Evaluating model specification when using the parametric g-formula in the presence of censoring.

The noniterative conditional expectation (NICE) parametric g-formula can be used to estimate the causal effect of sustained treatment strategies. In addition to identifiability conditions, the validity of the NICE parametric g-formula generally requires the correct specification of models for time-varying outcomes, treatments, and confounders at each follow-up time. An informal approach for evaluating model specification is to compare the observed distributions of the outcome, treatments, and confounders with their parametric g-formula estimates under the "natural course." In the presence of losses to follow-up, however, the observed and natural course risks can differ even if the identifiability conditions of the parametric g-formula hold and there is no model misspecification. Here, we describe two approaches to evaluate model specification when using the parametric g-formula in the presence of censoring: (1) comparing factual risks estimated by the g-formula with nonparametric Kaplan-Meier estimates, and (2) comparing natural course risks estimated by inverse probability weighting with those estimated by the g-formula. We also describe how to correctly compute natural course estimates of time-varying covariate means when using a computationally efficient g-formula algorithm. We evaluate the proposed methods via simulation and implement them to estimate the effects of dietary interventions in two cohort studies.