Propensity score methods are widely used to analyze observational studies in which patient characteristics might not be balanced by treatment group. These methods assume that exposure, or treatment assignment, is error-free, but in reality these variables can be subject to measurement error. This arises in the context of comparative effectiveness research, using observational administrative claims data in which accurate procedural codes are not always available. When using propensity score based methods, this error affects both the exposure variable directly, as well as the propensity score. We propose a two step maximum likelihood approach using validation data to adjust for the measurement error. First, we use a likelihood approach to estimate an adjusted propensity score. Using the adjusted propensity score, we then use a likelihood approach on the outcome model to adjust for measurement error in the exposure variable directly. In addition, we show the bias introduced when using error-prone treatment in the inverse probability weighting (IPW) estimator and propose an approach to eliminate this bias. Simulations show our proposed approaches reduce the bias and mean squared error (MSE) of the treatment effect estimator compared to using the error-prone treatment assignment.
Braun, Danielle; Gorfine, Malka; Zigler, Corwin; Dominici, Francesca; and Parmigiani, Giovanni, "Adjustment for Mismeasured Exposure using Validation Data and Propensity Scores" (January 2014). Harvard University Biostatistics Working Paper Series. Working Paper 172.