Estimating the optimal timing of surgery from observational data

Infants with hypoplastic left heart syndrome require an initial Norwood operation, followed some months later by a stage 2 palliation (S2P). The timing of S2P is critical for the operation's success and the infant's survival, but the optimal timing, if one exists, is unknown. We attempt to identify the optimal timing of S2P by analyzing data from the Single Ventricle Reconstruction Trial (SVRT), which randomized patients between two different types of Norwood procedure. In the SVRT, the timing of the S2P was chosen by the medical team; thus with respect to this exposure, the trial constitutes an observational study, and the analysis must adjust for potential confounding. To accomplish this, we propose an extended propensity score analysis that describes the time to surgery as a function of confounders in a discrete competing-risk model. We then apply inverse probability weighting to estimate a spline hazard model for predicting survival from the time of S2P. Our analysis suggests that S2P conducted at 6 months after the Norwood gives the patient the best post-S2P survival. Thus, we place the optimal time slightly later than a previous analysis in the medical literature that did not account for competing risks of death and heart transplantation.