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The use of instrumental variables for estimating the effect of an exposure onan outcome is popular in econometrics, and increasingly so in epidemiology.This increasing popularity may be attributed to the natural occurrence ofinstrumental variables in observational studies that incorporate elements ofrandomization, either by design or by nature (e.g., random inheritance ofgenes). Instrumental variables estimation of exposure effects is wellestablished for continuous outcomes and to some extent for binary outcomes. Itis, however, largely lacking for time-to-event outcomes because ofcomplications due to censoring and survivorship bias. In this paper, we make anovel proposal under a class of structural cumulative survival models whichparameterize time-varying effects of a point exposure directly on the scale ofthe survival function; these models are essentially equivalent with asemi-parametric variant of the instrumental variables additive hazards model.We propose a class of recursive instrumental variable estimators for theseexposure effects, and derive their large sample properties along withinferential tools. We examine the performance of the proposed method insimulation studies and illustrate it in a Mendelian randomization study toevaluate the effect of diabetes on mortality using data from the Health andRetirement Study. We further use the proposed method to investigate potentialbenefit from breast cancer screening on subsequent breast cancer mortalitybased on the HIP-study.

Instrumental variables estimation of exposure effects on a time-to-event response using structural cumulative survival models