Since its identification in April 2009 an A(H1N1) virus containing a unique combination of gene segments from both North American and Eurasian swine lineages has continued to circulate in humans. The 2009 A(H1N1) virus is distantly related to its nearest relatives, indicating that its gene segments have been circulating undetected for an extended period. Low genetic diversity among the viruses suggests the introduction into humans was a single event or multiple events of similar viruses. Molecular markers predicted for adaptation to humans are not currently present in 2009 A(H1N1) viruses, suggesting previously unrecognized molecular determinants could be responsible for the transmission among humans. Antigenically the viruses are homogeneous and similar to North American swine A(H1N1) viruses but distinct from seasonal human A(H1N1).

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Parameter estimation with non-ignorable missing data is a challenging problem in statistics. The fully parametric approach for joint modeling of the response model and the population model can produce results that are quite sensitive to the failure of the assumed model. We propose a more robust modeling approach by considering the model for the nonresponding part as an exponential tilting of the model for the responding part. The exponential tilting model can be justified under the assumption that the response probability can be expressed as a semi-parametric logistic regression model.In this paper, based on the exponential tilting model, we propose a semi-parametric estimation method of mean functionals with non-ignorable missing data. A semiparametric logistic regression model is assumed for the response probability and a non-parametric regression approach for missing data discussed in Cheng (1994) is used in the estimator. By adopting nonparametric components for the model, the estimation method can be made robust. Variance estimation is also discussed and results from a simulation study are presented. The proposed method is applied to real income data from the Korean Labor and Income Panel Survey.

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