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1.  On estimation of vaccine efficacy using validation samples with selection bias 
Biostatistics (Oxford, England)  2006;7(4):615-629.
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.
PMCID: PMC2766283  PMID: 16556610
Bayesian; Expert opinion; Identifiability; Influenza; Missing data; Selection model; Vaccine efficacy
2.  Incorporating prior beliefs about selection bias into the analysis of randomized trials with missing outcomes 
Biostatistics (Oxford, England)  2003;4(4):495-512.
In randomized studies with missing outcomes, non-identifiable assumptions are required to hold for valid data analysis. As a result, statisticians have been advocating the use of sensitivity analysis to evaluate the effect of varying asssumptions on study conclusions. While this approach may be useful in assessing the sensitivity of treatment comparisons to missing data assumptions, it may be dissatisfying to some researchers/decision makers because a single summary is not provided. In this paper, we present a fully Bayesian methodology that allows the investigator to draw a ‘single’ conclusion by formally incorporating prior beliefs about non-identifiable, yet interpretable, selection bias parameters. Our Bayesian model provides robustness to prior specification of the distributional form of the continuous outcomes.
PMCID: PMC2748253  PMID: 14557107
Dirichlet process prior; Identifiability; MCHC; Non-parametric Bayes; Selection model; Sensitivity analysis

Results 1-2 (2)