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re: st: RE: Multilevel modeling


From   "Ariel Linden" <ariel.linden@gmail.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   re: st: RE: Multilevel modeling
Date   Mon, 2 Dec 2013 10:32:13 -0500

I will add to Tim's excellent discussion, by suggesting that Christina read
the following article that describes the use of propensity score weighting
for longitudinal data (using the GEE model). 

Hernán, M. A., Brumback, B. & Robins, J. M. (2002) Estimating the causal
effect of zidovudine on CD4 count with a marginal structural model for
repeated measures. Statistics in Medicine, 21, 1689?1709. 

Date: Mon, 2 Dec 2013 14:33:18 +0800
From: Timothy Mak <tshmak@hku.hk>
Subject: st: RE: Multilevel modeling

The purpose of propensity-score weighting is to estimate what are called
"Average causal effects", that is, these are effects defined as in: 

\sum_i CE_i / N

where CE is the causal effect of subject i, and are assumed to be different
for different individuals. 

Note that there are no "random effects" in the definition. 

In "random effects"/multilevel model, we are (strictly speaking) assuming
that given the random effects, the individual effects are all the same. This
is very different from the assumptions in the average causal effects model. 

If subjects are recruited in clusters, or if the independence assumption is
being violated for whatever reason, then in the average causal effects
model, we should account for the lack of independence across observations
using Generalized Estimating Equations - These allow you to specify a
correlation matrix which represent the correlation in effect estimates
between individuals. This framework also naturally accounts for
over/under-sampling in subpopulation. 

On another note, although PS-weighting can give consistent estimates of the
average causal effects (provided your propensity scores are estimated
consistently), the estimates are generally not efficient, and in certain
cases, can lead to really big error. Thus, matching/stratification based on
PS are generally preferred approaches. 

HTH, 
Tim

- -----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Christina Wei
Sent: 30 November 2013 04:03
To: statalist@hsphsun2.harvard.edu
Subject: st: Multilevel modeling

Hi everyone!  Happy Holidays :)
I have a question about multilevel modeling.  I'm new to this type of
analysis, and am planning on doing the analysis in Stata 12.

The question is:  Is it possible to do a "propensity-score weighted"
multilevel modeling?  I searched the literature and have found none.

I plan to derive my propensity scores from a logistic regression model
regressing baseline group membership on the baseline values of some
selected covariates.  I have a panel/longitudinal data with 5 follow
up visits, but I plan to just use baseline data to derive a "baseline
cross-sectional" propensity score.  I plan to use the propensity
scores to weight-adjust my final multi-level model.  Theoretically,
the probability of being assigned to a specific treatment group is
only "valid" at baseline (e.g. prior to initiation of treatment).

I greatly appreciate any help I could get on this.

~Christina



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