Download Relative Risk

Risk and
Relative Risk
Suppose a news article claimed that drinking coffee
doubled your risk of developing a certain disease.
Assume the statistic was based on legitimate, wellconducted research.
Does this statistic provide any information on your
actual risk?
What additional information would you want
about the risk before deciding whether to quit
drinking coffee?
A study classified pregnant women according to
whether they smoked and whether they were
able to get pregnant during the first cycle in
which they tried to do so. What do you think is
the question of interest? Attempt to answer it.
Here are the results:
Pregnancy Occurred After
First Cycle Two or More Cycles Total
Smoker
29
71
100
Nonsmoker
198
288
486
Total
227
359
586
A recent study estimated that the
“relative risk” of a woman developing
lung cancer if she smoked was 27.9.
What do you think is meant by the
term relative risk?
Students in a statistics class were asked whether
they preferred an in-class or a take-home final
exam and were then categorized as to whether
they had received an A on the midterm.
Of the 25 A students, 10 preferred a take-home
exam, whereas of the 50 non-A students, 30
preferred a take-home exam.
How would you display these data in a table?
Displaying Variables:
Contingency Tables
• Count the number of individuals who
fall into each combination of
categories.
• Present counts in table = contingency
table.
• Row = explanatory variable.
• Column = response variable.
Example: Aspirin and Heart Attacks
Rows = explanatory variable = aspirin or placebo
Columns = response variable = heart attack or no heart attack
Contingency Table with explanatory as row variable,
response as column variable, four cells.
Heart Attack No Heart Attack Total
Aspirin
104
10,933
11,037
Placebo
189
10,845
11,034
Total
293
21,778
22,071
Open file HeartAttack.xls
Conditional Percentages and Rates
Question of Interest: Do the percentages in each
category of the response variable change when the
explanatory variable changes? Meaning does taking
aspirin change the chances of having a heart attack?
Find the percentage of the aspirin group who had a heart
attack and the percentage of the placebo group who had
a heart attack.
Note: When the percentages are very small it is common
to express as a rate per 1000 (or 100,000, etc)
Conditional Percentages and Rates
To Find the Conditional (Row) Percentages
Aspirin Group:
Percentage who had heart attacks = 104/11,037 = 0.0094 or 0.94%
Rate per 1000 = 9.4 (multiply the original rate person by 1000)
Placebo Group:
Percentage who had heart attacks = 189/11,034 = 0.0171 or 1.71%
Rate per 1000 = 17.1
•Percentage: rate per 100, written with % sign
•Rate: the number of heart attacks per person (or
per 1000 people or per 10,000 or per 100,000
depending on the size of the rate)
Conditional Percentages and Rates
Example: Percentage and Rate Added
Aspirin
Placebo
Total
Heart
Attack
104
189
293
No Heart
Attack
Total
10,933 11,037
10,845 11,034
21,778 22,071
Heart
Attacks (%)
0.94
1.71
Rate per
1000
9.4
17.1
Different Expressions: Risk,
Probability, and Odds
Percentage with trait =
(number with trait/total) expressed as %
Proportion or rate with trait = number with
trait/total
Probability of having trait = number with trait/total
or expressed as a percent
Risk of having trait = number with trait/total
Odds of having trait = (number with trait/number
without trait)
Relative Risk, Increased Risk,
and Odds
A population contains 1000 individuals,
of which 400 carry the gene for a disease.
Equivalent ways to express this proportion:
• Forty percent (40%) of all individuals carry the gene.
• The proportion who carry the gene is 0.40.
• The rate is .4 per person or 40 per 100 people.
• The probability that someone carries the gene is .40
or 40%.
• The risk of carrying the gene is 0.40.
• The odds of carrying the gene are 400 to 600
(or 2 to 3, or 2/3 to 1).
Baseline Risk and Relative Risk
The significance of a risk is hard to evaluate on its
own. One way to better understand the effect of
the explanatory variable is to calculate the
relative risk.
Relative Risk: of outcome for two categories of
explanatory variable is ratio of risks for each category.
Often a risk is compared to the baseline risk.
Baseline Risk: risk without treatment or changed
behavior
The baseline risk can be difficult to find. If placebo
included, baseline risk = risk for placebo group.
Meaning of Relative Risk
The meaning of the relative risk is how many
times more likely the outcome is with the
explanatory variable than without it. If the
relative risk is greater than 1, the risk is greater
with the explanatory variable. If the relative risk
is less than 1, the risk is lower with the variable
than without.
Relative Risk of Having a Heart Attack if
taking Aspirin
Aspirin
Placebo
Total
Heart
Attack
104
189
293
No Heart
Attack
10,933
10,845
21,778
Total
11,037
11,034
22,071
Heart
Attacks (%)
0.94
1.71
Rate per
1000
9.4
17.1
What is the relative risk of having a heart attack if you take
aspirin?
What is the meaning of Relative Risk?
Relative Risk of Having a Heart Attack if
taking Aspirin
Aspirin
Placebo
Total
Heart
Attack
104
189
293
No Heart
Attack
10,933
10,845
21,778
Total
11,037
11,034
22,071
Heart
Attacks (%)
0.94
1.71
Rate per
1000
9.4
17.1
Relative risk = risk of heart attack with aspirin / risk without
= 9.4/17.1 = .55
Meaning of Relative Risk
Risk of having a heart attack if you are taking aspirin is .55
times as great as the risk of having a heart attack if not taking
aspirin. One is less likely to suffer if taking aspirin.
Relative Risk of Developing Breast Cancer
What question do you think the researchers were trying
to answer?
What is the risk of breast cancer if a woman had her
first child at age 25 or older?
What is the risk of breast cancer if a woman had her
first child before age 25?
What is the relative risk?
Relative Risk of Developing Breast Cancer
• Risk for women having
firstquestion
child at 25
If your
is:or older
31/1628 = to
0.0190
What is the relative risk of A=compared
B?
• Risk for women having first child before 25
= 0.0143
1) Find the risk =of65/4540
A
• Relative risk = 0.0190/0.0143
1.33of B
2) Find the=risk
3) Relative risk = (risk of A) / (risk of B)
Meaning of Relative Risk
You shouldbreast
word cancer
your answer
this who
way:had
Risk of developing
for women
The first
risk child
of A is
timesisas1.33
great
as the
risk of
their
at_____
25 or older
times
as great
asB.
the risk for women who had their first child before 25.
Meaning of Relative Risk
A relative risk that is greater than 1.0
shows that there is an increased risk in the group in
question.
A relative risk that is equal to 1.0
shows that there is equal risk in both groups.
A relative risk that is less than 1.0
indicates that there is a lower risk in the group in
question.
Note: Relative risk is expressed in decimal form.
Increased Risk
Increased Risk = (relative risk – 1.0)
Example: Increased Risk of Breast Cancer
• Relative risk = 1.33
• Increased risk = 1.33 - 1 = 0.33 or 33%
There is a 33% increase in the risk of breast cancer
for women who have a child after 25 compared to women
who have a child before the age of 25 .
Note: Increased risk and decreased risk are expressed in
percent form.
Decreased Risk
Decreased Risk = (1.0 - relative risk)
For the heart attack example:
•Relative risk = .55.
•Decreased risk: 1 - .55 = .45 = 45%
There is a 45% decrease in risk of heart attack when
taking aspirin.
Relative Risk
Researchers often report relative risks adjusted to
account for confounding variables.
Example:
Suppose relative risk for getting cancer for those with
high-fat vs low-fat diet is 1.3, adjusted for age and
smoking status. =>
Relative risk applies (approx.) for two groups of
individuals of same age and smoking status, where
one group has high-fat diet and other has low-fat diet.
Misleading Statistics about Risk
Common ways the media misrepresent
statistics about risk:
1. The baseline risk is missing.
2. The time period of the risk is not identified.
3. The reported risk is not necessarily your risk.
Missing Baseline Risk
“Evidence of new cancer-beer connection”
Sacramento Bee, March 8, 1984, p. A1
• Reported men who drank 500 ounces or more of
beer a month (about 16 ounces a day) were three
times more likely to develop cancer of the rectum
than nondrinkers.
• Is this enough information to change your lifestyle
(or at least be concerned about your current) if you
were a man who drank 500 ounces of beer a month?
Missing Baseline Risk
• A common misrepresentation of relative or
increased risk is not including the baseline
risk.
• Need baseline risk to make an informed
decision.
• Less concerned if chances go from 1 in 100,000
to 3 in 100,000 compared to 1 in 10 to 3 in 10.
• If you knew that the baseline risk in this study
was about 1 in 180, what would you do?