Deep Learning Methods for the Noniterative Conditional Expectation G-Formula for Causal Inference from Complex Observational Data

Abstract: The g-formula can be used to estimate causal effects of sustained treatment strategies using observational data under the identifying assumptions of consistency, positivity, and exchangeability. The non-iterative conditional expectation (NICE) estimator of the g-formula also requires correct estimation of the conditional distribution of the time-varying treatment, confounders, and outcome. Parametric models, which have been traditionally used for this purpose, are subject to model misspecification, which may result in biased causal estimates. Here, we propose a unified deep learning framework for the NICE g-formula estimator that uses multitask recurrent neural networks for estimation of the joint conditional distributions. Using simulated data, we evaluated our model's bias and compared it with that of the parametric g-formula estimator. We found lower bias in the estimates of the causal effect of sustained treatment strategies on a survival outcome when using the deep learning estimator compared with the parametric NICE estimator in settings with simple and complex temporal dependencies between covariates. These findings suggest that our Deep Learning g-formula estimator may be less sensitive to model misspecification than the classical parametric NICE estimator when estimating the causal effect of sustained treatment strategies from complex observational data.