> From: "Lucke, Joseph F" <LUCKE@uthscsa.edu>
> Suna
> By using the "kitchen sink" approach to estimate the propensity score,
> aren't you increasing the underlying error in estimate? That is, the more
> variables in the propensity prediction equation, the more error there is in
> the propensity estimate itself.
> Joe
Actually, no. Even "statistically insignificant" variables can improve
the match. The accuracy of the estimate of the population propensity
score (what you would have gotten had the study been continued
indefinitely so you had a much larger dataset) might go down with more
variables. However, the matching in the sample at hand still gets
better. For example if the treated group sample has 4 men and 6 women
and the control group sample has 5 men and 5 women, sex is not a
significant predictor of group membership, but controlling for sex still
gives a better match of group characteristics. This is like doing a
covariance adjustment in a randomized trial; even if you know that the
differences between the groups are (by design) random, you can still
reduce the variance of the estimator by modeling out some of the random
differences.
The place where this breaks down is when you have so well separated the
treatment and control groups that you can no longer find matches ...
everybody is in the tails of the propensity score distribution. This is
related to the problem that Frank H. mentioned. Howver, adding a few
nonsignificant predictors will not necessarily cause this to happen.
See discussion of this issue in the following article (specifically at
page 253).
Rubin, Donald B. and Thomas, Neal
Matching using estimated propensity scores: Relating theory to
practice (1996)
Biometrics, 52, 249-264
Alan Zaslavsky
Harvard Med School
zaslavsk@hcp.med.harvard.edu
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