Simulation-based estimators of analytically intractable causal effects

In causal inference problems, one is often tasked with estimating causal effects which are analytically intractable functionals of the data-generating mechanism. Relevant settings include estimating intention-to-treat effects in longitudinal problems with missing data or computing direct and indirect effects in mediation analysis. One approach to computing these effects is to use the g-formula implemented via Monte Carlo integration; when simulation-based methods such as the nonparametric bootstrap or Markov chain Monte Carlo are used for inference, Monte Carlo integration must be nested within an already computationally intensive algorithm. We develop a widely-applicable approach to accelerating this Monte Carlo integration step which greatly reduces the computational burden of existing g-computation algorithms. We refer to our method as accelerated g-computation (AGC). The algorithms we present are similar in spirit to multiple imputation, but require removing within-imputation variance from the standard error rather than adding it. We illustrate the use of AGC on a mediation analysis problem using a beta regression model and in a longitudinal clinical trial subject to nonignorable missingness using a Bayesian additive regression trees model.