Model Assisted Sensitivity Analyses for Hidden Bias with Binary Outcomes

Abstract

In medical and health sciences, observational studies are a major data source for inferring causal relationships. Unlike randomized experiments, observational studies are vulnerable to the hidden bias introduced by unmeasured confounders. The impact of unmeasured covariates on the causal effect can be assessed by conducting a sensitivity analysis. A comprehensive framework of sensitivity analyses has been developed for matching designs. Sensitivity parameters are introduced to capture the association between the missing covariates and the exposure or the outcome. Fixing sensitivity parameter values, it is possible to compute the bounds of the p-value of a randomization test on causal effects. We propose a model assisted sensitivity analysis with binary outcomes for the general 1:k matching design, which provides results equivalent to the conventional nonparametric approach in large sample. By introducing a conditional logistic outcome model, we substantially simplify the implementation and interpretation of the sensitivity analysis. More importantly, we are able to provide a closed form representation for the set of sensitivity parameters for which the maximum p-values are non-significant. This methodology can be easily extended to matching designs with multilevel treatments. We illustrate our method using a U.S. trauma care database to examine mortality difference between trauma care levels.

The Use of the Generalized Linear Model to Assess the Speed and Uniformity of Germination of Corn and Soybean Seeds

“…These results demonstrate the importance of considering the choice of the correct link function, since the use of inaccurate models is potentially generating misleading conclusions [26,28]. Although the logit model is currently preferred in some areas-for example, in biometrics [22,29,30]-in this study, smaller deviances were obtained for most hybrid and/or cultivar studied; it is necessary to study this by comparing the link seeking functions that best describe the probability of interest [31].…”

Sharpening the Rosenbaum Sensitivity Bounds to Address Concerns About Interactions Between Observed and Unobserved Covariates

“…For examples of studies using the Rosenbaum bounds sensitivity analysis, see Normand et al (2001), Rosenbaum (2002), Rosenbaum (2004), Heller et al (2009), Silber et al (2009), Stuart and Hanna (2013), Zubizarreta et al (2013), Hsu et al (2015), Zubizarreta et al (2016), Ertefaie et al (2018), Fogarty (2019), Karmakar et al (2019), Zhao (2019), Sharpening the Rosenbaum Bounds and Zhang et al (2020). Many other sensitivity analysis models also build on the Rosenbaum bounds sensitivity analysis (e.g., Gastwirth et al, 1998;Ichino et al, 2008;Rosenbaum and Silber, 2009;Nattino and Lu, 2018;Fogarty and Hasegawa, 2019).…”