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In theory what would the $e_i$ (propensity scores) be, for $n_i$ observations already randomized into various treatment groups ?

I know $e_i$ (propensity scores) are calculated for $n_i$ observations in observation studies and RCT studies are assumed to be already randomized.

However I like to know what would be the hypothetical $e_i$ (propensity scores) values for observations in studies that already randomize patients into various treatment groups ? Could the propensity score values for everybody in an already randomized study would be 1 ?

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"Propensity may be defined as an individual's probability of being treated with the intervention of interest given the complete set of all information about that individual."

According to this definition, the propensity is the probability that patient being randomized to the treatment patient received, and generally it is 1/k, where k is # of treatment arms in that RCT.

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  • $\begingroup$ Thanks 158565, so what I understand is that the propensity score in theory for all the individuals in already randomized RCT study is 1/k. In theory. Is that correct ? $\endgroup$ – Science11 Dec 5 '18 at 2:57
  • $\begingroup$ Not "in theory", it is in practice. $\endgroup$ – user158565 Dec 5 '18 at 2:58
  • $\begingroup$ Excellent, can you please provide a citation for this 158565 ? Thanks. $\endgroup$ – Science11 Dec 5 '18 at 3:16
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    $\begingroup$ Maybe not exact, but the meaning comes from Rosenbaum PR, Rubin DB. The central role of the propensity score in observational studies for causal effects. Biometrika. 1983;70:41–55. $\endgroup$ – user158565 Dec 5 '18 at 3:23
  • $\begingroup$ Thanks 158565, I will go through that article. $\endgroup$ – Science11 Dec 5 '18 at 3:25

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