lecture 9

Question 1

Associations between two categorical variables

Answer 1

Contingency tables are often used to record and analyse the relationship between two or more categorical variables.

Recall, “Categorical” means that the data can be separated into mutually exclusive categories. Usually summarized in the form of count.

Examples: smoker/non-smoker, treated/control, disease/disease free.

The simplest case of an association between two binary variables can be summarized in a 2 by 2 table.

Examine membership in each individual subgroup and illustrate this with the simplest kind of categorical variable called the binary categorical variable (2 distinct groups rather than multiple distinct groups) - east to do a 2 by 2 table now

Question 2

2 by 2 table for

Answer 2

(binary) categorical variables

Question 3

2 by 2 table terminology and features

Answer 3

factor = categorical variable 
level = one of the categories 

no one is counted twice (each individual is represented once)

Look at image then try draw one from scratch

Question 4

a =

Answer 4

frequency of samples in level 1 of factor 1 and level 1 of factor 2

Question 5

b =

Answer 5

frequency of samples in level 1 of factor 1 and level 2 of factor 2

Question 6

c =

Answer 6

frequency of samples in level 2 of factor 1 and level 1 of factor 2

Question 7

d =

Answer 7

frequency of samples in level 2 of factor 1 and level 2 of factor 2

Question 8

relative risk define

Answer 8

ratio of two probabilities/proportions

Question 9

risk difference define

Answer 9

difference between two probabilities

Question 10

odds ratio define

Answer 10

ratio of two odds

Question 11

RR features

Answer 11

Relative risk (RR) gives the risk of an outcome relative to “exposure”.
It is calculated as the ratio of the risk of an outcome for an exposed and an unexposed group

look at how much bigger one estimate of risk is compared to the other

Question 12

RR equation

Answer 12

It is calculated as the ratio of the risk of an outcome for an exposed and an unexposed group….
RR = (a/(a+b) ) / (c/(c+d))

Question 13

RR interpretation

Answer 13

_______ were _____ times more likely to be _____ during (time period of study) than _____

alternatively turn the number into a percentage

Question 14

RR=1

Answer 14

there is no association between outcome and exposure

Question 15

RR conventional layout

Answer 15

conventionally the group ‘exposed’ to our exposure of interest goes on the top and ‘unexposed’ on the bottom

Question 16

RR less than one

Answer 16

protective factor for group that is the numerator

Question 17

RR greater than one

Answer 17

increased risk for numerator group

Question 18

RR and two by two tables

Answer 18

simplified measure with a two by two table means that we cannot control for confounding

think about confounding - simple table cannot control for confounding therefore just need to be aware, more sophisticated stats process is required

Question 19

Risk difference is …

Answer 19

The risk difference (RD) is given by the difference in the risk for the two groups: a/(a + b) − c/(c + d)

also called attributable risk because when you calculate the raw difference like this you are saying there is an additional amount of risk that is attributable to the exposed group

work out raw difference between the risks of 2 groups

Question 20

RD equation

Answer 20

a/(a + b) − c/(c + d)

Question 21

RD interpretation

Answer 21

in every (number) there will be _____ more/less injuries than in (same number) backs

gives you a per person estimate, different way of expressing the variable in response to the outcome

Question 22

Odd ratio is …

Answer 22

The odds ratio (OR) compares the odds of an outcome for two groups

measure of those who satisfy a condition over those who do not whereas risk = who have/total

for example it is number of successes over number of failures

exposed vs unexposed group with respect to the outcome

Ratio of the odds of the outcome for the exposed group to that for the unexposed group

Question 23

Difference between RR and OR

Answer 23

measure of those who satisfy a condition over those who do not whereas risk = who have/total

distinct difference between RR and OR in terms of denominator

Question 24

odds in exposed =

Answer 24

a/b

Question 25

odds in unexposed =

Answer 25

c/d

Question 26

odds ratio equation

Answer 26

ad/bc

Question 27

Symmetry in terms of OR

Answer 27

Note: that because it doesn’t use the row or column total, the odds ratio is symmetric with respect to the rows and columns in the table. This means there is no mathematical distinction between exposure and outcome variables.

symmetry - you will get exactly the same number for your odds ratio if you worked out the odds of the outcome in the exposed group vs the odds of the outcome in the not exposed group and you would get exactly the same number if you completely flipped the odds ratio
Respect to exposure rather than outcome, asking a different question but will get the same number and this works because these calculations do not take into account the row or column totals

In a case-control study the design compares the odds of exposure in cases to the odds of exposure in controls

This gives the same odds ratio as the ratio of the odds of disease in the exposed to the odds of disease in the unexposed.
This symmetry property of the odds ratio makes it particularly useful for quantifying associations between binary variables where there is no “direction” e.g. alcohol consumption (Yes/No) and Smoking (Yes/No), or fever and diarrhoea.

Question 28

Case control studies - OR vs RR and why

Answer 28

case controls should be using OR to analyse their outcome vs exposure as RR is easily manipulated by changing the number of controls

the relative risk can be made to vary by varying the number of controls selected. this means it is not an estimate of anything useful in a case control study - estimate of RR can be changed easily by simply changing the number of controls so if we are in a study where we ourselves tailor the number of controls then RR is useless therefore use OR. Odds is not affected by the total sample size of the controls

Question 29

Rare disease

Answer 29

for rare diseases the number of people with a disease is small therefore a and c are small

therefore a/b≈ a/a+b and c/d≈ c/c+d
Then relative risk = a/(a+b)/c/(c+d) ≈ a/b/ c/d , i.e. RR ≈ OR