Propensity Score Analysis With Fallible Covariates

Abstract

A latent variable modeling approach that permits estimation of propensity scores in observational studies containing fallible independent variables is outlined, with subsequent 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 differences. 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 modified score can be recommended to use for average treatment effect evaluation in circumstances where selection into groups occurs on corresponding underlying latent dimensions measured with error. The proposed propensity score procedure is illustrated with an example.