Effect Measures: RR, HR, and OR

While the risk (or incidence) in absolute numbers is an important measure from an individual and a public health perspective and for planning health care resources, the biological effect of a beneficial or harmful exposure is always measured and medically interpreted in terms of relative risk.

With some prospective study designs, the relative risk (RR) can be measured directly from risks or indirectly from incidence density rates. Other statistical methods produce other effect measures, such as the hazard ratio (HR) or odds ratio (OR), that sometimes can be used to approximate the RR. For example, RR can be estimated from cohort data or a randomised trial using a log-binomial regression model as well as other models (1), HR using a proportional hazards regression model, and OR using a logistic regression model.

However, it is a mistake to always interpret odds ratios and hazard ratios as relative risks. When common outcomes are studied, the odds ratio provides an inflated estimate of the relative risk. This phenomenon is well known but often neglected. As an example, in obesity research, nearly a quarter of articles presenting odds ratios misinterpreted them as relative risk despite common outcomes (2). Moreover, Sutradhar and Austin (3) show that for a given hazard ratio, the corresponding relative risk can vary substantially depending on factors like baseline event rate and duration of follow-up. The use of hazard ratios to approximate the relative risk can therefore be questioned.

In both cases, a better alternative may be to estimate the relative risk directly. The odds ratio can also be corrected (4) to better approximate the relative risk.

References

1. McNutt LA, Wu C, Xue X, Hafner JP. Estimating the relative risk in cohort studies and clinical trials of common outcomes. Am J Epidemiol. 2003 May 15;157(10):940-3. doi: 10.1093/aje/kwg074. PMID: 12746247.

2. Tajeu GS, Sen B, Allison DB, Menachemi N. Misuse of odds ratios in obesity literature: an empirical analysis of published studies. Obesity (Silver Spring). 2012 Aug;20(8):1726-31. doi: 10.1038/oby.2012.71. Epub 2012 Mar 22. PMID: 22436842; PMCID: PMC3399983.

3. Sutradhar R, Austin PC. Relative rates not relative risks: addressing a widespread misinterpretation of hazard ratios. Ann Epidemiol. 2018 Jan;28(1):54-57. doi: 10.1016/j.annepidem.2017.10.014. Epub 2017 Nov 7. PMID: 29239842.

4. Zhang J, Yu KF. What's the relative risk? A method of correcting the odds ratio in cohort studies of common outcomes. JAMA. 1998 Nov 18;280(19):1690-1. doi: 10.1001/jama.280.19.1690. PMID: 9832001.