<p>To examine the causal effects of time-varying treatments on survival, structural nested cumulative survival time models (SNCSTMs) are flexible and theoretically promising semiparametric models characterized by causally interpretable parameters. One concern is the prerequisite for uniformly scheduled data collection and complete data for time-varying confounders. For example, in pharmacoepidemiological studies using medical information databases, laboratory test results can be missing due to unscheduled hospital visits or non-compliance with health checkups. Furthermore, missing mechanisms data may be non-ignorable and non-monotone, invalidating the typical missing-data methods that assume ignorable or monotone missing mechanisms. We propose a novel g-estimation method for SNCSTMs with non-ignorable, non-monotonic missing data for time-varying confounders. We augment the g-estimation functions using missing probability and imputation models, incorporating a user-defined selection function, which allows sensitivity analyses to evaluate the departure of missing data from ignorable mechanisms. Using a proper selection function, our estimator is doubly robust in the sense that it is consistent if either model for missing probability or imputation of missing data is correct at each time point and if either model for propensity score or conditional expectation of counterfactual counting processes is correct. Moreover, applying frequentist-type multiple imputation yields a closed-form solution for calculating the estimator, even if time-varying confounders are missing. A simulation study evaluated our proposed method’s finite sample performance and the estimator’s double robustness. We also conducted sensitivity analyses in a pharmacoepidemiological study using a Japanese medical claims database, assessing the risk of hypoglycemia in sulfonylurea-treated patients with incomplete hemoglobin A1c values.</p>