A cautionary note on the inclusion of strong predictors of the exposure in propensity score analysis
Cousens et al. recently reviewed the utility and limitations of several methods for addressing confounding in non-randomized evaluations of public health interventions. Propensity score analysis was one of the analytic methods discussed in the review. The authors noted several limitations of propensity score analysis including potentially decreased power if multiple predictors of the exposure that lack a causal effect on the outcome are included in the estimation of propensity scores. Such predictors have the same structure as instrumental variables because they are related to the exposure and unrelated to the outcome (except through the exposure). We would like to raise awareness that the inclusion of such predictors in estimating propensity scores not only affects power but may also induce or amplify bias, an issue that is currently under- recognized in the health science literature.
Bias induction because of conditioning on (most often performed by statistical adjustment in regression models) colliders, intermediates, or descendants of intermediates is well-recognized. Several recent reports[2-4] also indicate that unwittingly conditioning on instrumental variables may be detrimental to valid effect estimation. Specifically, conditioning on instrumental variables in linear models invariably amplify an existing bias, whereas in non-linear models, conditioning on instrumental variables may amplify or attenuate an existing bias or induce a bias where none existed. This phenomenon also applies to a covariate that is a strong predictor of the exposure but weakly related to the outcome. The theoretical basis and simulation studies of this phenomenon have been extensively discussed by Pearl, Wooldridge, and Bhattacharya and Vogt. Ultimately, being a predictor of the exposure is an insufficient criterion for including the covariate for adjustment in a model.
The practical implication of this discovery is that analysts should consider both the exposure and outcome mechanisms in selecting covariates for propensity score analysis. Directed acyclic graphs offer a tool by which to encode assumptions regarding the structure of these mechanisms, identify covariates for adjustment through application of the back-door criterion, and facilitate the identification of problematic covariates. Furthermore, directed acyclic graphs may be used to encourage transparency regarding the assumptions that guide confounder selection as recommended by Cousens et al. and to decide whether baseline adjustment in analyses of change is even warranted, an issue that Cousens et al. did not elucidate.
1. Cousens S, Hargreaves J, Bonell C, Armstrong B, Thomas J, Kirkwood BR, Hayes R. Alternatives to randomisation in the evaluation of public- health interventions: statistical analysis and causal inference. J Epidemiol Community Health. 2010 Jul 13. [Epub ahead of print]
2. Pearl J. On a class of bias-amplifying variables that endanger effect estimates. In: Grunwald P, Spirtes P, eds. Proceedings of Uncertainty in Artificial Intelligence. Corvallis, OR: Association for Uncertainty in Artificial Intelligence; 2010: 417-424. Available at: http://ftp.cs.ucla.edu/pub/stat_ser/r356.pdf
3. Wooldridge JM. Should instrumental variables be used as matching variables? Technical Report. Michigan State University: July 2009. Available at: https://www.msu.edu/~ec/faculty/wooldridge/current%20research/treat1r6.pdf. Accessed August 2010.
4. Bhattacharya J, Vogt W. Do instrumental variables belong in propensity scores? National Bureau of Economics Technical Working Paper 343, National Bureau of Economic Research: 2007. Available at: http://ideas.repec.org/p/nbr/nberte/0343.html. Accessed August 2010.
5. Glymour MM, Weuve J, Berkman LF, Kawachi I, Robins JM. When is baseline adjustment useful in analyses of change? An example with education and cognitive change. Am J Epidemiol. 2005 Aug 1;162(3):267-78.
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