Abstract
SummaryInstrumental variable methods allow unbiased estimation in the presence of unmeasured confounders when an appropriate instrumental variable is available. Two‐stage least‐squares and residual inclusion methods have recently been adapted to additive hazard models for censored survival data. The semi‐parametric additive hazard model which can include time‐independent and time‐dependent covariate effects is particularly suited for the two‐stage residual inclusion method, since it allows direct estimation of time‐independent covariate effects without restricting the effect of the residual on the hazard. In this article, we prove asymptotic normality of two‐stage residual inclusion estimators of regression coefficients in a semi‐parametric additive hazard model with time‐independent and time‐dependent covariate effects. We consider the cases of continuous and binary exposure. Estimation of the conditional survival function given observed covariates is discussed and a resampling scheme is proposed to obtain simultaneous confidence bands. The new methods are compared to existing ones in a simulation study and are applied to a real data set. The proposed methods perform favorably especially in cases with exposure‐dependent censoring.
Highlights
Instrumental variables (IV) can be used in regression modelling to avoid bias from unmeasured confounding or dependent measurement error in covariates by providing a source of exogenous variation (Angrist et al, 1996)
In all scenarios we consider the coverage probability of the confidence intervals based on the unadjusted estimates of the standard errors, which do not account for the additional variation caused by including the estimated first stage residuals as covariates in the second stage
In Scenario 3, where the linearity assumption for the confounder is violated, 2SRI has a substantial bias, but the coverage probabilities are still close to the nominal level
Summary
Instrumental variables (IV) can be used in regression modelling to avoid bias from unmeasured confounding or dependent measurement error in covariates by providing a source of exogenous variation (Angrist et al, 1996). These methods are popular in epidemiology in the analysis of observational studies. In randomized clinical trials with survival endpoints unmeasured confounding may occur as a result of non-compliance, e.g. when patients switch to salvage treatment after a progression of the disease. Estimation of survival probabilities under treatment non-compliance using IV methods was considered by Nie et al (2011). The additive hazard model (Aalen, 1989) is amenable to IV methods, since it resembles the linear regression model, while the popular Cox proportional hazards model is inappropriate for IV methods as shown by Tchetgen Tchetgen et al (2015)
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