Outcome-Adaptive Lasso for Cox Proportional Hazards Model

While randomized controlled trials remain the gold standard for estimating causal effects in medical research, they are not always practical. Consequently, observational data become a necessary alternative, though it introduces confounding bias due to the lack of randomization. Propensity score modeling mitigates this bias but is highly sensitive to covariate selection. To address this critical limitation in survival analysis, we propose the outcome-adaptive Lasso (OAL)-Cox model-a novel variable selection framework for causal inference for right-censored data. The proposed method integrates the OAL with the Cox proportional hazards model by constructing penalty weights from coefficients estimated through the Cox partial likelihood. This design enables OAL-Cox to effectively identify outcome-related confounders while excluding irrelevant covariates, including instrumental and spurious variables, even under censoring and correlated covariate structures. Simulation studies demonstrate that OAL-Cox achieves stable variable selection across different censoring rates and correlation settings. Compared with the L-Cox and AL-Cox methods considered in this study, OAL-Cox more effectively reduces the inclusion of instrumental and spurious covariates while retaining outcome-related covariates, and it generally yields more stable restricted mean survival time-based causal effect estimates in the examined settings. We further illustrate the practical applicability of the proposed method by applying it to ovarian cancer recurrence time data to evaluate the effect of surgical sophistication on recurrence time.