Binary Logistic Regression

Question 1

What is a contingency table?

Answer 1

Summarises frequency distribution of each of two categorical variables and the association between them

Question 2

What can a contingency table allow us to check?

Answer 2

▪️How each potential explanatory variable is related to the DV
▪️The categories for explanatory variables are large enough (at least 5)
▪️How many missing cases for each

Question 3

What is the risk of an outcome?

Answer 3

The number of times the outcome of interest occurs divided by the total number of possible outcomes

Question 4

How do you calculate the risk ratio (relative risk)?

Answer 4

Risk of one outcome divided by risk of the other outcome

Question 5

What does a risk ratio of 1 indicate?

Answer 5

No difference between the groups

Question 6

How do you calculate the odds of an outcome?

Answer 6

The number of times it occurs divided by the number of times it doesn’t occur

Question 7

How do you calculate the odds ratio?

Answer 7

Odds of outcome in one group compared to odds of outcome in the other group

Question 8

What does an odds ratio of 1 mean?

Answer 8

▪️Outcome occurs half of the time
▪️Exposure doesn’t affect the odds (no difference between groups)

Question 9

What does an odds ratio <1 indicate?

Answer 9

Outcome occurs less than half the time

Indicates exposure is associated with reduced risk of developing outcome

Question 10

What does an odds ratio >1 indicate?

Answer 10

Outcome occurs more than half the time

Indicates exposure is associated with increased risk of developing outcome

Question 11

Which ratio can be used for case-control studies?

Answer 11

Odds ratio

Question 12

When can you NOT use risk ratios and why?

Answer 12

In case control studies where selection of subjects is based on the outcome

Question 13

What happens to RR and OR in rare outcomes?

Answer 13

They will be approximately equal

Question 14

What can you assume about a relationship where the outcome is binary?

Answer 14

It is nonlinear, S-shaped (sigmoid) relationship

Linear cannot make sense!
▪️Outcome is limited to 0,1
▪️Goal is to separate groups, not minimise mean squared error
▪️Linear regression is highly sensitive to influential cases
▪️Assumptions of linear are violated, particularly homogeneity of variance

Question 15

What is the link function?

Answer 15

A way of relating x and Y by way of a function in a logistic regression

To model the relationship between left and right hand side of the equation

g(y) = β0 + β1x1 + ε

Question 16

What is maximum likelihood?

Answer 16

An iterative process that estimates the best fitted equation

Find the coefficient that makes the observed data most likely

(try lots of models until tweaking it further doesn’t improve the fit)

Question 17

What does the coefficient in a logistic regression mean?

Answer 17

An increase of X of 1 unit will change the ODDS (log) by β

Question 18

How do you calculate the odds ratio for X?

Answer 18

The anti-log of the coefficient

(e to the power of the coefficient)

Question 19

When do you use the binary logistic regression?

Answer 19

To test whether there’s an association between variables, where the dependent variable is categorical on a binary scale

Question 20

What assumptions are needed for the binary logistic regression?

Answer 20

▪️Binary dependent variable has a Bernoulli distribution
▪️It’s linearly related to the predictor only after transforming into the logit scale
▪️observations are independent
▪️continuous variables have a linear effect on the log-odds scale

Question 21

If you have a continuous outcome/DV, what type of regression should you use?

Answer 21

Linear regression

Question 22

If you have a binary (categorical) outcome/DV, what type of regression should you use?

Answer 22

Binary logistic regression

Question 23

What ratio can you calculate in a case-control study?

Answer 23

Odds ratio

(NOT risk!)

Question 24

What ratio can you calculate in a prospective cohort study?

Answer 24

Odds OR risk ratio

Question 25

What is incidence?

Answer 25

Aka risk

e.g., number of people who got disease when exposed over the total number of people who were exposed