A flexible instrumental variable approach

Classical regression model literature has generally assumed that measured and unmeasured covariates are statistically independent. For many applications, this assumption is clearly tenuous. When unobservables are associated with included regressors and have an impact on the response, standard estimation methods will not be valid. This means that estimation results from observational studies, whose aim is to evaluate the impact of a treatment of interest on a response variable, will be biased and inconsistent in the presence of unmeasured confounders. One method for obtaining consistent estimates of treatment effects when dealing with linear models is the instrumental variable (IV) approach. Linear models have been extended to generalized linear models (GLMs) and generalized additive models (GAMs), and although IV methods have been proposed to deal with GLMs, fitting methods to carry out IV analysis within the GAM context have not been developed. We propose a simple but effective two-stage procedure for IV estimation when dealing with GAMs represented using any penalized regression spline approach and a correction procedure for confidence intervals. We explain under which conditions the proposed method works and illustrate its empirical validity through an extensive simulation experiment and a health study where unmeasured confounding is suspected to be present.