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\footnotesize \noindent Statistica Sinica {\bf 21} (2011), 1881-1899

\footnotesize \noindent doi:http://dx.doi.org/10.5705/ss.2009.252

\vspace{3pc} \normalsize \centerline{\large\bf A SEMIPARAMETRIC
APPROACH FOR ANALYZING} \vspace{2pt} \centerline{\large\bf
NONIGNORABLE MISSING DATA} \vspace{.25cm}
\author{Hui Xie, Yi Qian and Leming Qu}
\vspace{.4cm} \centerline{\it University of Illinois, Chicago,
Northwestern University and Boise State University} \vspace{.55cm}
\sz09
\begin{quotation}
\noindent {\it Abstract:} In missing data analysis, there is often a
need to assess the sensitivity of key inferences to departures from
untestable assumptions regarding the missing data process. Such
sensitivity analysis often requires specifying a missing data model
that commonly assumes parametric functional forms for the predictors
of missingness.  In this paper, we relax the parametric assumption
and investigate the use of a generalized additive missing data
model. We also consider the possibility of a nonlinear relationship
between missingness and the potentially missing outcome, whereas the
existing literature commonly assumes a more restricted linear
relationship.  To avoid computational complexity, we adopt an index
approach for local sensitivity. We derive explicit formulas for the
resulting semiparametric sensitivity index. The computation of the
index is simple, and  completely avoids the need to repeatedly fit
the semiparametric nonignorable  model.  Only estimates from the
standard software analysis are required, with a moderate amount of
additional computation. Thus, the semiparametric index provides a
fast and robust method to adjust the standard estimates for
nonignorable missingness. An extensive  simulation study is
conducted to evaluate the effects of misspecifying the missing data
model and to compare the performance of the proposed approach with
the commonly used parametric approaches. The simulation study
suggests that the proposed method helps reduce bias that might arise
from the misspecification of the functional forms of predictors in
the missing data model. We illustrate the method in a Wage Offer
dataset.\par \vspace{9pt} \noindent {\it Key words and phrases:}
Generalized additive model, MNAR, nonignorability, semiparametric
joint selection model, sensitivity analysis. \par
\end{quotation}

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