The management of chronic conditions is characterized by frequent re-assessment of therapy decisions in response to the patient’s changing condition over the course of the illness. Evidence most suitable to inform care thus often concerns the contrast of adaptive treatment strategies that repeatedly personalize treatment decisions over time using the latest accumulated data available from the patient’s previous clinic visits such as laboratory exams (e.g., hemoglobin A1c measurements in diabetes care). The frequency at which such information is monitored implicitly defines the causal estimand that is typically evaluated in an observational or randomized study of such adaptive treatment strategies. Analytic control of monitoring with standard estimation approaches for time-varying interventions can therefore not only improve study generalizibility but also inform the optimal timing of clinical surveillance. Valid inference with these estimators requires the upholding of a positivity assumption that can hinder their applicability. To potentially weaken this requirement for monitoring control, we introduce identifiability results that will facilitate the derivation of alternate estimators of effects defined by general joint treatment and monitoring interventions in the context of time-to-event outcomes. These results are developed based on the nonparametric structural equation modeling framework using a no direct effect assumption originally introduced in a prior paper that inspired this work. The relevance and scope of the results presented here are illustrated with examples in diabetes comparative effectiveness research.