Adjustment for time-dependent unmeasured confounders in marginal structural Cox models using validation sample data

Large databases used in observational studies of drug safety often lack information on important confounders. The resulting unmeasured confounding bias may be avoided by using additional confounder information, frequently available in smaller clinical validation samples. Yet, no existing method that uses such validation samples is able to deal with unmeasured time-varying variables acting as both confounders and possible mediators of the treatment effect. We propose and compare alternative methods which control for confounders measured only in a validation sample within marginal structural Cox models. Each method corrects the time-varying inverse probability of treatment weights for all subject-by-time observations using either regression calibration of the propensity score, or multiple imputation of unmeasured confounders. Two proposed methods rely on martingale residuals from a Cox model that includes only confounders fully measured in the large database, to correct inverse probability of treatment weight for imputed values of unmeasured confounders. Simulation demonstrates that martingale residual-based methods systematically reduce confounding bias over naive methods, with multiple imputation including the martingale residual yielding, on average, the best overall accuracy. We apply martingale residual-based imputation to re-assess the potential risk of drug-induced hypoglycemia in diabetic patients, where an important laboratory test is repeatedly measured only in a small sub-cohort.