Modeling Versus Balancing Approaches to Addressing Instrumental Variables in Weighting: A Comparison of the Outcome-Adaptive Lasso, Stable Balancing Weighting, and Stable Confounder Selection

Background: Variable selection is essential for propensity score (PS)-weighted estimators. Recent work shows that including instrumental variables (IVs), associated with only treatment but not with the outcome, can impact both the bias and precision of the PS-weighted estimators. Methods: The outcome-adaptive lasso (OAL) is an innovative model-based method adapting the popular adaptive lasso variable selection to causal inference. It attempts to identify IVs, so one can exclude them from the PS model. Unlike the model-based approach, stable balancing weighting (SBW) estimates inverse probability weights directly while minimizing the variance of the weights and covariate imbalance simultaneously. Based on its variance optimization algorithm, SBW may provide some protection against the impact of IVs. Lastly, we considered stable confounder selection (SCS), which assesses the stability of model-based effect estimates. Results: The authors present the results of simulation studies to investigate which method performs the best when moderate or strong IVs are used. The simulation studies consider IVs and spurious variables to generate extreme PSs. In simulations, SBW generally outperformed OAL and SCS in terms of reducing mean squared error, notably when the IVs were strong, and many covariates were highly correlated. Our empirical application to the effect of abciximab treatment demonstrates that SBW is a robust method to effectively handle limited overlap. Conclusions: Our numerical results support the use of SBW in situations where IVs or near-IVs may lead to practical violations of positivity assumptions.