On the Bias-Amplifying Effect of Near Instruments in Observational Studies
Author: Steiner, Peter M.
Date: 2014-00-00
Type: Reports - Research
Subjects: Observation,Research Methodology,Test Bias,Regression (Statistics),Nonparametric Statistics,Scoring,Test Items,Simulation,Models,Correlation,Reliability

In contrast to randomized experiments, the estimation of unbiased treatment effects from observational data requires an analysis that conditions on all confounding covariates. Conditioning on covariates can be done via standard parametric regression techniques or nonparametric matching like propensity score (PS) matching. The regression or matching estimators are causally unbiased (or at least consistent) if the selection mechanism is strongly ignorable, i.e., if all confounding covariates are reliably measured (Rosenbaum &amp; Rubin, 1983). However, for practitioners, the strong ignorability assumption is not very informative because it does not tell them which covariates should actually be included in a regression or PS analysis. In order to remove as much of the selection bias as possible, it is common advice to condition on all or at least a big set of covariates. However, recent studies have shown that conditioning on certain types of covariates such as &quot;instrumental variables&quot; (IVs) or &quot;collider variables&quot; can actually amplify or induce bias (e.g., Bhattacharya &amp; Vogt, 2007; Wooldridge, 2009). Neither IVs nor colliders are confounders because, with respect to the data-generating model, they do not simultaneously determine the outcome (Y) and the treatment (Z). Interestingly, though IVs and colliders are unrelated to the outcome, including them in a regression or PS model may result in a dramatically increased bias--the bias might be much larger than the bias of the naïve estimate (i.e., the simple mean difference between the treatment and control group, without any covariate adjustments). Even if IVs might be rare in practice, one is much more likely confronted with covariates that are almost like IVs, that is, covariates that strongly determine treatment Z but are only weakly related to the outcome (other than via Z). Due to their resemblance to pure IVs they are called &quot;near instrumental variables&quot; (near-IVs, Myers et al, 2011). Given that conditioning on near-IVs might actually increase bias some authors suggest excluding near-IVs from causal analyses (e.g., Pearl, 2011). In this paper the authors focus on the bias-amplifying effect of near-IVs--but not only of a single near-IV in the context of a simple data-generating model (e.g., Myers et al., 2011; Pearl, 2010), but of multiple near-IVs in the context of more complex and realistic data-generating models. With the exemption of some formal derivations, they investigate the effect of conditioning on near-IVs on bias reduction using simulated data that involve many (interrelated) confounders. In their simulations they vary the confounders' (1) degree of being a near instrument; (2) correlation structure; (3) heterogeneity with respect their relation to treatment Z and outcome Y (i.e., the strength and direction of the relation); and (4) measurement reliability. Simulation design and figures are appended.