Often called “the cornerstone” of public health, epidemiology is the study of the distribution and determinants of diseases, health conditions, or events among populations and the application of that study to control health problems. By applying the concepts learned in this course to current public health problems and issues, students will understand the practice of epidemiology as it relates to real life and makes for a better appreciation of public health programs and policies. This course explores public health issues like cardiovascular and infectious diseases – both locally and globally – through the lens of epidemiology.

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Measures of Association

This module introduces measures of association and confidence intervals.

Clinical Associate Professor Department of Epidemiology, UNC Gillings School of Global Public Health

Dr. Lorraine Alexander

Clinical Associate Professor, Director of Distance Learning (North Carolina Institute for Public Health) Department of Epidemiology, UNC Gillings School of Global Public Health

[MUSIC]

Welcome.

In this module, we're going to talk about the measures of association.

The most important things to remember about the measures of association.

Are that they could either help us tell some, tell us something

about the strength of the association between an exposure and a health outcome.

Or they can help us quantify the absolute

excess of the disease that's related to the exposure

of interest.

Just a quick reminder before we get started.

Please make sure that you understand the measures of health

outcome occurrence before you go forward with the measures of association.

Those measures of occurrence are the

building blocks of the measures of association.

So if you understand those, then it'll

be easy to understand the measures of association.

After you have reviewed all of

the week four lectures you should be able

to do the items listed in the learning objectives.

These include defining the different types of measures of association

including risk ratio, rate ratio, odds ratio and prevalence ratio.

And you should also be able to define risk difference.

Rate differences, odds differences and prevalence differences.

In addition you should be able to recognize which measures of

disease occurrence and association are often used with various study designs.

And interpret both statistically significant and

not statistically significant measures of association.

And their related confidence intervals.

Let's start with a few examples of measures of association.

These examples may be similar to ones you might have heard of in the news.

Epidemiologic research on smoking and

lung cancer has found that people who smoke are 15 to 30 times as likely

to get lung cancer, or die from lung cancer, than people who do not smoke.

This is an example of a measure of association.

We will learn about how understand and interpret

statistics such as this one during this weeks lectures.

Another example of a measure of association is

from Malaria researchers who conducted a study of mosquito

nets in Mozambique.

One of the measures of association, a

rate ratio, the researchers calculated was 0.16.

How is this interpreted?

Houses treated with insecticide treated mosquito nets had

a rate of mosquito entry that was 0.16 times.

The rate of mosquito entry in house with treated nets.

This ratio can also be

interpreted as houses treated with mosquito netting reduced

entry rates of an Offalese Gambia mosquitos by 84%.

Thus, the research provides evidence that the use of insecticide

treated mosquito nets, reduces exposure to mosquitoes in the home.

Another example, is injury prevention and motor vehicle safety.

An important topic.

This slide includes a measure of association.

In this case, an odds ratio from a study done on common driving distractions.

Drivers who are composing or sending a text message had 23 times the odds of

a safety critical event compared with drivers who

were not composing or sending a text message.

Let's talk now about the definitions and formulas for measures of association.

So, up to this point in the MOOC we have covered measures of disease occurrence.

You may

recall these include prevalence, risks, rates, and odds.

Here are the actual formulas for these measures of disease occurrence.

I want to review them with you now because

they are the building blocks of the measures of association.

Before we go any further, I'd like to

highlight the differences and similarities among these various measures.

Most importantly, risks and rates both use incident or new cases.

Whereas prevalence

uses prevalent, i.e existing cases.

And odds can use either incident or prevalent cases.

Note the denominators.

The denominators for each formula differ from each other.

Risk has the at risk study population, at the start of the

study period, while rate uses person time at risk during the study period.

Prevalence uses the entire

study population as the denominator.

And for odds, the non-cases form the denominator.

Measures of association compare the measure

of disease occurence in two different groups.

We compare the measure of disease occurence in the exposed group.

With the measure of disease occurrence in the unexposed group.

Our goal is to see if the disease occurrence is different in the two groups.

This comparison can be made by

division, i.e ration of effect measures

or by subtractions difference effect measures.

For the division you are comparing relative measures of effect.

One key question for this ratio measures is what

group you are comparing relative to which other group?

For example the groups being compared in the ration effect.

Are often exposed versus unexposed.

Or one population versus another.

For difference measures in which you use

subtraction you are comparing absolute differences in effect.

In the following lectures or segments we will

discuss each ratio and difference measure in more detail.

The ratio measures indicate the relative strength of the association between the

exposure and a disease or health outcome compared with the absence of exposure or

less exposure.

This strength of an association between a exposure

and a health outcome or disease is of

greater interest when we are trying to understand

causes of a disease or a health outcome.

In contrast, different measures, sometimes called

attributable risk measures, place the magnitude of

the association between and exposure and a

health outcome, in a public health prospective.

Difference measures tell us whether the exposure or risk factor is associated

with a large number of disease cases or small number of disease cases.

Consider this example.

The exposure of smoking has a risk ratio of about 10 for lung cancer mortality.

But a risk ratio of only 1.7 approximately for coronary heart disease mortality.

However the risk

difference for coronary heart disease is much higher, 125.

Compared with the risk difference for lung cancer 43.8, why is this?

This table shows us the base rates of death from cardiovascular

disease, which are 294.67 in smokers and

169.54 in non-smokers in the population. Are much higher

than the base rates of death from cancer, 49.33 and 4.49 in the population.

The risk differences for smoking and

coronary heart disease is also considerably

higher or larger, 125, than the risk difference for smoking and lung cancer.

43.84.

The risk difference can be used to compare the preventative impact

of a smoking cessation program on the rates of

coronary heat disease deaths compared with lung cancer deaths.

From this table, we see that smoking cessation program.

Would have a bigger impact on rates of

coronary heart disease deaths compared with lung cancer deaths.

Before we go any further, we'd like to add cautionary note on the term relative risk.

Please note that the term relative risk is an older.

Commonly used term for any ratio measure of effect that approximates risk.

This term is not precise, and we recommend using more precise

and specific terms such as risk ratio, rate ratio, or odds ratio.

However, you may see this term

regularly when reading epidemiologic articles or studies.

Here are the equations for risk and rate ratios.

Note that the risk ratio is abbreviated

RR and the rate ratio is abbreviated IRR. The I stands for incidence.

Here are the equations for odds and prevalence ratios.

Note that the odds ratio is abbreviated

OR and the prevalence ratio is abbreviated PR.

Here are the formulas for the risk and rate differences.

These formulas express the risk or rate among exposed in excess of

that among the unexposed or less exposed.

Difference measures consider the risk or rate among

the unexposed as a background risk or rate.

In other words a risk or rate that

occurs in the absence of the exposure of interest.

This background risk or rate may not be

a true absolute risk or rate because the unexposed.

Are not necessarily without some risk or rate associated with different population

based factors that are not the focus of the study.

Difference measures are sometimes called attributable risk measures.

In our previous example about smoking, we showed that the coronary heart disease

mortality rate in smokers was 125 in excess of the rate among non-smokers.

Now lets talk about two by two tables.

Two by two tables are commonly used to teach the concepts

of measures of association.

The two refers to two columns and two rows.

These tables are also known as contingency tables.

The two by two table starts with a square cordoned into four spaces.

With the two-by-two table we can show

exposures as two categories, exposed and non-exposed.

And the disease of interest or health

outcome in two categories, usually diseased and non-diseased.

For the minook our two-by-two convention will be disease

on the top and exposure on the left-hand side.

However, you may find it the other way

around in various textbooks or in the published literature.

Each of these sub squares is labeled with a letter, A, B, C, and D.

We'll present the formulas for measures of association in this context.

Let's start with Risk.

We can simplify the table by using E for

exposed and E with a line above it for non-exposed.

And D for diseased and D with a line above it for non-diseased.

Now applying our risk difference and risk ratio formulas the risk difference is a

divided by a plus b minus c divided by c plus d.

And the rate ratio

is a divided by a plus b divided by c divided c plus d.

Now.

Applying our rate difference and rate ratio formulas, the risk difference is

A divided by PT in the exposed, where PT stands for person

time, minus C divided by person time in the unexposed.

And the risk

ratio is a divided by person-time in the exposed.

Divided by c.

Divided by PT, or person time in the unexposed.

Note that for the following texting while driving example,

all data are fictitious and not from a published study.

However, there have been studies that show texting

while driving to be associated with traffic accidents.

Here is the data in a two by two table.

Note, the texting

exposure is on the left-hand side and the

disease outcome, traffic accidents, is on the top.

We calculate both the risk in the exposed,

9.09%, and the risk in the unexposed, 1.10%.

With the formulas on the slide. Now to calculate the risk difference you

subtract the risk in the exposed minus that in the unexposed and get 7.99%.

For the risk ratio you divide the risk in the

exposed by the risk in the unexposed to get 8.27.

Interpreting the risk for exposed and the risk

for the unexposed in the texting while driving examples.

Looks like this.

Among those who texted while driving, 9.09% reported

a traffic accident in a one year time period.

And among those who did not text

while driving, 1.10% reported a traffic accident in a one year time period.

So you can see it's higher in those that traffic

accidents were more common among those that texted while driving.

And here is how you interpret the

risk ratio and risk difference for this example.

For the risk ratio, those that texted while

driving were approximately eight times as likely to have

a traffic accident.

Compared to those who did not text while driving over a one year time period.

And the risk difference among those that

texted while driving, the risk of traffic accidents

was 7.99% higher then those who did not text while driving over a one year.

Time period.

Now to calculate the rate in the exposed

group, the texters, you divide 30 by the total

number of person-years, i.e 400 to get 7.5 cases per 100 person years.

The rate in the unexposed group is 5 divided by 337 person years.

Which gives you 1.48 cases per 100 person years.

Then to calculate the risk rate difference you subtract the rate in

the expose minus the rate in the unexposed to get 6.02 cases per

person 100 person years.

To get the rate ratio you divide the rate in

the exposed by the rate in the unexposed to get 5.06.

And here is how you would interpret the rate

in the exposed and the rate in the unexposed.

Among those who texted while driving the rate of

ext of traffic accidents was 7.05 per hundred person years.

Where as for

the rate in the unexposed, among those who did not text while

driving; the rate of traffic accidents was 1.48 per 100 person years.

And here's how you interpret the rate

ratio and rate difference for this texting example.

For the rate ratio, those that texted while driving had five times the

rate of traffic accidents compared to those who did not text while driving.

The rate difference among those that texted while driving, the

rate of traffic accidents was 6.02 cases per 100 person years.

Higher than the rate among those who did not text while driving.

In this segment we have learned about the different types of measures

of association including: Risk Ratios, Rate

Ratios, Odds Ratios and Prevalence Ratios.

We've also learned about Rate

Differences, Odds Differences and Prevalence Differences,

and Risk Differences.

This concludes our segment about the definition.

Formulas and interprenations of different types of measures of association.

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