Wensui Liu wrote:
Dear All,
My question is more a statistical question than a R question. The reason I
am posting here is that there are lots of excellent statistician on this
list, who can always give me good advices.
Per my understanding, the purpose of propensity score is to reduce the bias
while estimating the treatment effect and its implementation is a 2-stage
model.
1) First of all, if we assume that T = 1 if an individual belongs to
treatment group and T = 0 otherwise. We further assume that X is a covariate
matrix to explain the assignment of treatment. Then the propensity score
should be the probability of treatment exposure T = 1 and can be formulated
as
PPscore = Prob(T=1|X) = exp(A * X) / [1 + exp(A * X)] in the range between 0
and 1.
2) At the second stage, let Y = 1 / 0 is a binary outcome variable and Z the
covariate matrix to explain outcome. In order to balance the probability of
an individual assigned to the treatment group such that Prob(Y = 1) _|_
Prob(T = 1|X), we should model the outcome as
Prob(Y = 1|Z) = exp(B * Z) / [1 + exp(B * Z)] weighting or matching by
Prob(T=1|X)
The above is just my general understanding about propensity score. However,
I was critisized that my understanding is wrong and was also told that the
response variable should be Y instead of T in the propensity model at the
1st stage. I am very confused and like to have the opinion of experts like
you guys.
Wensui,
If the response were Y then this would not be a propensity model.
Whoever told you that is off the mark.
Think of the propensity score as a data reduction method that allows you
to model all known baseline variables against the treatment assignment
in order to remove confounding bias in all of them. Then the outcome
model can have the logit of propensity (plus nonlinear transformations
of it) as a covariate to account for confounding. The outcome model
also needs to have strong predictor variables in it to account for
outcome heterogeneity not related to confounding. You can also using
matching as you mentioned but I prefer to adjust for propensity by
covariate adjustment once I check the overlap of propensity in the two
groups.
Frank
Any insight will be appreciated.
Have a nice weekend!
wensui
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