Odds Ratio Calculation And Interpretation

4/11/2018

Odds Ratio Calculation and Interpretation

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Odds Ratio Calculation and Interpretation Probability and Statistics > Probability > Odds Ratio

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What is the Odds Ratio? An odds ratio (OR) is a measure of association between a certain property A and a second property B in a population. Speci cally, it tells you how the presence or absence of property A has an effect on the presence or absence of property B. The OR is also used to gure out if a particular exposure (like eating processed meat) is a risk factor for a particular outcome (such as colon cancer), and to compare the various risk factors for that outcome. You could use the OR to nd out how much alcohol use leads to liver disease. Or you might want to nd out if cell phone use has some link to brain cancer. As long as you have two properties you think are linked, you can calculate the odds.

How to Calculate the Odds Ratio You have two choices for the formula: (a/c) / (b/d) or, equivalently:

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(a*d) / (b*c)

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General Steps: Step 1: Calculate the odds that a member of the population has property “A”. Assume the person already has “B.” Step 2: Calculate the odds that a member of the population has property “A”. Assume the person does not have “B.” Step 3: Divide step 1 by step 2 to get the odds ratio (OR).

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Odds Ratio Calculation and Interpretation

Odds Ratio Example

Image: Michigan.gov

The above image shows two levels of exposure to ice cream: those who ate it, and those who didn’t. The 2×2 table also shows two outcome levels: people who were ill (“cases”) and people who were not (“controls”). The odds ratio is calculated as follows: 1. Ill people: people who ate ice cream / people who did not = 13/17 2. People who are not ill: people who ate ice cream / people who did not = 32/23 3. Dividing the two results, we get (13/17) / (32/23) = 0.55

The resulting odds ratio of .55 means that ill people were about half as likely to eat ice cream as well people.

Odds Ratio Interpretation; What do the Results mean?

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An odds ratio of exactly 1 means that exposure to property A does not affect the odds of property B. An odds ratio of more than 1 means that there is a higher odds of property B happening with exposure to property A. An odds ratio is less than 1 is associated with lower odds. However, it’s not quite as simple as that. You could think of the odds ratio as being a bit overly simplistic at describing real world situations. If, for example, you have a positive OR, it doesn’t mean that you have a statistically signi cant result. In order to gure that out, you need to consider the con dence interval and p-values (if you know it). The other issue is that even if you determine your results are statistically signi cant, that signi cance might not apply to all members of a population — there are nearly always a multitude of factors associated with risk. For example, this article points out that while overall, depression is strongly linked to suicide, “…in a particular sample, with a particular size and composition, and in the presence of other variables, the association may not be signi cant.”

Population Averaged vs. Subject Specific Odds Ratio Population averaged models compare marginal distributions and give an overview of the effect on a whole population. The margins of a contingency table contain the totals, so it makes sense for them to be used to calculate the marginal odds ratio for a whole population. On the other hand, subject-speci c models look at joint distributions: speci c conditions or experiences within the model. The joint distributions are used to calculate conditional odds ratios. Marginal Odds Ratio Example (for Population Averaged Models) Michael Radelet studied death sentence data from Florida from 1976-77.* Calculate the marginal odds ratio for the race of defendant and whether or not that made a different about if they got the death penalty:

Solution:

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Odds Ratio Calculation and Interpretation

1. Sum (marginalize) the values in the table. We’re interested in only the race of the defendant and whether or not they got the death penalty. Therefore, we can marginalize (sum up) values for the race of the victim. This creates a new 2×2 table:

2. Use the information in the marginal table to nd the OR (using the OR formula from above): OR = (a/c) / (b/d) = (19/17)/(141/149) = 1.12/0.95 = 1.18. The odds are 1.18 times higher that a white defendant will get the death penalty compared to a black defendant. *If you’re interested in his ndings, he concluded that there isn’t any clear evidence to support the hypothesis that the defendant’s race is strongly associated with imposition of the death penalty. Subject speci c models calculate the odds ratio using the same formula as all of the examples above. The only difference is that instead of summing all the variables together, you’ll hold one variable constant (i.e. you’ll use joint distributions). Reference: Radelet, M. L. Racial Characteristics and the Imposition of the Death Penalty. American Sociological Review, v46 n6 p918-27 Dec 1981

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Facebook page and I'll do my best to help! Odds Ratio Calculation and Interpretation was last modi ed: November 14th, 2017 by Stephanie By Stephanie | April 6, 2014 | Statistics How To | ← Logistic Regression (Logit Model): a Brief Overview

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6 thoughts on “Odds Ratio Calculation and Interpretation” Maria

1.

June 29, 2015 at 7:01 am

Hi, in the 2×2 Table it would be good to have a “case” concept, to make it more ilustrative. thanks

2.

Andale

Post author

September 1, 2015 at 9:48 am

Thanks for your suggestion. I added an example.

3.

Iris

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Odds Ratio Calculation and Interpretation November 16, 2016 at 6:45 pm

Can you explain to me the difference between a population averaged odds ratio and a subject speci c odds ratio and how to compute them?

Andale

4.

Post author

November 22, 2016 at 11:44 am

Hi Iris, I expanded the article today to include an explanation of the difference between the two. Hope it helps :)

Kathryn Greenwood

5.

April 7, 2017 at 6:20 pm

The example “Marginal Odds Ratio Example (for Population Averaged Models)” seems a little mixed up. You state “to see if those murdering Whites were more likely to be sentenced to death than those accused of murdering Blacks” So you are interested in victim’s race and not the defendant’s race. Had you said “to see if Whites were more likely to be sentenced to death than Blacks for murder” then the focus would shift to the defendant. Also 11 + 9 does not equal 17. The remainder are correct i.e. 19+0=19; 132+9=141; 52+97=149.

Andale

6.

Post author

April 8, 2017 at 6:10 am

Thanks for the correction. It’s xed, — math error xed, and I deleted the offending sentence to avoid confusion.

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