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Sensitivity Analyses for Sparse-Data ProblemsUsing Weakly Informative Bayesian Priors

Hamra, Ghassan B.a; MacLehose, Richard F.b,c; Cole, Stephen R.a

doi: 10.1097/EDE.0b013e318280db1d
Methods

Sparse-data problems are common, and approaches are needed to evaluate the sensitivity of parameter estimates based on sparse data. We propose a Bayesian approach that uses weakly informative priors to quantify sensitivity of parameters to sparse data. The weakly informative prior is based on accumulated evidence regarding the expected magnitude of relationships using relative measures of disease association. We illustrate the use of weakly informative priors with an example of the association of lifetime alcohol consumption and head and neck cancer. When data are sparse and the observed information is weak, a weakly informative prior will shrink parameter estimates toward the prior mean. Additionally, the example shows that when data are not sparse and the observed information is not weak, a weakly informative prior is not influential. Advancements in implementation of Markov Chain Monte Carlo simulation make this sensitivity analysis easily accessible to the practicing epidemiologist.

From the aDepartment of Epidemiology, UNC Chapel Hill, Chapel Hill, NC; bDivision of Biostatistics, University of Minnesota, Minneapolis, MN; and cDivision of Epidemiology and Community Health, University of Minnesota, Minneapolis, MN.

Submitted 13 June 2012; accepted 30 November 2012; posted 18 January 2013.

Supported by the Centers for Disease Control and Prevention (grant number 1R03OH009800-01), National Institute of Environmental Health Sciences (training grant ES07018), and National Institute of Health (grant number 1U01-HD061940).

Supplemental digital content is available through direct URL citations in the HTML and PDF versions of this article (www.epidem.com). This content is not peer-reviewed or copy-edited; it is the sole responsibility of the author.

Correspondence: Ghassan Hamra, Department of Epidemiology, CB# 7435, Chapel Hill, NC 27599-7435. E-mail: ghassan.hamra@unc.edu.

© 2013 Lippincott Williams & Wilkins, Inc.