PROPENSITY SCORE

Question 1

What does a propensity score represent?

Answer 1

The predicted probability of exposure in a particular individual based on a set of relevant characteristics (because confounders increase the propensity of being exposed)

Question 2

What is the role of the propensity score?

Answer 2

Estimates treatment effects by controlling for confounding in observational cohort studies

Question 3

What’s the best distribution of exposure/outcome for a propensity score?

Answer 3

Common exposure, rare outcome

Question 4

Which variables should we
a) include
b) not include
in a logistic regression to estimate the propensity score?

Answer 4

a) All variables related to the outcome, whether or not they are related to the exposure
b) UNLESS they are a consequence of the exposure (collider); also exclude variables unrelated to the outcome

Question 5

What is the impact of including variables that are unrelated to the exposure despite being related to the outcome?

Answer 5

None, it’s fine.

It decreases the variance without increasing the bias.

Question 6

What is the impact of including variables that are unrelated to the outcome despite being related to the exposure?

Answer 6

It increases the variance without decreasing the bias.

Question 7

What are the main 2 steps of creating/using propensity scores?

Answer 7

1. Model the exposure variable in a regression as a function of potential confounders. This calculates the predicted probability of exposure for every individual as a function of these covariates.
2. Apply the propensity score by matching, stratifying, controlling or weighting.

Question 8

For a given propensity score, what is the chance of control/experimental arm the same as?

Answer 8

The choice of control or experimental arm is the same as a random process, given that the patient had a real choice

Question 9

What is the C statistic?

Answer 9

• Means: concordance
• A measure of model discrimination, but cannot judge adequacy
• Estimates the probability that a patient randomly selected from the treatment arm has a higher propensity score than a patient randomly selected from control arm (should be high)

Question 10

What should the area under a ROC curve be for a propensity score?

Answer 10

0.5 (random)

Question 11

Summary of propensity score matching?

Answer 11

• Finding individuals with similar propensity score in both arms and matching them (e.g., 1:1 nearest-neighbor-matching, with a match of 0.1 distance)
• Calculate treatment effect with matched pair analysis
• Equivalent to simulated randomization (distributes confounding evenly)

Question 12

Summary of propensity score adjusting?

Answer 12

• Including the propensity score as a covariate in a regression model (ideally, with the individual covariates, leading to a doubly robust model)

Question 13

Summary of propensity score stratifying?

Answer 13

• Splitting the dataset on the basing of the propensity score alone, and then estimating the treatment effect in each stratum and taking the weighted average for overall effect

Question 14

Summary of inverse probability weighting?

Answer 14

• Re-weighting individuals from the whole dataset to increase the weight of those with unexpected exposure
• Equivalent to producing additional observations for where there is few observations
• Creates a pseudopopulation with near-perfect covariate balance

Question 15

Weight given to treatment and control arm in inverse probability weighting? Any problem with that?

Answer 15

Tx: 1/PS
Control: 1/(1-PS)

Problem: when the PS is close to 0 for the tx arm, and close to 1 for control arm

Question 16

Which methods eliminate systematic differences the best?

Answer 16

• Matching

- IPW

Question 17

What is a potential problem with propensity score adjustment?

Answer 17

• May bias if the assumption about the functional relationship between the propensity score and the outcome is wrong (e.g., linearity)

Question 18

Which methods are potentially doubly robust? Which are not?

Answer 18

Yes: Propensity score adjustment (if adding also individual covariates), IPW (how?)
No: Matching, stratifying (N is too small)

Question 19

What are the pros and cons of traditional covariate adjustment?

Answer 19

Pros: performs well, provides prognostic model for outcome of interest
Cons: not good for small n and many covariates

Question 20

What are the pros and cons of propensity score matching?

Answer 20

Pros: reliable, good balance of covariates, simple
Cons: unmatched subjects are not analysed, less precise due to small n

Question 21

What are the pros and cons of propensity score adjustment?

Answer 21

Pros: performs well
Cons: very similar to traditional adjustment, without necessarily being better

Question 22

What are the pros and cons of propensity score stratifying?

Answer 22

Pros: keeps all the data, can look at interactions
Cons: not as good with few outcome events, does not account for strong confounding

Question 23

What are the pros and cons of inverse probability weighting?

Answer 23

Pros: keeps all the data, easy, the pseudopopulation has a perfect covariate balance
Cons: Unstable when extreme weights

Question 24

What are the limitations to propensity score methods in general?

Answer 24

• Only binary treatment/exposures
• No balancing of unmeasured covariates
• Can’t get the effect of the covariates that are adjusted for
• Not for prediction
• Cannot handle time-varying exposures or confounder

Question 25

4 sources of residual confounding

Answer 25

1. Bad definition
2. Imperfect proxy
3. Not included
4. Misclassified

Question 26

What is an instrumental variable?

Answer 26

One that is:

1) Causes the exposure
2) Affects the outcome only through the exposure (=’exclusion criteria’)
3) Not associated with any confounders (=’independence criteria’)

Question 27

Looking at instrumental variable is equivalent to…

Answer 27

Intent to treat estimate in RCTs

Question 28

What are endogenous regressors? Exogenous regressors? And what are instrumental variables?

Answer 28

Endogenous are correlated with the exposure, while exogenous are not (often proxy, for example extreme weather for stress during pregnancy)

Instrumental variables are exogenous

Question 29

An instrumental variable analysis trades…

Answer 29

The ignorability of the treatment variable
for
the ignorability of the instrument (that we think is more plausible)

Question 30

What if the instrumental variable is weak?

Answer 30

It’s biased toward the null due to non-differential misclassification

Question 31

What are the two stages to calculate IV estimates?

Answer 31

1 . Each endogenous explanatory variable is regressed on all exogenous variables in the model (both in the equation of interest and the excluded instruments). We take the predicted values of these regressions.

2. We estimate the regression of interest, but we replace each endogenous covariate with the predicted value from the first stage.