 • ## Summary

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• 00:00

SPEAKER: So we said that the relative risk comparestwo incidence rates--that in the exposed to that in the not exposed group.We start out with exposed and not exposed individuals,A plus B and C plus D, and look at how many people ineach group develop disease.That will be A in exposed and C in not exposed.

• 00:21

SPEAKER [continued]: Then we calculate the incidence rates A divided by A plusB and C divided by C plus D and divide those, in turn,in order to arrive at a relative risk.We said that in case-control studies,we cannot determine incidence rates.We can only look at the proportion of exposedin cases and in controls.So we start with cases A plus C and look

• 00:43

SPEAKER [continued]: at what proportion is exposed.That will be A divided by A plus C.Then we look at the controls, B plus D,and see what proportion of those were exposed.That will be B divided by B plus D.So what are we to do with these proportions?How can we express association if we can't calculaterelative risk with them?

• 01:03

SPEAKER [continued]: And the answer is we can calculate the so-called oddsratios.The odds ratio can, in fact, be calculated and usedin both case-control and cohort studies.So what are odds, anyway?Let's say Peter Blocker wanted to run a race.Since he's one of the strongest runners in the race,the probability of him winning the race is 70%, or 0.7.

• 01:25

SPEAKER [continued]: The probability is defined as the number of timesPeter wins the race divided by all the timeshe participates in the race.So if he participated 100 times, he would win 70 times.So 70 divided by 100 equals 0.7, or 70%.Now, the odds are defined as the numberof times he wins the race divided

• 01:46

SPEAKER [continued]: by the number of times he loses the race-- so 70 divided by 30.In other words, the odds are the probabilityof him winning the race divided by the probability of himlosing the race--so again, 70 divided by 30, or 2.3.So you see the difference?The probability of Peter winning is 70%.And the odds of him winning are 2.3.

• 02:08

SPEAKER [continued]: So we said that you could use odds ratios in cohort studiesand case-control studies.Let's turn to cohort studies first.Here's our familiar two-by-two table again.So the probability or incidence of disease in exposedis A divided by A plus B. What are the odds of diseasein exposed?That's the probability of disease in exposed

• 02:28

SPEAKER [continued]: divided by the probability of no disease in exposed,or A divided by A plus B divided by B divided by A plus B.So A plus B cancels out.And we end up with A divided by B.Similarly, the probability or incidenceof disease in unexposed is C dividedby C plus D. What are the odds of disease in non-exposed?

• 02:50

SPEAKER [continued]: That's the probability of disease in unexposed,or C divided by C plus D divided by the probabilityof no disease in unexposed, or D divided by C plus D. Again,C plus D cancels out.And we end up with C divided by D.Just like we can compare incidence rates in orderto arrive at a relative risk, can wecompare the odds to arrive at a so-called odds ratio?

• 03:13

SPEAKER [continued]: The odds ratio in a cohort study wouldbe A divided by B divided by C divided by D.So we solve that and multiply A and Dand divide that by B times C.If we had to express this odds ratio in words,we'd say that this is the ratio of oddsthat exposed developed disease to the odds that

• 03:33

SPEAKER [continued]: not exposed developed disease.So you see, we really could have just written the oddsof disease in exposed as A divided by B and thatin non-exposed as C divided by D instead of usingthe probabilities since the denominators cancelled out,anyway.Now let's turn to the odds ratios in case-control studies.Again, we're not looking at probabilities or incidence

• 03:55

SPEAKER [continued]: rates in exposed and not exposed.Instead, we're looking at proportions of exposurein cases and controls.However, what we can calculate hereare the odds that a case or a control were exposed.So the odds of a case being exposed is A divided by C,and that of a control being exposed is B divided by D.So in case-control studies, we can calculate the ratio of odds

• 04:19

SPEAKER [continued]: that the cases were exposed to the oddsthat controls were exposed.And that will be A divided by C divided by B divided by D. Thenwe multiply A and D and divide that by B times C. You see,that's the same as the odds ratio just calculatedin cohort studies.An easier way how one can arrive at an odds ratio is to just

• 04:39

SPEAKER [continued]: perform a so-called cross-product ratio--so A times D divided by B times C.That's why the odds ratio is also sometimes calledcross-product ratio.So we've just shown that the odds ratios in cohort studiesand those in case-control studies are the same.Both times, they're A times D divided by B times C.In other words, dividing the odds of disease

• 05:01

SPEAKER [continued]: in exposed by the odds of disease in non-exposedis the same thing as dividing the odds of exposurein diseased, or cases, by the odds of exposurein non-diseased, or controls.And that beautiful coincidence is the reasonwhy we can calculate odds ratios from case-control studiesand use them as an approximation for relative risk.

• 05:22

SPEAKER [continued]: The odds ratio is interpreted in just the same wayas the relative risk.If it's equal to 1, there's no associationbetween the exposure and the disease.If it's above 1, the exposure is a risk factor.And if it's below 1, the exposureis a protective factor.Now, for the odds ratio to be a valid approximationof the relative risk, the disease needs to be rare.

• 05:43

SPEAKER [continued]: Let me use an example to explain what I mean.Here we have a relatively rare disease.We have 10,000 exposed and non-exposed individuals.Of the exposed, 500 develop disease.And of the non-exposed, 100 develop disease.Let's calculate the relative risk.That's 500 divided by 10,000 dividedby 100 divided by 10,000.

• 06:03

SPEAKER [continued]: And that's 5.What's the odds ratio?Well, let's calculate the cross-product ratio.That's 500 times 9,900 divided by 100 times 9,500.And that's 5.2-- so a pretty good approximationof the relative risk, right?Now, let's turn to a more common disease,

• 06:24

SPEAKER [continued]: where we have 200 exposed and 200 non-exposed.Of the exposed, 100, or 50%, have the disease.And of the non-exposed, 20, or 10%, have the disease.So the relative risk is 100 divided by 200divided by 20 divided by 200.So again, the relative risk is 5.

• 06:44

SPEAKER [continued]: And what's the odds ratio?That's 100 times 180 divided by 20 times 100, or 9, notsuch a good approximation of the relative risk.So the odds ratio provides a good approximationof the relative risk if the disease is rare.[MUSIC PLAYING]

### Video Info

Series Name: Measuring Association

Episode: 2

Publisher: Medmastery GmbH

Publication Year: 2017

Video Type:Tutorial

### Segment Info

Segment Num.: 1

Persons Discussed:

Events Discussed:

Keywords:

## Abstract

Calculating the odds ratio for cohort and case-control studies when measuring association is explained, including the use of a cross-product ratio.