The therapy of some diseases involves multiple rounds of invasive treatment. For example, infants with hypoplastic left heart syndrome typically require an initial Norwood operation, followed some months later by a stage 2 procedure (S2P). The timing of the S2P is typically up to the surgeon and the infant’s family, and the optimal timing, if one exists, is unknown. In the Single Ventricle Reconstruction (SVR) trial, the procedure used in the initial Norwood operation was randomized, but the timing of the S2P was left to the surgeon. Because there was systematic collection of surgery times and patient follow-up information, the trial database constitutes a thoroughly documented observational study. We seek to identify the optimal timing of S2P by using an extension of propensity score analysis. We describe the time to surgery as a function of confounders using a discrete competing-risk model. We then apply inverse probability weighting to estimate a spline model for predicting the time to death as a function of the time of S2P. Our analysis suggests that conducting the S2P at 7 months post-Norwood gives the patient the best chance of survival.