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.