School of Veterinary Medicine and Science
Stats are fun!
School of Veterinary Medicine and Science
Apply to everything
School of Veterinary Medicine and Science
ODDS RATIOS AND
RELATIVE RISK
School of Veterinary Medicine and Science
F D Roosevelt
‘...the only thing we have to fear is fear
itself – nameless, unreasoning, unjustified
terror which paralyses needed efforts to
convert retreat into advance’
School of Veterinary Medicine and Science
Cause and effect
• Relationship between a risk factor and an
outcome
• Risk Factors –associated/decreased
probability that the disease will develop
later
• Comparison of risk between the animals
exposed and not exposed
• Causal relationships are complex
School of Veterinary Medicine and Science
Type of data
• Disease or not disease
• Binary outcome
• Categorical data is coming your way!!
School of Veterinary Medicine and Science
Plan
•
•
•
•
Definitions
Study types that you will see them in
How you calculate them?
What do they mean?
• How are they different?
• Look at some papers
School of Veterinary Medicine and Science
ODDS
The chances or likelihood of something
happening or being the case.
The ratio between the amounts staked by the
parties to a bet, based on the expected
probability either way: "odds of 8-1".
School of Veterinary Medicine and Science
Odds ratio
• Ratio between the odds of disease in
exposed animals and the odds of disease
in non-exposed animals
School of Veterinary Medicine and Science
When do you see them?
• Case control studies
• Casecontrol study – compare risk factors
between animals with disease (cases) to
those without (controls)
• Its about DISEASE
• Animals start with disease
• Risk Factors – presence of the factor is
associated with a increase/decrease
probability that the disease will develop
later
School of Veterinary Medicine and Science
Advantages and
disadvantages
• Good
–
–
–
–
Quick, cheap and easy
Rare disease
Lots of risk factors
No loss to follow-up
• Bad
– Recall bias
– Not good when exposures are rare
• Can’t directly measure risk because you
already know who has disease
School of Veterinary Medicine and Science
When are they used?
• We know the disease state
• We look back at exposure
• Cancer
• Exposure must be fairly common
School of Veterinary Medicine and Science
How do they work?
• Case control studies
Population
D+
D-
exposed
Un-exposed
exposed
cases
controls
Un-exposed
Then
Now!
School of Veterinary Medicine and Science
So.........
Exposed
Not-exposed
Disease +ve
a
b
Disease -ve
c
d
OR= Ratio between the odds of disease in
exposed animals and the odds of disease
in non-exposed animals
OR= odds of being a case in exposed group
odds of being a case in non-exposed groups
School of Veterinary Medicine and Science
So.........
Exposed
Not-exposed
Disease +ve
a
b
Disease -ve
c
d
Odds of disease/case in exposed =a/a+c = a/c
c/a+c
Odds of disease/case in non-exposed = b/b+d =b/d
d/b+d
OR = a/c or OR = ad
b/d
cb
School of Veterinary Medicine and Science
Values
•
•
•
•
Values always >0
1 – no difference
<1 – exposure is protective
>1 – exposure increases odds of disease
• Confidence intervals
School of Veterinary Medicine and Science
Odds ratios
• Case-control studies
• Not a direct measure of risk, you cant do
this
• But when a disease is really rare OR = RR
School of Veterinary Medicine and Science
RISK
• Risk is the potential that a chosen action
or activity (including the choice of
inaction) will lead to a loss (an undesirable
outcome). The notion implies that a choice
having an influence on the outcome exists
(or existed). Potential losses themselves
may also be called "risks". Almost any
human endeavour carries some risk, but
some are much more risky than others.
School of Veterinary Medicine and Science
Relative risk
• Increased or decreased risk of disease in
animals with an exposure of interest
School of Veterinary Medicine and Science
When do you see them?
• Cohort studies
• Cohort study – compare disease animals
with exposed to a risk factor compared to
those not exposed to a risk factor
• It’s about EXPOSURE
• Start disease free
• Risk Factors – presence of the factor is
associated with a increase/decrease
probability that the disease will develop
later
School of Veterinary Medicine and Science
Advantages and
disadvantages
• Good
–
–
–
–
Time sequence of events
Lots of risk factors and outcomes
Can measure incidence
Can study rare exposures
• Bad
–
–
–
–
Take a long time
Not good when outcomes are rare
Lost to follow-up can be a problem
Things change over time!
School of Veterinary Medicine and Science
When are they used?
• When there are lots of risk factors of
interest
• Disease must be fairly common
• Cancer
School of Veterinary Medicine and Science
How do they work?
• Cohort studies
(Randomised controlled trial)
Population
D+
Dexposure
Diseased
No disease
Cohort
Now!
No
exposure
Diseased
No disease
Later
School of Veterinary Medicine and Science
So.........
Exposed
Not-exposed
Disease +ve
a
b
Disease -ve
c
d
Overall risk of disease = number of animals
with disease, regardless of exposure
compared to total number of animals
Risk = a+b
n
School of Veterinary Medicine and Science
So.........
Exposed
Not-exposed
Disease +ve
a
b
Disease -ve
c
d
Relative risk of disease = number of animals with
disease that were exposed compared to total
number of animals with disease that weren’t
exposed
Relative risk = risk of disease in the exposed
risk of disease in un-exposed
School of Veterinary Medicine and Science
So.........
Exposed
Not-exposed
Disease +ve
a
b
Disease -ve
c
d
Risk of disease in exposed=a/a+c
Risk of disease in non-exposed = b/b+d
Relative risk =a/(a+c)
b/(b+d)
School of Veterinary Medicine and Science
Values
•
•
•
•
Values always >0
1 – risk is the same
<1 – decreased risk in exposed animals
>1 – Increased risk in exposed animals
• ALWAYS remember underlying risk of
disease
School of Veterinary Medicine and Science
Relative risk
• Cohort studies
• A direct measure of risk, as the animals
start off without disease
School of Veterinary Medicine and Science
So.........
Exposed
Not-exposed
Disease +ve
a
b
Disease -ve
c
d
If a is tiny....
Even if an OR or RR due to a risk factor is big e.g.
10
We still dont need to panic!
Remember the biology
School of Veterinary Medicine and Science
Remember
• These are point estimates so……
You need a confidence interval…..
School of Veterinary Medicine and Science
What is a confidence
interval?
Confidence interval: Confident that the
true population value of whatever we are
measuring is within this range of values
……………………………….not entirely true!
School of Veterinary Medicine and Science
So……
• To see how believable something is – you
want a confidence interval
• Don’t just believe the point estimate of a
sample is the true value in your population
School of Veterinary Medicine and Science
Look for…
• The point estimate, the P value and the
confidence interval – you want the actual
numbers not ‘95% confidence’
E.g.
Cases were 3 times more likely to be over the age
of 15 rather than 5-10 years old, when compared
to controls (OR = 2.87, 95% CI 1.38 – 5.99, p =
0.005).
Cases were significantly more likely to have ever
have received a vaccine of any type in their
lifetime compared to controls cats (OR = 6.8,
95% CI = 1.9 - 50.4, p = 0.03).
School of Veterinary Medicine and Science
Now what?
1. How wide is it?
2. What does the interpretation of the CI
mean? Clinically? Biologically?
3. Does it include the null value?
School of Veterinary Medicine and Science
Sooooo…..
• Small sample = bigger standard error =
bigger CI
• More variation in sample bigger CI
• Wide CI = imprecise estimate
• Narrow CI = more precise estimate
School of Veterinary Medicine and Science
Examples
Cases were 3 times more likely to be over
the age of 15 rather than 5-10 years old,
when compared to controls (OR = 2.87,
95% CI 1.38 – 5.99, p = 0.005).
Cases were significantly more likely to have
ever have received a vaccine of any type
in their lifetime compared to controls cats
(OR = 6.8, 95% CI = 1.9 - 50.4, p =
0.03).
School of Veterinary Medicine and Science
2. Interpretation
• The upper and lower limits can be used to
see whether the results are useful
• A value can be significant with a low p
value but the CI interval can help tell you
whether you should get excited about it or
not!
School of Veterinary Medicine and Science
Examples
Cases were 3 times more likely to be over
the age of 15 rather than 5-10 years old,
when compared to controls (OR = 2.87,
95% CI 1.38 – 5.99, p = 0.005).
Cases were significantly more likely to have
ever have received a vaccine of any type
in their lifetime compared to controls cats
(OR = 6.8, 95% CI = 1.9 - 50.4, p =
0.03).
School of Veterinary Medicine and Science
Now what?
1. How wide is it?
2. What does the interpretation of the CI
mean? Clinically? Biologically?
3. Does it include the null value?
School of Veterinary Medicine and Science
The null value?
• In Odds Ratios and Risk Ratios where you
compare two groups and a value of 1
means there is no difference then 1 is the
null value
• If 1 is included in the CI e.g. 0.56-1.2,
then there is no statistically significant
effect
………………………………..dont worry I will
remind of this later in the year
School of Veterinary Medicine and Science