Background: Orthogonalized regression is a simple and efficient alternative to g-methods for causal inference with time-varying treatments and confounders that avoids the g-null paradox. Orthogonalized regression consists of fitting a sequence of regression models, where the model for the first time point is fit and the residuals from this model are used as a predictor for the second time point, repeating this process for all time points.
Objectives: To compare the relative statistical efficiency of orthogonalized regression with the parametric g-formula and marginal structural models.
Methods: We compare these estimators (parametric g-formula, marginal structural models, and orthogonalized regression) across six scenarios--two different outcome types (binary and continuous) and varying number of follow-up times (1, 5, or 10). In each scenario, the true treatment effect is 0. For each scenario, we simulated 500 longitudinal datasets with 10000 participants. For each scenario and estimation method, the bias, standard error, and the confidence interval coverage probability was evaluated.
Results: Across all six simulation scenarios, the parametric g-formula demonstrated moderate bias due to the g-null paradox with the maximum bias of -12.7 occurring in the continuous outcome scenario with 10 follow-up times. Marginal structural models and orthogonalized regression had negligible bias across all six scenarios, with maximum bias of 0.7 and -0.3 respectively. Orthogonalized regression had the smallest standard error across all six scenarios. The maximum standard error observed for parametric g-formula, marginal structural models, and orthogonalized regression was 10.1, 12.3, and 7.8 respectively. Across the six scenarios, the 95% confidence interval coverage probability ranged from 74% to 98% for parametric g-formula, 89% to 97% for marginal structural models, and 91% to 97% for orthogonalized regression.
Conclusions: As expected, parametric g-formula demonstrated vulnerability to the g-null paradox, while marginal structural models and orthogonalized regression were immune. Across the six scenarios, orthogonalized regression consistently had the smallest standard error of these methods while providing correct confidence interval coverage. In addition to being the most statistically efficient of these methods, orthogonalized regression is the simplest method to implement using standard regression models available in all statistical packages. There is no nuisance model (marginal structural models) or need for Monte Carlo simulation (parametric g-formula); there is simply a sequence of regression models where the residuals from a model are used as a predictor in the subsequent model.
