Hierarchical Priors for Bias Parameters in Bayesian Sensitivity Analysis for Unmeasured Confounding

Key, J and Fisher, S and Best, Nicky and Richardson, Sylvia (2010) Hierarchical Priors for Bias Parameters in Bayesian Sensitivity Analysis for Unmeasured Confounding. Technical Report. Imperial College London. (Unpublished)

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Abstract

Recent years have witnessed new innovation in Bayesian techniques to adjust for unmeasured confounding. A challenge with existing methods is that the user is often required to elicit prior distributions for high dimensional parameters that model competing bias scenarios. This can render the methods unwieldy. In this paper we propose a novel methodology to adjust for unmeasured confounding that derives default priors for bias parameters for observational studies with binary covariates. The confounding e�ects of measured and unmeasured variables are treated as exchangeable within a Bayesian framework. We model the joint distribution of covariates using a loglinear model with pairwise interaction terms. Hierarchical priors constrain the magnitude and direction of bias parameters. An appealing property of the method is that the conditional distribution of the unmeasured confounder follows a logistic model, giving a simple equivalence with previously proposed methods. We apply the method in a data example from pharmacoepidemiology and explore the impact of di�erent priors for bias parameters on the analysis results.

Item Type:Working Paper (Technical Report)
Subjects:5. Quantitative Data Handling and Data Analysis > 5.5 Regression Methods
5. Quantitative Data Handling and Data Analysis > 5.6 Multilevel Modelling
ID Code:1693
Deposited By: BIAS user
Deposited On:06 Apr 2011 14:20
Last Modified:06 Apr 2011 14:20

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