Semiparametric regression models and sensitivity analysis of longitudinal data with non-random dropouts

We propose a family of regression models to adjust for non-random dropouts in the analysis of longitudinal outcomes with fully observed covariates. The approach conceptually focuses on generalized linear models with random effects. A novel formulation of a shared random effects model is presented and shown to provide a dropout selection parameter with a meaningful interpretation. The proposed semiparametric and parametric models are made part of a sensitivity analysis to delineate the range of inferences consistent with observed data. Concerns about model identifiability are addressed by fixing some model parameters to construct functional estimators that are used as the basis of a global sensitivity test for parameter contrasts. Our simulation studies demonstrate a large reduction of bias for the semiparametric model relative to the parametric model at times where the dropout rate is high or the dropout model is mis-specified. The methodology's practical utility is illustrated in a data analysis.