School of Veterinary Medicine and Science. Stats are fun!

School of Veterinary Medicine and Science


Stats are fun!


Apply to everything


ODDS RATIOS AND RELATIVE RISK


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’


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


Type of data

• Disease or not disease• Binary outcome

• Categorical data is coming your way!!


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


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".


Odds ratio

• Ratio between the odds of disease in exposed animals and the odds of disease in non-exposed animals


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


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


When are they used?

• We know the disease state• We look back at exposure

• Cancer

• Exposure must be fairly common


How do they work?

• Case control studies

D+ D-

controls

cases

exposed

Un-exposed

exposed

Un-exposed

Now!Then

Population


So.........

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

Exposed Not-exposed

Disease +ve a b

Disease -ve c d


So.........

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 = adb/d cb

Exposed Not-exposed

Disease +ve a b

Disease -ve c d


Values

• Values always >0• 1 – no difference• <1 – exposure is protective• >1 – exposure increases odds of disease

• Confidence intervals


Odds ratios

• Case-control studies

• Not a direct measure of risk, you cant do this

• But when a disease is really rare OR = RR


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.


Relative risk

• Increased or decreased risk of disease in animals with an exposure of interest


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


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!


When are they used?

• When there are lots of risk factors of interest

• Disease must be fairly common

• Cancer


How do they work?

• Cohort studies (Randomised controlled trial)

D+ D-

Cohort

Diseased

No disease

Diseased

No disease

Now! Later

Population

exposure

Noexposure


So.........

Overall risk of disease = number of animals with disease, regardless of exposure compared to total number of animals

Risk = a+bn

Exposed Not-exposed

Disease +ve a b

Disease -ve c d


So.........

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 exposedrisk of disease in un-exposed

Exposed Not-exposed

Disease +ve a b

Disease -ve c d


So.........

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)

Exposed Not-exposed

Disease +ve a b

Disease -ve c d


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


Relative risk

• Cohort studies

• A direct measure of risk, as the animals start off without disease


So.........

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

Exposed Not-exposed

Disease +ve a b

Disease -ve c d


Remember

• These are point estimates so……

You need a confidence interval…..


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!


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


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).


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?


Sooooo…..

• Small sample = bigger standard error = bigger CI

• More variation in sample bigger CI

• Wide CI = imprecise estimate• Narrow CI = more precise estimate


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).



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!


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).



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?


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. Stats are fun!

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