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Biostatistics Advance Access published online on March 23, 2006
Biostatistics, doi:10.1093/biostatistics/kxj031
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© The Author 2006. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org
Received July 25, 2005
Revised March 6, 2006
Accepted March 22, 2006

Article

On Estimation of Vaccine Efficacy Using Validation Samples with Selection Bias

Daniel O. Scharfstein 1 *, M. Elizabeth halloran 2, Haitao Chu 3, and Michael J. Daniels 4

1 Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore MD 21205 USA
2 Program in Biostatistics and Biomathematics, Fred Hutchinson Cancer Research Center Seattle, WA 98109 USA; Department of Biostatistics, University of Washington. Seattle, WA 98195 USA
3 Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore MD 21205 USA
4 Department of Statistics, University of Florida, Gainesville, FL 32611 USA

* To whom correspondence should be addressed.
Daniel O. Scharfstein, E-mail: dscharf{at}jhsph.edu


  Abstract

Using validation sets for outcomes can greatly improve the estimation of vaccine efficacy (VE) in the field (Halloran and Longini 2001; Halloran et al. 2003). Most statistical methods for using validation sets rely on the assumption that outcomes on those with no cultures are missing at random. However, often the validation sets will not be chosen at random. For example, confirmational cultures are often done on people with influenza-like illness as part of routine influenza surveillance. VE estimates based on such non-MAR validation sets could be biased. Here we propose frequentist and Bayesian approaches for estimating vaccine efficacy in the presence of validation bias. Our work builds on the ideas of Rotnitzky et al. (1998, 2001), Scharfstein et al. (1999, 2003) and Robins et al. (2000). Our methods require expert opinion about the nature of the validation selection bias. In a re-analysis of an influenza vaccine study we found, using the beliefs of a flu expert, that within any plausible range of selection bias the VE estimate based on the validation sets is much higher than the point estimate using just the nonspecific case definition. Our approach is generally applicable to studies with missing binary outcomes with categorical covariates.

Keywords: Bayesian; Expert Opinion; Vaccine Efficacy; Identifiability; Influenza; Missing data; Selection Model.
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