Fellow Allstatters:
A query about the method of propensity scores, introduced by Rosenbaum and
Rubin (1983) and used increasingly in the last few years as a method to
measure exposure effects on an outcome, adjusted for large confounder sets.
(Two recent review articles on the method are Rubin (1997) and Joffe and
Rosenbaum (1999).) So far, they have been used mainly for binary exposures
(and computed using logistic regression), and sometimes for ordinal
categorical exposures (and computed using ordinal logistic regression - see
Lu et al. (2001) for an example). Does anybody out there know a reason why
they should not be used with continuous exposures? In the
continuous-exposure case, the propensity score would presumably be
calculated by fitting a linear regression model, with the continuous
exposure as the Y-variable and the confounders as the X-variables, and
defining the propensity score to be the fitted value of the continuous
exposure arising from this linear regression model. Once the propensity
score has been calculated in this way, we could then proceed in the usual
way, defining equal-sized propensity categories (in the case of a cohort
study) or propensity-matched pairs (in the case of a nested matched-pairs
study). By my reckoning, the mathematical arguments justifying propensity
scores for binary exposures can be generalised fairly readily to justify
propensity scores for continuous exposures, and are subject to the same
cautions. However, my literature searches so far have failed to uncover any
examples of propensity scores for continuous exposures, although they seem
to be well-established for binary exposures. Does anybody out there know of
any objections to using them for continuous exposures? And does anybody
know of examples where they have been used for continuous exposures?
Best wishes (and thanks in advance)
Roger Newson
References
Joffe MM, Rosenbaum PR. Propensity scores. American Journal of Epidemiology
1999; 150(4): 327-333.
Lu B, Zanutto E, Hornik R, Rosenbaum PR. Matching with doses in an
observational study of a media campaign against drug abuse. Journal of the
American Statistical Association 2001; 96(456): 1245-1253.
Rosenbaum PR, Rubin DB. The central role of the propensity score in
observational studies for causal effects. Biometrika 1983; 70(1): 41-55.
Rubin DB. Estimating causal effects from large data sets using propensity
scores. Annals of Internal Medicine 1997; 127: 757-763.
--
Roger Newson
Lecturer in Medical Statistics
Department of Public Health Sciences
King's College London
5th Floor, Capital House
42 Weston Street
London SE1 3QD
United Kingdom
Tel: 020 7848 6648 International +44 20 7848 6648
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Opinions expressed are those of the author, not the institution.
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