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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\u2010S2P 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\u2010S2P 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\u00a0months after the Norwood procedure.<\/jats:p>","DOI":"10.1002\/sim.9217","type":"journal-article","created":{"date-parts":[[2021,10,12]],"date-time":"2021-10-12T06:30:43Z","timestamp":1634020243000},"page":"6900-6917","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Estimating the optimal timing of surgery by imputing potential outcomes"],"prefix":"10.1002","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8086-4746","authenticated-orcid":false,"given":"Xiaofei","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Statistical Science Southern Methodist University Dallas Texas USA"},{"name":"Department of Population &amp; Data Sciences UT Southwestern Medical Center Dallas Texas 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