When do you use odds ratio

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Purchase access. Rent article Rent this article from DeepDyve. Access to free article PDF downloads. Save your search. Mary L. There are a number of statistics that are helpful for making decisions about clinical interventions or drawing conclusions about effects of various substances or events in health-related situations, and one seen frequently is called the odds ratio.

The OR evaluates whether the odds of a certain event or outcome is the same for two groups. Specifically, the OR measures the ratio of the odds that an event or result will occur to the odds of the event not happening. Clinically, that often means that the researcher measures the ratio of the odds of a disease occurring or a death from a specific injury or illness happening to the odds of the disease or death not occurring.

The odds ratio is used when one of two possible events or outcomes are measured, and there is a supposed causative factor. The odds ratio is a versatile and robust statistic. For example, it can calculate the odds of an event happening given a particular treatment intervention 1. It can calculate the odds of a health outcome given exposure versus non-exposure to a substance or event 2. The clinical literature exhibits many instances of the odds ratio being used in research to estimate reduction in disease or disease complications if patients receive a particular drug or vaccine 3,4,5.

The odds ratio is a measure of effect size as is the Pearson Correlation Coefficient and therefore provides information on the strength of relationship between two variables. It is an indirect measure however, as will be seen in the section on interpretation of the statistic. The calculation of the odds ratio is quite simple. The formula is as follows:. Another way to represent the formula is in table format:. Standard New. Treatment Treatment.

Event does c d. Given the algebraic rule of cross products, the second formula will produce the same result as the other two formulae for odds ratio and is the more commonly reported formula.

The first thing to understand when considering a significance test for the OR is that the true neutral value indicating equal odds for both conditions is one 1 , not 0 zero. Several significance tests can be used for the Odds Ratio. The Chi-Square formula is:. The Likelihood Ratio Chi-Square, like all likelihood ratio statistics is a logarithmic formula. If the data are entered into a statistical analysis program, this is the most appropriate test of significance for the Odds Ratio.

Its formula is as follows:. The odds ratio is skewed, so it is not possible to directly calculate the standard error of the statistic. However, the standard error for the natural logarithm of the odds ratio is quite simple to calculate.

It is calculated as follows:. Then all one needsto do to construct confidence intervals about the natural logarithm is to calculate the standard error using the above formula and add that value or a multiple of that value to the log of the odds ratio value for the upper CI confidence interval and subtract that value or a multiple of that value to the log of the odds ratio value for the lower CI.

More advanced information on direct computation of the confidence intervals for odds ratios can be obtained from the paper published by Sorana Bolboaca and Andrei Achimas Cadariu 7 and from the paper published by Simundic 8. The OR is different. One common use of the OR is in determination of the effect size of a difference in two drug interventions. As an example, consider the treatment of patients with endocarditis caused by Staphylococcus aureus SA. The question is this: What are the odds of dying with the new drug as opposed to the standard antibiotic therapy protocol?

The odds ratio is a way of comparing whether the odds of a certain outcome is the same for two different groups 9. The odds ratio is simply the ratio between the following two ratios: The ratio between standard treatment and the new drug for those who died, and the ratio between standard treatment and the new drug for those who survived.

Obstet Gynecol —6. Relationship between prevalence rate ratios and odds ratios in cross-sectional studies. Int J Epidemiol —3. An odd measure of risk: use and misuse of the odds ratio. Obstet Gynecol —8. Spiegelman D, Hertzmark E. Easy SAS calculations for risk or prevalence ratios and differences. Am J Epidemiol — Prevalence odds ratio or prevalence ratio in the analysis of cross sectional data: what is to be done?

Occup Environ Med —7. Bayesian models as a unified approach to estimate relative risk or prevalence ratio in binary and polytomous outcomes. Emerg Themes Epidemiol Greenland S. Model-based estimation of relative risks and other epidemiologic measures in studies of common outcomes and in case-control studies.

Am J Epidemiol —5. Application of different statistical methods to estimate relative risk for self-reported health complaints among shoe factory workers exposed to organic solvents and plastic compounds. Nor Epidemiol —6. Estimating the relative risk in cohort studies and clinical trials of common outcomes. Am J Epidemiol —3. Different methods to calculate effect estimates in cross-sectional studies. A comparison between prevalence odds ratio and prevalence ratio.

Methods Inf Med —9. Alternatives for logistic regression in cross-sectional studies: an empirical comparison of models that directly estimate the prevalence ratio. Interpretation of odds and risk ratios.

J Vet Intern Med —3. Tips for teachers of evidence-based medicine: understanding odds ratios and their relationship to risk ratios. J Gen Intern Med — Martin J. Odds Ratio. CTSpedia What is so odd about odds? Can J Surg —8. PubMed Abstract Google Scholar. A practical guide for multivariate analysis of dichotomous outcomes. Ann Acad Med Singapore —9. Wacholder S. Binomial regression in GLIM: estimating risk ratios and risk differences.

Approaches for estimating prevalence ratios. Occup Environ Med 65 —6. Zou G. A modified poisson regression approach to prospective studies with binary data. Am J Epidemiol —6. Relative risk estimation in randomized controlled trials: a comparison of methods for independent observations.

Int J Biostat — Blizzard L, Hosmer DW. Parameter estimation and goodness-of-fit in log binomial regression. Biom J — Chu H, Cole SR. Estimation of risk ratios in cohort studies with common outcomes: a Bayesian approach. Epidemiology — Beaudeau F, Fourichon C. Estimating relative risk of disease from outputs of logistic regression when the disease is not rare. Prev Vet Med — Technical note: the risk ratio, an alternative to the odds ratio for estimating the association between multiple risk factors and a dichotomous outcome.

J Dairy Sci — Issues of reporting in observational studies in veterinary medicine. Methods and processes of developing the strengthening the reporting of observational studies in epidemiology-veterinary STROBE-Vet statement. Deeks J. When can odds ratios mislead? Odds ratios should be used only in case-control studies and logistic regression analyses. BMJ —7. PLoS Med 6:e Grant MJ, Booth A. A typology of reviews: an analysis of 14 review types and associated methodologies. Health Info Libr J — Aviva P, Watson P.

Statistics for Veterinary and Animal Science. London: Wiley-Blackwell What variables are important in predicting bovine viral diarrhea virus? A random forest approach. Vet Res Making BUGS open. R News —7. R Development Core Team.

Vienna: R Foundation for Statistical Computing R News — Gelman A, Rubin DB. Inference from iterative simulation using multiple sequences. Stat Sci — Quasi-likelihood estimation for relative risk regression models.

Biostatistics —