Extending time-dependent instrumental variable estimation to estimate the causal effect of time-dependent exposure

Abstract

Objectives: The purpose of the study was to compare the traditional models with the instrumental variable estimation method to estimate the causal effect of time-dependent exposure on the time-dependent outcome in the presence of unmeasured confounders for this effect. Methods: In recent studies, the instrumental variable (IV) estimation method of exposure effect frequently was used to collect information on potentially confounding variables. This is the case in particular where the time-dependent exposure is affected by the pervious events. We develop IV estimation method to estimate the effect of time-dependent exposure or treatment on timedependent outcome. This estimation method is designed for settings in which the exposure in time t is influenced by the exposure and outcome at time t − 1. Specifically, we extend IV estimation method in 2 stages in to a situation where exposure and outcome vary over the time. We show that our approach estimation in nonlinearity/additivity model is more consistent in comparison with the classical regression estimation method. This is done through simulation studies. Results: Our estimation strategy has larger mean square error (MSE) for the effect estimate in spite of having smaller bias in comparison with the tradition regression estimation method. However, this result might be the weak correlation between the time-dependent of instrumental variable and treatment. The case where the degree of correlation between time-depended instrumental variable and treatment at time t is stronger, we have more consistent estimate of causal effect. That is, our effect estimate tended to have less bias and less MSE, and more likely to have better confidence intervals and coverage probabilities. In the simulations study, we added interaction effect between exposures and measured confounder (nonadditivity model). In this model, by changing the association between outcome and confounders through different covariates, we could obtain more consistent estimate of the causal effect through our method than the classical method. The same results have been observed in case where we consider nonlinearity relationship between confounders and treatment. Alternatively, in some cases, we have better MSE for the classical estimation method, but we must note that its confidence intervals would not include the null causal effect value. Conclusions:We sketched a model for estimating the effect of timedependent treatment in settings in which classical methods may fail because of unmeasured confounding variables. We represented time-dependent instrumental variable to control the impact of measured and unmeasured confounders. We showed, after controlling confounding variables effect, that the effect of the previous treatment of interest that we wish to estimate could play the role of confounding variables under our assumptions and should be adjusted in the analysis. We showed that our approach has less bias than the classical regression models. Moreover, the mean square error of our method is large in some cases; this might be because our method performs in 2 steps. Not so surprisingly, strong association between instrument and treatment in each time reduces bias and the mean square error of the causal effect estimator. We showed also that our estimator is more efficient in coverage probabilities and confidence intervals in nonadditivity and nonlinearity/additivity models.