Week 7: Logistic Regression and Odds Ratio

Question 1

What type of data is logistic regression used for?

Answer 1

Dichotomous/binary outcomes

Question 2

How is “odds” defined in logistic regression?

Answer 2

Odds = number with the event / number without the event

Question 3

How is the odds ratio (OR) interpreted?

Answer 3

• OR < 1: Outcome is less likely to occur
• OR > 1: Outcome is more likely to occur
• OR = 1: No difference in likelihood

Question 4

What does it mean if the 95% CI for OR includes 1?

Answer 4

The result is not statistically significant at p < 0.05

Question 5

How are logistic regression models fitted in statistical software?

Answer 5

Using the natural log of the odds (ln(odds)) as the outcome variable. Ln(odds) can take any positive or negative value. In Stata, ln(odds) is referred to as coefficient.

Question 6

Why use logistic regression instead of chi-square tests?

Answer 6

Logistic regression allows the inclusion of multiple explanatory variables and continuous variables

Question 7

What is the rule of thumb for the number of explanatory variables in logistic regression?

Answer 7

One explanatory variable for every 10 participants in the smallest outcome group

Question 8

What assumptions must be met?

Answer 8

• Data must be independent
• Explanatory variables should not be highly correlated

Question 9

How do you calculate a 95% CI for ln(odds)?

Answer 9

Lower limit = coefficient - (SE1.96), upper limit = coefficient + (SE1.96)

Question 10

What is the significance of the Wald test?

Answer 10

Tests the H0 that there is no relationship between variables by examining if true parameter ln(OR) = 0
If z is greater than +/- 1.96 then it is statistically significant

Question 11

How does logistic regression handle categorical explanatory variables with more than two categories?

Answer 11

It assigns one category as the reference and calculates ORs for the others relative to it

Question 12

How can logistic regression coefficients be interpreted for continuous variables?

Answer 12

They represent the change in ln(odds) for a one-unit increase in the variable

Question 13

What is the formula to convert coefficients and ORs to ORs for larger units (e.g., 10-unit changes)?

Answer 13

If using coefficients, multiply by 10 then exponentiate i.e., exp(coefficient*10)
If using ORs, raise to the power of 10

Question 14

What is ln?

Answer 14

Natural logarithm (sometimes written log or log_e, although log has a different mathematical meaning). Ln(odds) are not usually reported in papers and reports (ORs are presented instead)

Question 15

What is exp?

Answer 15

Exponentiate - inverse function to natural logarithm

Question 16

How do cohort and case-control studies differ?

Answer 16

• Cohort study - select two groups of people based on exposure (e.g., smokers versus non-smokers), compare outcome (e.g., cancer/non-cancer)
• Case-control study - select two groups of people based on outcome (cancer versus non-cancer), compare exposure (e.g., smoking/non-smoking)

Question 17

How do you calculate OR?

Answer 17

Odds in those with a characteristic / odds in those without a characteristic

Question 18

How is Z calculated?

Answer 18

Z = coefficient / SE

Question 19

What is the equation for ln(odds)?

Answer 19

ln(odds) = β0 + β1 * x

Question 20

How do you calculate odds from ln(odds)?

Answer 20

Exponentiate ln(odds)
Odds = exp(ln(odds))

Question 21

On ln(odds) scale, what does it mean if the 95% CI includes 0?

Answer 21

There is not enough evidence to reject H0

Question 22

What does ‘i’ signify in logistic regression syntax?

Answer 22

Ensures a separate OR for each category (applicable to variables with > 3 categories)

Question 23

What is ‘b1’ used for in syntax?

Answer 23

Switch reference category without recoding (applicable to variables with 2 categories)