Propensity Score Analysis With Fallible Covariates: A Note on a Latent Variable Modeling Approach

A latent variable modeling approach that permits estimation of propensity scores in observational studies containing fallible independent variables is outlined, with subse-quent examination of treatment effect. When at least one covariate is measured with error, it is indicated that the conventional propensity score need not possess the desirable property of bias adjustment with respect to possible prior group differ-ences. For this setting, a modified propensity score is discussed that is based on true scores on fallible covariates and perfectly measured covariates, if available. This mod-ified score can be recommended to use for average treatment effect evaluation in cir-cumstances where selection into groups occurs on corresponding underlying latent dimensions measured with error. The proposed propensity score procedure is illu-strated with an example. Keywords latent variable modeling, measurement error, observational study, propensity score, treatment effect Observational studies are frequently conducted in the behavioral, educational, social, and biomedical sciences. This is often the case when evaluation of the effect of a cer-tain treatment, therapy, prevention, program, or intervention is of concern. A main reason for the popularity of these studies is the fact that in these disciplines it is fre-quently rather difficult if at all possible to assign randomly studied subjects t