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 Table of Contents  
CURRICULUM IN CARDIOLOGY - STATISTICS
Year : 2016  |  Volume : 2  |  Issue : 1  |  Page : 49-51

The odds ratio: Principles and applications


Institute of Economic Growth, Delhi University, New Delhi, India

Date of Web Publication26-May-2016

Correspondence Address:
Aakshi Kalra
Institute of Economic Growth, Delhi University, New Delhi
India
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Source of Support: None, Conflict of Interest: None


DOI: 10.4103/2395-5414.182992

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  Abstract 

The odds ratio (OR) is a simple tool, widely utilized in clinical research. As a simple statistic, it can be hand calculated to determine the odds of a particular event or a disease, and the information provided can be useful for understanding the results of a treatment/intervention. This article discusses the application of OR with examples and shows a simple way of performing the test using an online calculator.

Keywords: Hand calculation, odds ratio, online calculators


How to cite this article:
Kalra A. The odds ratio: Principles and applications. J Pract Cardiovasc Sci 2016;2:49-51

How to cite this URL:
Kalra A. The odds ratio: Principles and applications. J Pract Cardiovasc Sci [serial online] 2016 [cited 2019 May 20];2:49-51. Available from: http://www.j-pcs.org/text.asp?2016/2/1/49/182992

The odds ratio (OR) is a measurement of association which compares the odds of disease or an event of those exposed to the odds of disease/event in those unexposed. It serves to determine the relation between exposure and outcome.

OR is a numeric expression of the strength of association between cause and an effect when both are expressed as categorical variables. As a rule of thumb, larger the OR, more will be the effect on the outcome.

The odds of an outcome are the ratio of occurrences in the presence of an event to the occurrences in the absence of an event. While odds can be calculated for any event, odds raitio is always with reference to a two different outcomes (like cases and controls).

We wish to answer a question like “what is the likelihood of a person to face an outcome, when a medical condition is present, compared to those where the medical condition is not present.” This is then answered as the ratio of the odds of outcome under the two conditions.

The OR can be used to evaluate whether the odds of an event is same for two groups in a study sample. The OR measures the ratio of the odds that an outcome will occur given a particular exposure to the odds of the outcome occurring in the absence of the exposure.[1],[2],[3],[4]

The OR can also be a measure of the effect size.

Formula

  • OR = (odds of disease in exposed)/(odds of disease in the nonexposed)


A contingency table for the OR is created as shown in [Table 1].
Table 1: 2×2 Contingency table

Click here to view


The OR is calculated as the odds of being exposed if a case (a:c) divided by the odds of being exposed if a control (b:d) and by transformation, can be depicted as above.

Usually, beginners find it confusing between probability and odds. To simplify, the difference can be explained from the following example:

If the probability of a heart attack in the chronic heavy smoker is 0.80 (80%), then the probability that the event will not occur is 1–0.80 = 0.20, or 20%. However, the odds of an event represent the ratio of the (probability that the event will occur)/(probability that the event will not occur) for a given exposure/risk factor.


  Use Top


ORs are most commonly used in case–control studies; however, it can be used for other study designs with few modifications and assumptions. In a case–control study, the group of exposed individuals consists of a few cases and few controls, and they are not usually a representative sample of all exposed persons in the population. The same holds true for unexposed group. Here, the OR compares the chances of a case being exposed to the risk factor with the odds of control being exposed. OR can be used to determine whether a particular exposure is a risk factor for the outcome of interest, and to compare the magnitude of various risk factors for that outcome.[4] Analysis of this sort has been commonly employed in large-scale studies as well.


  Taking an Example Top


Supposing twenty children from a school went to a restaurant and eight of them ate a new type of pizza. Of the total school children, seven fell ill. Now, the question arises how to test if it was due to the new pizza they ate or not?

To solve this, OR can be used [Table 2].
Table 2: Example to calculate odds ratio

Click here to view



  What Does Value of Odds Ratio Means? Top


  • OR of 1: There is no difference between the groups; i.e., there would be no association between the exposure (pizza) and the outcome (being ill)
  • OR of >1: Suggests that the odds of exposure are positively associated with the adverse outcome compared to the odds of not being exposed
  • OR of <1 Suggests that the odds of exposure are negatively associated with the adverse outcomes compared to the odds of not being exposed.



  Interpretation of Odds Ratio Top


In the example above, those who ate the pizza (exposure) were 8.3 times more likely (OR = 8.33) to be ill (outcome), compared to those who did not eat the pizza.


  Testing the Significance of the Odds Ratio Top


Since the OR is calculated based on sample data, we need to test for the significance of the observed value comparing it with a hypothetical value.

Testing the significance of the OR is done as per the calculations below but with available online calculators and software such as STATA, SPSS, and R, all these calculations are now done on computers. The significance can also be tested by a Chi-square test.[5],[6],[7]

The OR standard error and 95% confidence interval (CI) calculations are shown below:

With the standard error of the log OR is:



and 95% CI:

95% CI = Exp (In(OR) −1.96× {In(OR)}) to exp (In(OR) +1.96× {In(OR)})

Basically, the precision of the OR is estimated by the 95% CI. The 95% CI is often used as a proxy for the presence of statistical significance if it does not overlap the null value (e.g., OR = 1).[7],[8],[9],[10],[11],[12]

Calculation of OR can be done easily with the help of an online calculator as discussed below.


  A Free Online Calculator Is Available at the Site below Top


There are many calculators available online which are free to use. One of them is MedCalc; following is the link for this calculator:

https://www.medcalc.org/calc/odds_ratio.php

For computation, values of a, b, c, and d (as per the formula of OR) are required. Importantly, along with OR, this calculator provides value of 95% CI, Z-statistic, and significance level.

Following are few examples using this calculator:

  • An example of change of mortality in coronary artery disease with high-dose statins [Figure 1]
  • The second example shows testing the results of smoking in a group [Figure 2].
  • One of the important parts of understanding scientific research is effective analysis and interpretation, and OR is one such statistical tool. This article covered basics about OR-learning how it is calculated, principles behind, application, and interpretation.
Figure 1: Online calculation of odds ratio.

Click here to view
Figure 2: Online calculation of odds ratio.

Click here to view



  Summary of Some Points Top


  • The numerator is the odds in the intervention/treatment arm
  • The denominator is the odds in the control arm
  • If the outcome is the same in both groups, the ratio will be one, which implies there is no difference between the two arms of the study


    • If the OR is >1 the control is better than the intervention
    • If the OR is <1 the intervention is better than the control (protective effect).


  • The 95% CI is often used as a proxy for the presence of statistical significance if it does not overlap the null value (e.g., OR = 1).



  Conclusion Top


Odds are the ratio of probability of an event occurring in one group to probability of the event not occurring. An OR is the odds of the event in one group, divided by the odds in another group not exposed. The OR is used in case–control studies and logistic regression analysis. This article has introduced the reader to some of the concepts of OR and ways of calculated the OR.

Financial support and sponsorship

Nil.

Conflicts of interest

There are no conflicts of interest.

 
  References Top

1.
Altman DG. Practical Statistics for Medical Research. Boca Raton, FL: Chapman & Hall/CRC; 1991. p. 611.  Back to cited text no. 1
    
2.
Altman DG, Deeks JJ, Sackett DL. Odds ratios should be avoided when events are common. BMJ 1998;317:1318.  Back to cited text no. 2
    
3.
Deeks JJ, Higgins JP. Statistical Algorithms in Review Manager 5. Statistical Methods Group of the Cochrane Collaboration; 2010. p. 1-11.  Back to cited text no. 3
    
4.
Szumilas M. Explaining odds ratios. J Can Acad Child Adolesc Psychiatry 2010;19:227-9.  Back to cited text no. 4
    
5.
Parshall MB. Unpacking the 2×2 table. Heart Lung 2013;42:221-6  Back to cited text no. 5
    
6.
Sheskin DJ. Handbook of Parametric and Nonparametric Statistical Procedures. 3rd ed. Boca Raton: Chapman and Hall/CRC; 2003.  Back to cited text no. 6
    
7.
Cornfield J. A method of estimating comparative rates from clinical data; applications to cancer of the lung, breast, and cervix. J Natl Cancer Inst 1951;11:1269-75.  Back to cited text no. 7
[PUBMED]    
8.
Mosteller F. Association and estimation in contingency tables. J Am Stat Assoc 1968;63:1.  Back to cited text no. 8
    
9.
Edwards AW. The measure of association in a 2×2 table. J R Stat Soc Ser Gen 1963;126:109.  Back to cited text no. 9
    
10.
Lamorte WW. Case-Control Studies, Overview of Analytic Studies. Boston: University School of Public Health; 2016. Available from: http://www.sphweb.bumc.bu.edu/otlt/MPH-Modules/EP/EP713_AnalyticOverview/EP713_AnalyticOverview5.html. [Last accessed on 2016 Apr 22].  Back to cited text no. 10
    
11.
Morris JA, Gardner MJ. Calculating confidence intervals for relative risks (odds ratios) and standardised ratios and rates. Br Med J (Clin Res Ed) 1988;296:1313-6.  Back to cited text no. 11
    
12.
Viera AJ. Odds ratios and risk ratios: What's the difference and why does it matter? South Med J 2008;101:730-4.  Back to cited text no. 12
    


    Figures

  [Figure 1], [Figure 2]
 
 
    Tables

  [Table 1], [Table 2]



 

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   Interpretation o...
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