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Generalized Sensitivity Analysis

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Abstract

This study introduces the Generalized Sensitivity Analysis (GSA), which is a simple computational method for sensitivity analysis for unobserved confounder. Specifically, GSA generates the two dimensional figure similar to those in Imbens (2003), in which the magnitude of potential bias due to the omission of an unobservable is measured in terms of the partial R-square of an unobservable in an outcome equation and that in treatment assignment equation. Although the sensitivity analysis by Imbens (2003) provides more information than that by Rosenbaum (2002), it can deal with only a binary treatment variable and requires an unobservable to be binary. On the other hand, GSA allows any combination of treatment and outcome variables, and requires no special knowledge. This study presents the procedure of GSA and two examples to show the versatility of GSA. GSA significantly broadens the scope of observational studies.

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... Optimization methods are used to estimate the treatment effect conditional on specific values of the sensitivity parameters. 7 The second method was proposed by Harada (2013). It uses residualized versions of the outcome (from a linear model conditional on the treatment and covariates) and the treatment variable (from a linear model conditional on the covariates) to generate candidate values of the unmeasured confounder in a constrained range. ...
... 7 isa (Harada, 2011) performs the sensitivity analysis of Imbens (2003) in Stata. 8 gsa (Harada, 2012) performs the sensitivity analysis of Harada (2013) in Stata. ...
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... show the results from the general sensitivity analysis performed using the algorithm developed byHarada (2012). InFigure 4the solid curve represents the set of partial R-squares for U corresponding to an ATE which is half of the baseline one (i.e., 0.37), while inFigure 5it 18 See Imbens (2003) for further details on this method and Blattman and Annan (2010) for an application. ...
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