LETTER TO THE EDITOR
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Published online 25 October 2006 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/sim.2722
LETTER TO THE EDITOR
Conditioning on the propensity score can result in biased
estimation of common measures of treatment effect:
A Monte Carlo study (p n/a)
by Peter C. Austin, Paul Grootendorst, Sharon-Lise T. Normand, Geoffrey M. Anderson,
Statistics in Medicine, Published Online: 16 June 2006, DOI: 10.1002/sim.2618
From:Edwin P. Martens1,2, Wiebe R Pestman2and Olaf H. Klungel1
1Department of Pharmacoepidemiology and Pharmacotherapy, Utrecht University,
Utrecht, The Netherlands
2Centre for Biostatistics, Utrecht University, Utrecht, The Netherlands
In a recent simulation study Austin et al. conclude that conditioning on the propensity score gives
biased estimates of the true conditional odds ratio of treatment effect in logistic regression analysis.
Although we generally agree with this conclusion, it can be easily misinterpreted because of the
word bias. From the same study one can similarly conclude that logistic regression analysis will
give a biased estimate of the treatment effect that is estimated in a propensity score analysis.
Because propensity score methods aim at estimating a marginal treatment effect, we believe that
the last statement is more meaningful.
DIFFERENT TREATMENT EFFECTS
The authors raise an important issue, which is probably unknown to many researchers, that in
logistic regression analysis a summary measure of conditional treatment effects will in general not
be equal to the marginal treatment effect. This phenomenon is also known as non-collapsibility of
the odds ratio , but is apparent in all non-linear regression models and generalized linear models
with a link function other than the identity link (linear models) or log-link function . In other
words, even if a prognostic factor is equally spread over treatment groups, the inclusion of this
variable in a logistic regression model will increase the estimated treatment effect. This increasing
effect of a conditional treatment effect compared to the overall marginal effect is larger when more
Copyright q 2006 John Wiley & Sons, Ltd.
Statist. Med. 2007; 26:3205–3212