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Re: st: multiple imputation and propensity score


From   Austin Nichols <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: multiple imputation and propensity score
Date   Thu, 25 Aug 2011 10:26:41 -0400

Stefano Di Bartolomeo:
I agree with Stas, except that I would say you can get good standard
errors by reweighting instead of matching, but you might be better off
bounding the effect per Rosenbaum, rather than using MI at all:
http://www.amazon.com/Observational-Studies-Springer-Statistics-Rosenbaum/dp/0387989676

On Wed, Aug 24, 2011 at 1:48 PM, Stas Kolenikov <skolenik@gmail.com> wrote:
> On Wed, Aug 24, 2011 at 11:39 AM, Stefano Di Bartolomeo
>> In truth I am trying to be humble and apply the best methodology I can. I got tricked into this problem in 2 simple steps. First I read  'A Guide to Imputing Missing Data with Stata by Mark Lunt', which is a step by step guide for non-pundits like me. Throughout the guide a propensity score is the main goal of the examples. So I got the feeling that multiple imputation is good for propensity score and did that. Then, I reviewed the recent literature on propensity scores and it seems that matching is the technique that most reduces bias as compared to stratification on quintiles  or inclusion of PS as covariate. And again, tried to follow the suggestion. Now I understand I have to give up one of the two techniques.
>
> I believe you could still see through your approach with both MI and
> PS. For that, you would need:
>
> 1. create multiple imputations using -ice- or the official -mi-.
> 2. write your own estimation program (say you named it -mi_ps_st-) that would
> 2a. run logistic regression as a matter of propensity score modeling
> 2b. generate propensity scores
> 2c. run your survival model
> 2d. Ideally, you'd want to correct the standard errors in the survival
> model for the fact that you have created some of the regressors. It is
> possible to do that in the linear regression context (see Hardin
> (2002, http://stata-journal.com/article.html?article=st0018), but I
> don't know if this approach is generalizable to -streg-.
> 3. run your -mi_ps_st- prefixed by -mim- (or, respectively, -mi
> estimate-) to combine the estimates and standard errors. Remember that
> MI only makes sense when you have the final parameter estimates and
> their standard errors. The intermediate results, like specific
> imputations, or observation-level averages across them, as you thought
> initially for your propensity scores, may not be very meaningful.
>
> The guide you referred to is dated, in the sense that Stata 12
> incorporates MICE methodology in the official -mi-. The guide would
> still be applicable to Stata 11. I also did not like it relying on the
> author's written programs, although that is sometimes inevitable (I
> tend to trust the stuff that underwent some minimal checks at SJ or
> SSC a little bit better).
>
> BTW, I don't think it is at all possible to get the right standard
> errors from matching, so you would probably have to let that
> methodology go, anyway. So you would have to look into other options
> with your survival model.

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