ARM - week 1

Question 1

causal inference

Answer 1

In causal inference we are not interested in the outcome per se, but we are interested in the role of the treatment in achieving this outcome

Question 2

causal effect

Answer 2

In an individual, a treatment has a causal effect if the outcome under treatment 1 would be different from the outcome under treatment 2.

Question 3

counterfactual outcome

Answer 3

Potential outcome that is not observed because the subject did not experience the treatment.

Question 4

Average treatment effect

Answer 4

average of individual effects in a population

Question 5

fundamental problem of causal inference

Answer 5

1.Individual causal effect cannot be observed; no information about the counterfactual outcome.

2.Average causal effect can be estimated if, and only if, (all) 3 identifiability conditions are met.

Question 6

identifiability conditions

Answer 6

positivity
consistency
exchangeability

If, and only if, all 3 identifiability conditions are met, then association of exposure and outcome is an unbiased estimate of the causal effect

Question 7

positivity

Answer 7

There has to be a positive probability for everyone in the sample of being assigned to each of the treatment levels.

all the differences between the 2 groups are because of chance

Question 8

Consistency.

Answer 8

There has to be a clear definition of treatments.

beforehand everyone could get treatment or could not get the treatment

Question 9

Exchangeability.

Answer 9

Treatment groups must be exchangeable → it does not matter who gets treatment A and who gets treatment B. Potential outcomes are independent of the treatment that was actually received

the interventions have to be defined before assigning people to the different groups

Question 10

meeting the exchangeability condition

Answer 10

1. randomized control trial
2. matching
3. stratification
4. adjustment

Question 11

randomized control trial

Answer 11

automatically achieves exchangeability (all the differences between the 2 groups are because of chance) positivity (beforehand everyone could get treatment or could not get the treatment) and consistency (the interventions have to be defined before assigning people to the different groups).

Question 11

matching

Answer 11

for each individual with characteristics x, y, and z who gets treatment A, there is an individual with characteristics x, y, and z who gets treatment B. Statistical methods can be applied when perfect matching (i.e., use identical twins, triplets, …) is not possible (e.g., propensity score matching).

Question 12

stratification

Answer 12

randomly select individuals from different subsets (i.e., strata) of the larger population. Difficult to meet the positivity condition (i.e., individuals in all strata). Stratification quickly becomes infeasible

Question 12

adjustment

Answer 12

control for factors that influence (i.e., bias) the association between the treatment and outcome in regression analysis. Individuals are assigned to all treatment arms within all levels of adjustment factors. Can also be combined with an RCT, stratification, and matching. Complete and correct adjustment leads to exchangeability

Question 13

wherefore are dags used

Answer 13

to meet the exchangeability condition

Question 14

correlation

Answer 14

a statistical relationship. Knowing the value of one variable may provide information on the value of another variable, but that does not mean that one caused the other.

causation if and only if the identifiability conditions hold. In order to see an association as a valid and unbiased estimate of a causal effect, you need theory/subject knowledge and a causal structure. A directed acyclic graph is a tool that helps to present the causal structure.

correlation implies association (not causation)

Question 14

causation

Answer 14

a difference between potential outcomes.

Question 14

Directed acyclic graph (DAG)

Answer 14

• Directed: each connection is an arrow
  o Connection between X and Y follows the direction of the arrows (X precedes Y in time)
  o Each arrow represents a possible causal effect
  o No arrow means certainly no causal effect
• Acyclic: a path of arrows does not come back to its own origin → a variable cannot cause itself

Question 14

path

Answer 14

a route between the exposure (X) and the outcome (Y). A path may contain several arrows, but it does not have to follow the direction of the arrows.

Question 15

causal path

Answer 15

path follows the direction of the arrows

Question 16

backdoor path

Answer 16

path does not follow the direction of the arrow.

Question 17

open path

Answer 17

All paths are open, unless arrows collide somewhere along the path. then it is a closed path.

Question 18

Open paths transmit association

Answer 18

the association of X and Y is the combination of all open paths between them. An open path is blocked when we adjust for a variable along the path → we then remove the influence of L on the association between X and Y by including L in the regression analysis. In this way backdoor paths can be removed from the DAG.

Question 19

confounding bias

Answer 19

Bias caused by a common cause of the exposure and the outcome → open backdoor path.

Question 20

confounder

Answer 20

The variable that can be used to remove the confounding

Question 21

collider

Answer 21

A collider is a situation where 2 arrows collide → a collider blocks a path. A collider is always a backdoor path → the path does not contribute to the association of exposure and outcome. Adjusting for a collider opens the path and should therefore not be done.

Question 22

collider bias

Answer 22

occurs when you control for a variable on a path between x and y where arrows collide