Re: st: Treatment by propensity score interaction

[Adam Olszewski <adam.olszewski@gmail.com>]

Hi Perry,
This is a very interesting question and is currently a subject of
research. It has a lot to do with the "subset analyses" and
"heterogeneity of treatment effect" issue that comes up in the
randomized trials. It may indeed uncover unobserved confounding,
although not necessarily - it might just indicate heterogeneous
treatment effect (i.e. patients at high-end of propensity score may
just benefit from the treatment more).
Here are two interesting articles that have dealt with this problem:

Lunt M, Solomon D, Rothman K, et al. Different methods of balancing
covariates leading to different effect estimates in the presence of
effect modification. Am J Epidemiol. 2009;169(7):909-917.
(they propose the interaction test as a sensitivity analysis)

Kurth T, Walker AM, Glynn RJ, et al. Results of multivariable logistic
regression, propensity matching, propensity adjustment, and
propensity-based weighting under conditions of nonuniform effect. Am J
Epidemiol. 2006;163(3):262-270.
(an extreme example of a failed propensity score analysis in a setting
of poor overlap and highly heterogeneous effect)

I hope it's a start of an interesting reading direction. Of course
there is also a wealth of literature on the interaction testing for
treatment heterogeneity in the randomized trials.

Adam Olszewski

On Mon, Apr 8, 2013 at 9:33 AM, Perry Wilson <fpwilson3@gmail.com> wrote:
> 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!
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