Undersmoothed LASSO Models for Propensity Score Weighting and Synthetic Negative Control Exposures for Bias Detection

The propensity score (PS) is often used to control for large numbers of covariates in high-dimensional healthcare database studies. The least absolute shrinkage and selection operator (LASSO) has become the most widely used tool for fitting large-scale PS models in these settings. LASSO uses L1 regularized regression to prevent overfitting by shrinking coefficients toward zero (setting some exactly to zero). The degree of regularization is typically selected using cross-validation to minimize out-of-sample prediction error. Both theory and simulations have shown, however, that when using LASSO models for PS weighting, less regularization is needed to minimize bias in PS weighted estimators. This is referred to as undersmoothing the LASSO model, where the optimal degree of undersmoothing can be derived from the target causal parameter's efficient influence function. In many settings, however, the efficient influence function is unknown or difficult to derive. Here, we consider the use of balance metrics as a simple and generally applicable approach to select the degree of undersmoothing when the efficient influence function is unknown. Because LASSO models that are tuned using balance metrics alone are not assured to minimize bias in PS weighted estimators -- as such metrics are blind to the efficient influence function -- we propose a framework to generate synthetic negative control exposures for bias detection. We show that synthetic negative control exposures can identify analyses that likely violate partial exchangeability due to lack of control for measured confounding. Finally, we use a series of numerical studies to investigate the finite sample performance of using balance criteria to undersmooth LASSO PS-weighted estimators, and the use of synthetic negative control exposures to detect biased analyses.