ARM - week 3

Question 1

difference between OLS and logistic

Answer 1

Results of an OLS regression can be used to predict the outcome (the expected weight of a 50 year old man of 1.80 m is 80 kg) and results of a logistic regression can be used to predict the probability of an event (the probability that a 50 year old man of 1.80 m weighs more than 90 kg is 15%). In an OLS regression results show the association of explanatory variables with the outcome (1 cm in additional height is associated with 800 grams of extra weight) and in a logistic regression results show the association of explanatory variables with the probability of an event (probability of being heavy increases with height).

Question 2

Interpretable measures of association for continuous variables

In this experiment the average weight for men and women are compared. In 2019, the average weight for men was 85 kg and the average weight for women was 72 kg.

what is relative risk?

Answer 2

Difference in means / mean difference: 85 – 72 = 13 kg
Relative difference: 85 / 72 = 1.18 → on average men are 18% heavier than women.

Question 3

Interpretable measures of association for dichotomous variables

In this experiment the proportion of men with overweight and the proportion of women with overweight are compared. The dichotomous outcome is overweight (yes or no). The proportion of men with overweight is 48% and the proportion of women with overweight is 40%.

what is risk difference, relative risk and relative difference?

Answer 3

Risk difference: 48% - 40% = 8%-points –> men are 5%-points more likely to be overwight than women
Relative risk: 48% / 40% = 1.20 → men are 1.20 times as likely to be overweight than women
Relative difference: 48% / 40% = 1.20 → men are 20% more likely to be overweight than women

Question 4

Risk ratio

Answer 4

Ratio of risks (probabilities)

Question 5

Odds ratio

Answer 5

Ratio of odds

Question 6

Odds

Answer 6

The ratio of the probability that the event will happen and the probability that the event will not happen

Question 7

Relative risk and risk difference after logistic regression
- After randomized controlled trial

Answer 7

o We can calculate the relative risk and risk difference from observed proportions (without regression)
o What we observe in treatment group, is what we would have expected if the entire sample had been treated
o Marginal effect: the outcome if everyone would have been treated compared to the outcome if nobody would have been treated

Question 8

Relative risk and risk difference after logistic regression
- For observational study, after logistic regression

Answer 8

o Observed proportions may be biased (lack of exchangeability)
o We can calculate adjusted proportions for each treatment → what we would have observed if the entire sample had (not) been treated
o Use adjusted proportions to calculate the relative risk and the risk difference

Question 9

Assessing causal inference studies

Answer 9

1. what was the quetion? what was the underlying question?
2. what was actually estimated? biased/unbiased and full/partial effect
3. is the estimate realy an answer to the question?
4. how was the anaylsis designed?
5. which statistical methods were used?
6. were these methods applied correctly?
7. what is the (type of) estimate? big/ small/ good/ bad? how certain is the estimate?
8. what do the researches conclude? is that conclusion justified?
9. is the conlusion supported with strong or weak evidence?
10. how does the conclusion compare to what we (already/ thought we) knew?