A flexible, interpretable framework for assessing sensitivity to unmeasured confounding

Abstract

When estimating causal effects, unmeasured confounding and model misspecification are both potential sources of bias. We propose a method to simultaneously address both issues in the form of a semi‐parametric sensitivity analysis. In particular, our approach incorporates Bayesian Additive Regression Trees into a two‐parameter sensitivity analysis strategy that assesses sensitivity of posterior distributions of treatment effects to choices of sensitivity parameters. This results in an easily interpretable framework for testing for the impact of an unmeasured confounder that also limits the number of modeling assumptions. We evaluate our approach in a large‐scale simulation setting and with high blood pressure data taken from the Third National Health and Nutrition Examination Survey. The model is implemented as open‐source software, integrated into the treatSens package for the R statistical programming language. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Making Sense of Sensitivity: Extending Omitted Variable Bias

“…() and Dorie et al . () required specifying the distribution of the confounder as well as modelling the treatment assignment mechanism; in another direction, the methods that were put forward in Robins (), Brumback et al . () and Blackwell () need to specify directly a confounding function parameterizing the difference in potential outcomes among treated and control units.…”

“…For the task at hand, however, any proposal must meet the minimal criterion of solving the correct identification problem-essentially, this means that the chosen measure of relative strength must be sufficient to identify (or bound) the bias, and a new function (or bound) in terms of that measure must be derived (Cinelli et al, 2019). Previous work has proposed informal benchmarking procedures that fail this minimal criterion and can generate misleading sensitivity analysis results, even if researchers had correct knowledge about the relative strength of Z (Frank, 2000;Imbens, 2003;Frank et al, 2008;Blackwell, 2013;Dorie et al, 2016;Carnegie et al, 2016a;Middleton et al, 2016). We elaborate on the pitfalls of this informal approach in Section 6.2 of the discussion.…”

“…First, the assumptions that many methods impose on the nature and distribution of unobserved confounders as well as on the treatment assignment mechanism may be difficult to sustain in some cases. For instance, Rosenbaum and Rubin (1983b), Imbens (2003), Carnegie et al (2016a) and Dorie et al (2016) required specifying the distribution of the confounder as well as modelling the treatment assignment mechanism; in another direction, the methods that were put forward in Robins (1999), Brumback et al (2004) and Blackwell (2013) need to specify directly a confounding function parameterizing the difference in potential outcomes among treated and control units. Although assessing the sensitivity to some forms of confounding is an improvement over simply assuming no confounding (and users may be able to make suitable parameteric assumptions in some circumstances), widespread adoption of sensitivity analysis would benefit from methods that do not require users to make those restrictions a priori.…”

“…Finally, we introduce a novel bounding procedure that aids researchers in judging which confounders are plausible or could be ruled out, using the observed data in combination with expert knowledge. Whereas prior work (Frank, ; Imbens, ; Hosman et al ., ; Blackwell, ; Dorie et al ., ; Carnegie et al ., ; Middleton et al ., ; Hong et al ., ) has suggested an informal practice of benchmarking the unobserved confounding by comparison with unadjusted statistics of observables, we show that this practice can generate misleading conclusions due to the effects of confounding itself, even if the confounder is assumed to be independent of the covariate(s) that are used for benchmarking. Instead, our approach formally bounds the strength of unobserved confounding with the same strength (or a multiple thereof) as a chosen observable or group of observables.…”

“…A variety of sensitivity analyses have been proposed, dating back to Cornfield et al (1959), with more recent contributions including Rosenbaum and Rubin (1983b), Robins (1999), Frank (2000), Rosenbaum (2002), Imbens (2003), Brumback et al (2004), Frank et al (2008Frank et al ( , 2013, Hosman et al (2010), Imai et al (2010), Vanderweele and Arah (2011), Blackwell (2013), Carnegie et al (2016b), Dorie et al (2016), Middleton et al (2016), Oster (2019) and Franks et al (2019). Yet, such sensitivity analyses remain underutilized.…”