An improved multiply robust estimator for the average treatment effect

BACKGROUND: In observational studies, double robust or multiply robust (MR) approaches provide more protection from model misspecification than the inverse probability weighting and g-computation for estimating the average treatment effect (ATE). However, the approaches are based on parametric models, leading to biased estimates when all models are incorrectly specified. Nonparametric methods, such as machine learning or nonparametric double robust approaches, are robust to model misspecification, but the efficiency of nonparametric methods is low. METHOD: In the study, we proposed an improved MR method combining parametric and nonparametric models based on the previous MR method (Han, JASA 109(507):1159-73, 2014) to improve the robustness to model misspecification and the efficiency. We performed comprehensive simulations to evaluate the performance of the proposed method. RESULTS: Our simulation study showed that the MR estimators with only outcome regression (OR) models, where one of the models was a nonparametric model, were the most recommended because of the robustness to model misspecification and the lowest root mean square error (RMSE) when including a correct parametric OR model. And the performance of the recommended estimators was comparative, even if all parametric models were misspecified. As an application, the proposed method was used to estimate the effect of social activity on depression levels in the China Health and Retirement Longitudinal Study dataset. CONCLUSIONS: The proposed estimator with nonparametric and parametric models is more robust to model misspecification. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12874-023-02056-7.