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Abstract:
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Structural mean models are popular causal models which parameterize the contrast between the means of counterfactual outcomes as a function of exposure. Such models admit continuous, count, or binary outcomes via the identity, log, and logit link functions, respectively. Estimation of the parameters is straightforward when using the identity or log link functions, but requires additional care with the logit link. Literature on the Bayesian estimation of these parameters exists but is sparse. We present two new semi-parametric Bayesian implementations of structural mean models with continuous and binary outcomes, using Gaussian Processes (GP) and Bayesian additive regression trees (BART). We obtain posterior distributions of the parameters of interest across a number of simulations and compare the GP estimates to the BART estimates as well as to more commonly employed estimation procedures. Our methods may be an attractive alternative to the current literature. We also discuss some limitations of our methods (such as speed of the processes) and provide possible solutions.
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