Estimating the optimal timing of surgery by imputing potential outcomes

Hypoplastic left heart syndrome is a congenital anomaly that is uniformly fatal in infancy without immediate treatment. The standard treatment consists of an initial Norwood procedure (stage 1) followed some months later by stage 2 palliation (S2P). The ideal timing of the S2P is uncertain. The Single Ventricle Reconstruction Trial (SVRT) randomized the procedure used in the initial Norwood operation, leaving the timing of the S2P to the discretion of the surgical team. To estimate the causal effect of the timing of S2P, we propose to impute the potential post-S2P survival outcomes using statistical models under the Rubin Causal Model framework. With this approach, it is straightforward to estimate the causal effect of S2P timing on post-S2P survival by directly comparing the imputed potential outcomes. Specifically, we consider a lognormal model and a restricted cubic spline model, evaluating their performance in Monte Carlo studies. When applied to the SVRT data, the models give somewhat different imputed values, but both support the conclusion that the optimal time for the S2P is at 6 months after the Norwood procedure.