Applicability of Rubin’s rules to g-method estimators

Determine the applicability of Rubin’s rules for variance estimation when used with g-method estimators (including g-computation) in causal mediation analysis estimating interventional indirect and direct effects, given that g-methods are not maximum likelihood estimators. Specifically, ascertain whether Rubin’s rules yield valid standard errors and confidence intervals in this non-maximum likelihood context and delineate any necessary conditions for their validity.

Background

In the paper, multiple imputation is employed to handle multivariable missing data in estimating interventional mediation effects via g-computation, a g-method. Rubin’s rules are commonly used to pool estimates and derive standard errors across multiply imputed datasets, but their validity generally relies on compatibility between the imputation and analysis models and on maximum likelihood estimation.

The authors note that g-methods, including g-computation, are not maximum likelihood estimators, which raises uncertainty about the appropriateness of Rubin’s rules for variance estimation in this setting. They therefore compare alternative approaches (BootMI versus MIBoot) but also explicitly state that the general applicability of Rubin’s rules to g-methods remains unclear.