Deficiency of the Odds Ratio for Common Outcomes

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.