Use of instrumental variables with survival analysis in an observational study of cardiovascular and cerebrovascular events

In a retrospective study of over 41,000 people in the Veterans Administration system to assess the risk of cardiovascular and cerebrovascular events among those exposed to highly active antiretroviral therapy, we used instrumental variables (IVs) with our survival analysis to attempt to overcome possible selection bias. We assessed how well each of our candidate IVs predicted treatment and considered how plausible it was that each met the requirement of affecting outcome only through treatment. We combined a logistic regression month-by-month binary treatment selection model with a structural outcome model based on proportional hazards regression. Parameters were estimated using a likelihood-type function which contained one factor per non-censored non-post-first-event person-month in the study, with each factor that represented an event month having the general form [{(probability of event given treatment that month) x (probability of treatment that month)} + {(probability of event given no treatment that month) x (probability of no treatment that month)}], where these terms were variously conditioned on instrument, cumulative treatment (in lieu of complete treatment history), and other covariates.

Showing how the likelihood was derived in our case can serve as an illustration of the flexibility of an IV approach in being able to accommodate some non-linear as well as more familiar linear models. At the same time consideration of the modeling assumptions that would be required to hold in our situation for causal inference to be valid serves to emphasize the cautions that should be heeded in attempting to use IVs to accommodate unobserved confounders.