title: Instrumental variable estimation in a survival context.
abstract: Bias due to unobserved confounding can seldom be ruled out with certainty when estimating the causal effect of a nonrandomized treatment. The instrumental variable (IV) design offers, under certain assumptions, the opportunity to tame confounding bias, without directly observing all confounders. The IV approach is very well developed in the context of linear regression and also for certain generalized linear models with a nonlinear link function. However, IV methods are not as well developed for regression analysis with a censored survival outcome. In this article, we develop the IV approach for regression analysis in a survival context, primarily under an additive hazards model, for which we describe 2 simple methods for estimating causal effects. The first method is a straightforward 2-stage regression approach analogous to 2-stage least squares commonly used for IV analysis in linear regression. In this approach, the fitted value from a first-stage regression of the exposure on the IV is entered in place of the exposure in the second-stage hazard model to recover a valid estimate of the treatment effect of interest. The second method is a so-called control function approach, which entails adding to the additive hazards outcome model, the residual from a first-stage regression of the exposure on the IV. Formal conditions are given justifying each strategy, and the methods are illustrated in a novel application to a Mendelian randomization study to evaluate the effect of diabetes on mortality using data from the Health and Retirement Study. We also establish that analogous strategies can also be used under a proportional hazards model specification, provided the outcome is rare over the entire follow-up.
authors.affiliation: From the aDepartments of Biostatistics and Epidemiology, Harvard University, Boston, MA; bDepartment of Epidemiology and Biostatistics, University of California, San Francisco, CA; cDepartment Applied Mathematics, Computer Science and Statistics, Ghent University, Ghent, Belgium; and dDepartment of Biostatistics, University of Copenhagen, Copenhagen, Denmark.
authors.forename: Eric J
authors.initials: EJ
authors.lastname: Tchetgen Tchetgen
authors.forename: Stefan
authors.initials: S
authors.lastname: Walter
authors.forename: Stijn
authors.initials: S
authors.lastname: Vansteelandt
authors.forename: Torben
authors.initials: T
authors.lastname: Martinussen
authors.forename: Maria
authors.initials: M
authors.lastname: Glymour
mesh_terms: D015984:Causality; D015986:Confounding Factors, Epidemiologic; D003920:Diabetes Mellitus / Q000401:mortality; D006801:Humans; D016014:Linear Models; D057182:Mendelian Randomization Analysis; D015233:Models, Statistical; D016016:Proportional Hazards Models; D016019:Survival Analysis