Chapter 25. Bringing balance and technical accuracy to reporting odds ratios and the results of Logistic Regression analyses

Jason W. Osborne

Logistic regression is becoming more widely used in the social sciences as more texts (e.g., Pedhazur 1997) include chapters on the technique and more articles aimed at the social science researcher introduce the concept (e.g., Davis & Offord 1997; Peng, Lee et al. 2002).  However, with more widespread adoption of the technique comes more opportunity for researchers to incorrectly interpret the results of this analysis.  As Pedhazur (1997) and others (e.g., Davies, Crombie et al. 1998; Holcomb, Chaiworapongsa et al. 2001); have pointed out, correctly interpreting odds ratios for either a scientific or practitioner audience is particularly challenging, and usually done incorrectly.  For example, Holcomb et al (2001) reported that in a survey of high-quality medical journals over one-quarter of the articles explicitly mis-interpreted odds ratios.  As the technique is newer to the social sciences, it is more likely that misinterpretation is happening in these literatures.

The goal of this chapter is to briefly review the challenges to successfully and (more importantly) correctly interpreting the odds ratio (as compared to the more intuitive probability ratio or relative risk estimate), to highlight a simple way for transforming odds ratios to the more easily interpreted relative risk estimate, and to highlight a method of dealing with ORs and RRs that are less than 1.0 to bring them into perceptual balance with those mathematically identical (but perceptually different) ratios over 1.0.

Summary

In sum, procedures such as logistic regression are powerful and useful tools to scientists.  However, the commonly-reported odds ratio is difficult to understand conceptually, quite often mis-interpreted, and particularly difficult to disseminate to a lay/practitioner audience.  Relative risk (probability ratios) are more intuitive and much easier to disseminate, so when possible researchers should report and interpret RRs rather than ORs. Secondly,  ORs/RRs are relatively unique in the effect size world in that they are asymmetrical.  Ratios below 1.0 behave very differently than ratios above 1.0 because they asymptote toward 0.0 whereas ratios above 1.0 are unbounded.  More importantly, this creates asymmetry in perception of effect size, which is also undesirable.  The second recommendation therefore is to convert all ratios < 1.0 to their corresponding ratio counterpart above 1.0 by taking the inverse of the RR/OR and adjusting the narrative accordingly.

Table 1.
Sample Data for Student Sex and Remedial Reading Classification