st: Treatment by propensity score interaction

[Perry Wilson <fpwilson3@gmail.com>]

Hi Statalisters,

I have an intuition about a propensity score model and I'm wondering if I'm
out in left field or if there is some literature to support this.

-I have a treatment X and an outcome of interest Y.
-I estimate the probability of receiving treatment X via a logistic
regression model.
-I can then match on that probability for patients who are treated (X1) and
not treated (X0) and assess the effect of X on Y.

One question that always arises is unmeasured confounding - are matched
treated / untreated patients similar on non-measured characteristics.
-If there is some large unmeasured confounder, I would suspect it to be
present preferentially at the lower range of propensity score (why, after
all are these treated patients getting treated if their probability of
treatment is so low?).

Here's where I get a little bit more abstract...
-Therefore, if one detects a strong treatment-by-propensity score
interaction on Y, it suggests the presence of such a confounder
-Conversely, if the treatment-by-propensity interaction is not significant,
that would suggest minimal unmeasured confounding?

Does this make sense?  Any literature to back up such a statement?

Thanks!
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/