Notation
Pr[A=1|L]=π(L)
What is a propensity score?
The conditional probability of being exposed (treated)
What is a propensity score?
Measurement error is _______ if UA and UY are independent A of and Y.
What is non-differential measurement error?
weights for each individual calculated as the inverse of the probability of receiving his/her actual exposure level
What is inverse probability weighting?
the values of treatment under comparison correspond to well-defined interventions that, in turn, correspond to the versions of treatment in the data
What is consistency?
A⊥⊥L|b(L)
What is a balancing score?
Matching
What is 'Manually' creating a (matched) population in which the treated and the untreated are exchangeable because they have the same distribution of π(L)?
Measurement error is _______ if UA (or UY) are not independent of Y (or A).
What is differential measurement error?
fit a regression model to the pseudo-population created through IP weighting
What is marginal structural modeling?
the conditional probability of receiving every value of treatment, though not decided by the investigators, depends only on measured covariates
What is exchangeability?
(pr[A=a])/(pr[A=a|L=l])
What is stabilized weights?
estimand for traditional inverse probability weighting
What is the average treatment effect?
Measurement error is ___________if UA is independent of UY
What is independent measurement error?
Goal of IPW
What is creating a pseudo-population in which there is no association between the covariates L and treatment A
the probability of receiving every value of treatment conditional on is greater than zero
What is positivity?
1/(pr[A=a|L=l])
What is unstabilized weighting?
trimming
What is excluding patients with PS outside of a certain range, either symmetrically (certain distance) or asymmetrically (the common PS range formed by the treated and control patients among all units, further exclude those whose PS is below some quantile of the treated units among all units, exclude those whose PS is above a certain quantile of the control units)?
Measurement error might be ___________ if A and Y are collected in the same survey, or due to response effects.
What is dependent measurement error?
structural and random positivity violations
What are:
structural: occur when it is impossible for people with some levels of confounders to receive a particular level of treatment.
random: when certain combinations of and are missing from our data by chance
truncation
What is change the PS for patients whose estimated PS is below α, and whose estimated PS is above 1−α?
threats to internal validity
What are:
exchangeability/confounding
selection bias (collider-stratification bias)
information bias (misclassification/measurement error; differential/non-differential)
two sources of lack of exchangeability
What are confounders that haven't been conditioned on and colliders that have been conditioned on?