# [R] [OT] propensity score implementation

From: Wensui Liu <liuwensui_at_gmail.com>
Date: Sat, 08 Nov 2008 19:15:02 -0500

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.

Any insight will be appreciated.

Have a nice weekend!

wensui

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