physicians’ referrals for cardiac catheterization.  N Engl J Med 1999; 341:279–283; Discussion 286–287
[PubMed]
[CrossRef]
 
Knol  MJ;  Duijnhoven  RG;  Grobbee  DE;  Moons  KG;  Groenwold  RH:  Potential misinterpretation of treatment effects due to use of odds ratios and logistic regression in randomized controlled trials.  PLoS ONE 2011; 6:e21248
[PubMed]
[CrossRef]
 
Austin  PC:  Absolute risk reductions, relative risks, relative risk reductions, and numbers needed to treat can be obtained from a logistic regression model.  J Clin Epidemiol 2010; 63:2–6
[PubMed]
[CrossRef]
 
Bender  R;  Kuss  O;  Hildebrandt  M;  Gehrmann  U:  Estimating adjusted NNT measures in logistic regression analysis.  Stat Med 2007; 26:5586–5595
[PubMed]
[CrossRef]
 
References Container
+
+

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