Assessing penalized approaches for estimating causal treatment effects under extremely limited overlap in oncology

Overlap weighting (OW) is increasingly used to estimate treatment effects in observational cancer studies. OW has attractive features: it targets the clinical equipoise population and mitigates the influence of extreme propensity score (PS) weights. Additionally, under regularity conditions, when the PS model is fitted using a standard logistic regression model (LRM) with all observed covariates included, OW achieves exact covariate balance between treated and control groups, meaning that the standardized mean differences for the included covariates are zero. However, in oncology data, imbalanced treatment patterns, small subgroups, and limited PS overlap frequently cause separation and non-convergence, undermining stable estimation in logistic regression.

We evaluated five methods for constructing PSs for estimating the average treatment effect in the overlap population (ATO): standard logistic regression, Firth's penalized logistic regression, a double-penalized logistic regression method that combines Firth's correction with ridge regularization, and two variants designed to preserve exact covariate balance. Performance was assessed through Monte Carlo simulations under varying overlap, data complexity, and model misspecification. We also applied these methods to a retrospective cohort of 5348 patients with early-stage breast adenocarcinoma and Charlson Comorbidity Index ≥2 from the multi-institutionally linked nationwide data to estimate the effect of definitive surgery on 3-year all-cause mortality.

In simulations, standard LRMs showed unstable estimation or non-convergence in finite-sample settings characterized by low treatment prevalence and limited effective overlap. Penalized methods improved numerical stability, reduced extreme PS values, and generally showed better finite-sample performance, particularly when the LRM is not converged. In the breast cancer study, only 2.1% of patients did not undergo surgery, indicating marked treatment imbalance. Overall estimates were similar across methods, but in patients aged <40 years, a LRM yielded an extreme ATO estimate, whereas Firth's and double-penalized methods produced more stable and consistent results.

In oncology subgroups where low treatment prevalence and limited effective overlap lead to unstable or non-convergent LRMs, penalized regression approaches provide a practical strategy for improving ATO estimation.