Abstract:
|
Propensity scores are commonly used in "balancing" observational data to more closely resemble the design of a randomized study. Work in Bayesian propensity score analysis has thus far concentrated on marginalizing over the uncertainty in estimating propensity scores by implementing a Bayesian propensity score estimation step which can be used in conjunction to Bayesian or Frequentist analysis methods. However, propagating this uncertainty into estimation of treatment effects is not straightforward. The purpose of this paper is twofold. One, to introduce a theoretical framework for "design uncertainty" which encompasses uncertainty from statistical steps taken using treatment and covariate information only, in contrast to "analysis" steps which use outcome information. Uncertainty from propensity score estimation is just one example of design uncertainty. Second, this paper will compare various methods to marginalize over design uncertainty in two-step Bayesian propensity score analysis, the results of which will be proven empirically through simulation.
|