Odds ratio
The odds ratio is a technical term often used in medical statistics. The odds ratio is the ratio of the relative incidence of a target disorder in the experimental group relative to the relative incidence in a control group. Essentially, it reflects how the risk of having a particular disorder is influenced by the treatment. An odds ratio of 1 means that there is no benefit of treatment compared to the control group.[1]
The odds ratio is a difficult concept for non mathematicians and recommendations for how to teach its use are available.[2]
For a mathematician, an odds ratio is merely the ratio between the odds on some event under two circumstances.
Example
This example is from the Titanic (example from Power[3]):
| Survival | ||
|---|---|---|
| Yes | No | |
| Males | 142 | 709 |
| Females | 308 | 154 |
Male passengers:
142 survived, 709 died
- Odds of survival = 142/709 = 0.20
- Probability (risk or chance) of survival = 142/(142+709) = 17%
Female passengers:
308 survived, 154 died
- Odds of survival = 308/154 = 2.00
- Probability (risk or chance) of survival = 308/(308+154) = 67%
Comparison:
- Odds ratio (OR) for survival = 0.20/2.00 = 0.10
- Relative risk (RR) for survival = 17%/67% = 0.25
The odds on a male passenger surviving the Titanic disaster was 1 to 5 against surviving. The odds on a female passenger surviving the Titanic disaster was 2 to 1 in favour of surviving. The odds ratio is (1/5) / (2/1) = 1/10
Interpretation
The odds ratio is generally used to measure the association between a risk factor and disease. However, using the odds ratio to measure the ability of a risk factor to diagnose disease is problematic.[4] The odds ratio should be at least 16 to have reasonable diagnostic ability.[5]
The odds ratio is similar to the relative risk ratio. The two ratios will be numerically similar is the rates in the two groups being compared are both similar and both less than 20% to 30%.[6][7][8]
The odds ratio may be the most stable ratio across different prevalences.[9]
The odds ratio may be used to derive the number needed to treat:[9][10]
For odds ratios less than 1:[10]
For odds ratios greater than 1:[10]
References
- ↑ Anonymous. Odds and odds ratio. Bandolier.
- ↑ Prasad K, Jaeschke R, Wyer P, Keitz S, Guyatt G (May 2008). "Tips for teachers of evidence-based medicine: understanding odds ratios and their relationship to risk ratios". J Gen Intern Med 23 (5): 635–40. DOI:10.1007/s11606-007-0453-4. PMID 18181004. Research Blogging.
- ↑ Power M (2008). "Resource reviews". Evidence-based Medicine 13 (3): 92. PMID 18515638. [e]
- ↑ Boyko EJ, Alderman BW (1990). "The use of risk factors in medical diagnosis: opportunities and cautions". J Clin Epidemiol 43 (9): 851–8. PMID 2213074. [e]
- ↑ Pepe MS, Janes H, Longton G, Leisenring W, Newcomb P (May 2004). "Limitations of the odds ratio in gauging the performance of a diagnostic, prognostic, or screening marker". Am. J. Epidemiol. 159 (9): 882–90. PMID 15105181. [e]
- ↑ Sinclair JC, Bracken MB (August 1994). "Clinically useful measures of effect in binary analyses of randomized trials". J Clin Epidemiol 47 (8): 881–9. PMID 7730891. [e]
- ↑ Altman DG, Deeks JJ, Sackett DL (November 1998). "Odds ratios should be avoided when events are common". BMJ 317 (7168): 1318. PMID 9804732. PMC 1114216. [e]
- ↑ Page J, Attia J (2003). "Using Bayes' nomogram to help interpret odds ratios". ACP J. Club 139 (2): A11–2. PMID 12954046. [e] Helpful chart
- ↑ 9.0 9.1 Furukawa TA, Guyatt GH, Griffith LE (February 2002). "Can we individualize the 'number needed to treat'? An empirical study of summary effect measures in meta-analyses". Int J Epidemiol 31 (1): 72–6. PMID 11914297. [e]
- ↑ 10.0 10.1 10.2 McQuay HJ, Moore RA (May 1997). "Using numerical results from systematic reviews in clinical practice". Ann. Intern. Med. 126 (9): 712–20. PMID 9139558. [e]