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Biostatistics Advance Access originally published online on March 23, 2006
Biostatistics 2006 7(4):615-629; 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.

On estimation of vaccine efficacy using validation samples with selection bias

Daniel O. Scharfstein*

Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21205, USA dscharf{at}jhsph.edu

M. Elizabeth Halloran

Program in Biostatistics and Biomathematics, Fred Hutchinson Cancer Research Center, Seattle, WA 98109, USA and Department of Biostatistics, University of Washington, Seattle, WA 98195, USA

Haitao Chu

Department of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21205, USA

Michael J. Daniels

Department of Statistics, University of Florida, Gainesville, FL 32611, USA

* To whom correspondence should be addressed.

Using validation sets for outcomes can greatly improve the estimation of vaccine efficacy (VE) in the field (Halloran and Longini, 2001; Halloran and others, 2003). Most statistical methods for using validation sets rely on the assumption that outcomes on those with no cultures are missing at random (MAR). 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 VE in the presence of validation bias. Our work builds on the ideas of Rotnitzky and others (1998, 2001), Scharfstein and others (1999, 2003), and Robins and others (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 non-specific case definition. Our approach is generally applicable to studies with missing binary outcomes with categorical covariates.

Keywords: Bayesian; Expert opinion; Identifiability; Influenza; Missing data; Selection model; Vaccine efficacy


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