Relative Risk & Odds Ratios

Summary

This video introduces the concepts of relative risk and odds ratio, explaining how they are calculated and interpreted in epidemiological studies. It covers the differences between the two measures, their applications in cohort and case-control studies, and the importance of statistical significance. The video also discusses how to construct and use a 2x2 contingency table for these calculations and emphasizes the distinctions between odds and probability. Finally, it highlights the conditions under which each measure should be used and potential pitfalls in their interpretation.

Takeaways

• 📊 The video introduces the concepts of relative risk and odds ratio, explaining how they are used to compare the occurrence of events between two groups in studies.
• 🔍 An association is identified when the risk among the exposed is higher than among those not exposed, highlighting the relationship between exposure and outcome.
• 📈 The interpretation of relative risk or odds ratio involves two components: the point estimate (the actual number) and the statistical significance (p-value and/or confidence interval).
• 🚬 Relative risk is used for comparing the probability of an event occurring to all possible events, such as the risk of developing lung cancer in those exposed to secondhand smoke.
• 📝 A 2x2 contingency table is essential for calculating incidence rates and relative risk in cohort studies, providing frequency counts of events for both exposed and unexposed groups.
• 🔢 The formula for relative risk is the proportion of individuals with the event in the exposed group divided by the proportion in the unexposed group.
• 📉 A relative risk of one indicates no difference between groups, greater than one suggests a positive association, and less than one indicates a negative association or protective effect.
• ⚠️ The significance of relative risk is determined by the p-value and confidence interval; if the p-value is ≥ 0.05 or the interval includes 1, the risk is not statistically significant.
• 🚫 Case-control studies cannot calculate relative risk because they compare cases with the event to controls without the event, making them retrospective and not suitable for incidence or risk calculation.
• 🎰 Odds ratio is used when relative risk cannot be calculated, such as in case-control studies, and is based on the odds of an event occurring rather than the probability.
• 🔄 The formula for odds ratio is the cross product of a 2x2 table, dividing the odds of the exposed group by the odds of the unexposed group.
• 📚 Odds ratios can be calculated for both cohort and case-control studies and are comparable in magnitude to relative risk only when the outcome is rare.
• 📉 Odds ratios may overestimate risk when the outcome is common, so relative risk should be used if possible, and caution is advised when interpreting odds ratios.
• 📘 The video concludes by noting that odds ratios are common in medical literature for both study types and are often the result of logistic regression analysis.

Q & A

What are the two main statistics used to compare the occurrence of events between two groups in studies?

The two main statistics used are relative risk and odds ratio.

What is the purpose of calculating relative risk or odds ratio in a study?

The purpose is to determine whether an association exists between exposure and outcome and to assess how strong that association is.

What is the difference between the point estimate and statistical significance in the context of relative risk or odds ratio?

The point estimate is the actual number representing the relative risk or odds ratio, while statistical significance is indicated by the p-value and/or confidence interval, showing the reliability of the point estimate.

When is the relative risk used in a study?

Relative risk is used when comparing the probability of an event occurring to all possible events considered in a study, typically in cohort studies.

How is the relative risk calculated using a 2x2 contingency table?

Relative risk is calculated by dividing the proportion of individuals who suffered the event in the exposed group by the proportion of individuals who suffered the event in the unexposed group.

What does a relative risk of 5.41 imply in the context of the secondhand smoke example?

A relative risk of 5.41 implies that the risk of developing lung cancer in the exposed group is 5.41 times higher than in the unexposed group.

What are the three interpretations of relative risk values?

A relative risk of one indicates no difference between groups, a value greater than one suggests a positive association or risk factor, and a value less than one indicates a negative association or protective effect.

Why can't relative risk be calculated from a case-control study?

Relative risk cannot be calculated from a case-control study because it compares cases that have experienced the event with controls who have not, and it does not provide the necessary data to calculate incidence or risk.

What is the difference between odds and probability, and how do they relate to odds ratio?

Odds are calculated as the probability of an event divided by the probability of the event not happening, while probability is the chance of an event occurring. The odds ratio compares the odds of an event in the exposed group to the odds in the unexposed group.

Why are odds ratios preferred over relative risk in case-control studies?

Odds ratios are preferred in case-control studies because they can be calculated without needing incidence rates, which are not available in this study design.

How do you interpret an odds ratio of 1.48 in a case-control study?

An odds ratio of 1.48 suggests that the odds of the exposed group experiencing the event (e.g., children with leukemia) are 1.48 times higher than the odds of the unexposed group.

When are relative risk and odds ratios comparable in magnitude?

Relative risk and odds ratios are comparable in magnitude when the outcome under study is rare, as their formulas yield more similar results in such cases.

Why should caution be exercised when interpreting odds ratios?

Caution is needed because odds ratios can overestimate risk when the outcome is more common, and they should not be assumed to represent the true risk ratio.

Why are odds ratios common in both case-control and cohort studies?

Odds ratios are common because they are the result of logistic regression, a widely used statistical method in medical research for both types of study designs.

Outlines

00:00

📊 Introduction to Relative Risk and Odds Ratio

This paragraph introduces the concepts of relative risk and odds ratio, explaining their importance in comparing event occurrences between two groups. It discusses how these statistical measures help determine the strength of an association between exposure and outcome. The paragraph outlines the process of interpreting these numbers, emphasizing the point estimate and statistical significance indicated by the p-value and confidence interval. It also explains the calculation of relative risk using a 2x2 contingency table, providing an example with secondhand smoke exposure and lung cancer risk, resulting in a relative risk of 5.41. The interpretation of relative risk values is detailed, noting that values greater than, less than, or equal to one indicate positive association, negative association, or no difference, respectively. The paragraph concludes with a discussion on the statistical significance of relative risk, highlighting the importance of the p-value and confidence interval in determining the strength of the association.

05:00

🎲 Understanding Odds Ratio and Its Calculation

The second paragraph delves into the concept of the odds ratio, contrasting it with relative risk by explaining the difference between odds and probability. It clarifies that odds ratios are used when the study design is retrospective, such as in case-control studies, where relative risk cannot be calculated due to the nature of the data. The paragraph provides the formula for calculating the odds ratio using the cross product method from a 2x2 table and illustrates this with a real-life example of a case-control study on leukemia and parental smoking. It discusses the interpretation of odds ratios, which mirrors that of relative risk, and the conditions under which they are statistically significant. The paragraph also addresses the limitations of odds ratios, noting that they overestimate risk when the outcome is common, and emphasizes the importance of using relative risk when possible. It concludes by mentioning that odds ratios are common in medical literature and can result from logistic regression, a favored method in biomedical research.

Keywords

💡Relative Risk

Relative Risk is a statistical measure that quantifies the strength of the association between an exposure and an outcome, specifically the likelihood of an event occurring in an exposed group compared to an unexposed group. In the video, it is used to compare the probability of developing lung cancer in individuals exposed to secondhand smoke versus those unexposed, with a relative risk of 5.41 indicating a significantly higher risk in the exposed group.

💡Odds Ratio

Odds Ratio is another measure of association that compares the odds of an event occurring in one group to the odds of it occurring in another group. Unlike relative risk, odds ratios can be calculated from case-control studies and are used when the outcome is not rare. The video script provides an example of an odds ratio of 1.48 in a study examining the association between parental smoking and leukemia in children.

💡Association

In the context of the video, association refers to the relationship between exposure to a particular stimulus and the occurrence of an outcome, such as disease. The script discusses how an association exists when the risk among the exposed is higher than among those not exposed, which is a key concept in understanding both relative risk and odds ratio.

💡Point Estimate

A point estimate is a single value that serves as the best guess for the parameter of interest. In the video, the point estimate is the actual number given by the relative risk or odds ratio, which provides an immediate sense of the strength of the association without considering statistical significance.

💡Statistical Significance

Statistical significance is a measure that determines whether an observed effect is likely to be real or due to chance. The video explains that a relative risk or odds ratio is not considered significant if the p-value is greater than 0.05 or if the 95% confidence interval includes 1, indicating that the observed association could be due to random variation.

💡Two-by-Two Contingency Table

A two-by-two contingency table is a type of frequency table used in statistical analysis to display the frequency of outcomes in two groups based on their exposure status. The video uses this table to calculate both relative risk and odds ratio, providing the necessary data to assess the association between exposure and outcome.

💡Cohort Study

A cohort study is a type of observational study where a group of individuals is followed over time to determine the incidence of an event in relation to exposure to a particular factor. The video explains that relative risk can be calculated from cohort studies, as they provide the data needed to assess the probability of an event occurring.

💡Case-Control Study

A case-control study is a retrospective observational study that compares individuals with a specific condition (cases) to those without it (controls) to identify potential risk factors. The video clarifies that relative risk cannot be calculated from case-control studies due to their design but odds ratios can be used as an alternative.

💡Odds

Odds are a way of expressing the likelihood of an event occurring, calculated as the probability of the event divided by the probability of the event not happening. The script explains that odds are used in the calculation of odds ratios, contrasting with the use of probabilities in relative risk calculations.

💡Confidence Interval

A confidence interval is a range of values within which the true population parameter is likely to fall with a certain level of confidence. The video mentions that a 95% confidence interval is used alongside the p-value to assess the statistical significance of a relative risk or odds ratio.

💡Logistic Regression

Logistic regression is a statistical method used to model the relationship between a binary outcome and one or more predictors. The video script mentions that odds ratios are commonly the result of logistic regression, which is a favored method in biomedical research for both case-control and cohort studies.

Highlights

Introduction to relative risk and odds ratio and their calculation.

Relative risk compares the probability of an event occurring between two groups.

An association exists when the risk among the exposed is higher than the risk among the unexposed.

Relative risk is calculated by dividing the incidence in the exposed group by the incidence in the unexposed group.

Example: Calculating relative risk for lung cancer in those exposed to secondhand smoke.

Interpretation of relative risk: a value of 1 indicates no difference, greater than 1 indicates a positive association, and less than 1 indicates a negative association.

Statistical significance of relative risk is shown by the p-value and/or confidence interval.

Relative risk cannot be calculated from case-control studies because they do not provide incidence data.

Odds ratio is used in case-control studies and compares the odds of exposure among cases and controls.

Calculation of odds ratio using a 2x2 table: a times d divided by b times c.

Example: Calculating odds ratio for leukemia in children with parental smoking history.

Interpretation of odds ratio: similar to relative risk, values indicate positive or negative association.

Odds ratios can be calculated for both cohort and case-control studies.

Relative risk and odds ratios are comparable only when the outcome is rare.

Caution is needed when interpreting odds ratios as they can overestimate risk in common outcomes.

Logistic regression commonly yields odds ratios in medical research.

Transcripts

hello this video will introduce relative

risk and odds ratio and how they are

calculated throughout the class we have

discussed comparing the occurrence of

events between two groups studies can

characterize these associations by using

one of two statistics relative risk or

odds ratio when evaluating the relative

risk or nadh's ratio we are really

trying to determine whether an

association exists and how strong it is

when we talk about an association think

of it as a relationship between exposure

and outcome as we discussed earlier this

semester there is an association when

the risk among the exposed is higher

than the risk among those who are not

exposed there are two components to your

interpretation of a number first is the

actual number which we refer to as the

point estimate and the second is the

statistical significance which is shown

by the p-value and/or the confidence

interval relative risk is used when

comparing the probability of an event

occurring to all possible events

considered in a study for example

consider the risk of developing lung

cancer in those who are exposed and

unexposed to secondhand smoke over

ten-year study period con study

conclusion the two-by-two contingency

table shown here is created containing

frequency counts of events for two

groups exposed and unexposed to the

secondhand smoke stimulus this table

provides all necessary data to calculate

the incidence of the event for both

exposed and unexposed individuals in a

cohort study relative risk is calculated

by dividing the proportion of

individuals who suffered the event in

the exposed group here it is a divided

by a plus B by the proportion of

individuals who suffered the event in

the unexposed group here it is C divided

by C plus D using our secondhand smoke

example let's input some numbers into

our 2x2 table and calculate relative

risk in our examples the risk of lung

cancer in the exposed group is 0.92 this

risk is divided by the risk in the

unexposed group 0.17 for a relative risk

of 5.41

relative risk provides a single number

ranging from zero to infinity

and there are three resulting

interpretations provided below when

interpreting the relative risk we

consider one to be null a relative risk

of one means there is no difference

between the two groups and the incidence

and risk in the exposed is the same as

the risk and the incidence in the non

exposed there is no increased risk and

no association if the relative risk is

greater than one the incidence of needs

posed is greater than the incidence in

the non exposed there is a positive

association or detrimental effect also

known as the risk factor of being

exposed to the stimulus if the relative

risk is less than 1 the incidence in the

exposed is less than the incidence in

the non expose there is a negative

association or protective effect of

being exposed to the stimulus remember

the further the relative risk is from 1

the stronger the Association when you

interpret a relative risk remember to

take into account whether the

Association is significant this applies

the odds ratio as well the relative risk

will be reported alongside a p-value

and/or a 95% confidence interval if the

p-value is not less than 0.05 or if the

confidence interval includes 1 the

relative risk is not statistically

significant this is true no matter how

large or small the relative risk is you

may have noticed that I said you have

all the information you need to

calculate a relative risk when we do a

cohort study this is not true for case

control studies you cannot calculate

incidence or risk in a case control

study thus you cannot calculate relative

risk from a case control study why not a

case control study compares cases that

have experienced the event and controls

who have not and then assesses whether

each individual was exposed to a

stimulus or not in the example here the

researcher compared 300 people of cancer

to 300 people without cancer the disease

rate is 50% just because of the way the

study was designed not because 50% of

people under 15 years of age of cancer

thus the case control study is

retrospective when relative risk cannot

be calculated like in case control

studies researchers will often present

an odds ratio before I show you the

formula for calculating an odds ratio

here's a reminder about the difference

between odds and probability relative

risk uses probability of getting disease

AHS ratio uses odds which is calculated

as probability divided by one minus

probability so if there's a 60%

probability that I will win this race

the odds are 1.5 that I will win so

thinking in terms of odds and

probability the relative risk is the

probability that an exposed person gets

disease divided by a probability that an

unexposed person gets the disease the

odds ratio is odds that a case or person

with disease was exposed divided by the

odds a control or person without disease

was exposed

remember that even though you can

mathematically convert between odds and

probability it is never okay to

calculate a relative risk from case

control study data odds are calculated

by dividing the proportion of people

experiencing events by the proportion of

people not experiencing event thus an

odds ratio is a ratio of two odds one

for individuals exposed to the stimulus

and the other for those not exposed to

the stimulus here is the calculation for

the odds ratio it is the same as the

cross product using the 2x2 table that

we designed earlier the calculation is a

times B divided by B times C let's look

at a real-life example this is a case

control study of children with leukemia

compared to children without leukemia

which look to see whether history of

parental smoking was associated with

cancer here is a 2x2 table created just

as was done in the earlier example to

get the odds ratio we divide the number

of kids with parental smoking by the

number of kids without parental smoking

in the cancer group for an odds of 0.43

this is divided by the odds of parental

smoking in the non cancer group 0.294 an

odds ratio of one point four eight

this is different from the relative risk

equation because we don't use total

exposed or total unexposed anywhere in

the equation odds ratios can range from

zero to infinity

they have three interpretations

identical to those presented above for

relative risk the rule for determining

whether an odds ratio statistically

significant is also the same as with

relative risk odds ratios can be

calculated for both cohort and

case-control designs odds ratios are

used when comparing events to non-event

with this calculation depending on the

study design for example consider

comparing a group of individuals who

develops measles to those who did not

and then determining whether they

received all the recommended

vaccinations in a cohort study the odds

ratio is calculated by dividing the odds

of experiencing the event in the exposed

group a divided by B by the odds the

unexposed group experiences the effect C

divided by B in a case control study the

odds ratio is calculated by dividing the

odds that cases works both to the risk a

divided by C by the odds that the

controls were exposed B divided by D

relative risk can only appear in cohort

studies or possibly at times and

randomized control studies relative risk

and odds ratios are comparable in

magnitude only when the outcome under

study is rare for instance some cancers

this is because the results of the

relative risk formula and odds ratio

formula become more similar as the

denominator gets larger and as the

number of disease cases gets smaller it

is important to consider that odds

ratios consistently overestimate risk

when the outcome is more common for

instance in hyperlipidemia as a result

eliten risk should be used if possible

and caution should be exhibited when

interpreting odds ratios additionally

don't assume that a case is a case

control study just because you see an

odds ratio and the results ratios are

very common in the medical literature

for both case control and cohort studies

they are the result of logistic

regression which is every bi

medical researchers favorite mystical

method this concludes the video