  The use of instrumental variables for estimating the effect of an exposure on
an outcome is popular in econometrics, and increasingly so in epidemiology.
This increasing popularity may be attributed to the natural occurrence of
instrumental variables in observational studies that incorporate elements of
randomization, either by design or by nature (e.g., random inheritance of
genes). Instrumental variables estimation of exposure effects is well
established for continuous outcomes and to some extent for binary outcomes. It
is, however, largely lacking for time-to-event outcomes because of
complications due to censoring and survivorship bias. In this paper, we make a
novel proposal under a class of structural cumulative survival models which
parameterize time-varying effects of a point exposure directly on the scale of
the survival function; these models are essentially equivalent with a
semi-parametric variant of the instrumental variables additive hazards model.
We propose a class of recursive instrumental variable estimators for these
exposure effects, and derive their large sample properties along with
inferential tools. We examine the performance of the proposed method in
simulation studies and illustrate it in a Mendelian randomization study to
evaluate the effect of diabetes on mortality using data from the Health and
Retirement Study. We further use the proposed method to investigate potential
benefit from breast cancer screening on subsequent breast cancer mortality
based on the HIP-study.
