Generalized additive selection models for the analysis of studies with potentially nonignorable missing outcome data

Rotnitzky, Robins, and Scharfstein (1998, Journal of the American Statistical Association 93, 1321-1339) developed a methodology for conducting sensitivity analysis of studies in which longitudinal outcome data are subject to potentially nonignorable missingness. In their approach, they specify a class of fully parametric selection models, indexed by a non- or weakly identified selection bias function that indicates the degree to which missingness depends on potentially unobservable outcomes. Estimation of the parameters of interest proceeds by varying the selection bias function over a range considered plausible by subject-matter experts. In this article, we focus on cross-sectional, univariate outcome data and extend their approach to a class of semiparametric selection models, using generalized additive restrictions. We propose a backfitting algorithm to estimate the parameters of the generalized additive selection model. For estimation of the mean outcome, we propose three types of estimating functions: simple inverse weighted, doubly robust, and orthogonal. We present the results of a data analysis and a simulation study.