Bayesian propensity score analysis for clustered observational studies.

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There is increasing demand to investigate questions in observational study. The propensity score is a popular confounding adjustment technique to ensure valid causal inference for observational study. Observational data often has multilevel structure that would lead to one or more levels of confounding. Multilevel models are employed in Bayesian propensity score analysis to account for cluster and individual level confounding in the estimation of both propensity score an in turn exposure effect. In an extensive simulation study, several propensity score nalaysis approches with varing complexity of multilevel modelling structures are examined in terms of absolute mean bias and mean squared error. The Bayesian propensity score analysis for multilevel data is further developed to accomodate misclassified binary responses. Errors in response would distort the exposure to response relationship. The true exposure-response surface can be recovered through two classification probabilities: sensitivity and specificity that links observed misclassified response and unobserved true response. Incorpating misclassification greatly reduces bias in exposure effect estimation and yields coverage rate of 95% creditable set close to nomial level. The strong ignorability is the fundamental assumption for propensity score. Few literature discuss this important but untestable assumption. Without the confidence that there are no unmeasured confounders, we assmue the existence of unmeasured confounding and assess the sensitivity of exposure effect estimation to unmeasured confounding through two sensitivity parameters which characterize the associations of the unmeasured confounder with the exposure status and response variable. The influence of unmeasured confounding can be examined by possible change in exposure effect estimation with hypothetical values of sensitivity parameters.

Propensity score. Bayesian statistics. Multilevel models. Classifications.Unmeasured confounding.