Semi-parametric methods of handling missing data in mortal cohorts under non-ignorable missingness

We propose semi-parametric methods to model cohort data where repeated outcomes may be missing due to death and non-ignorable dropout. Our focus is to obtain inference about the cohort composed of those who are still alive at any time point (partly conditional inference). We propose: i) an inverse probability weighted method that upweights observed subjects to represent subjects who are still alive but are not observed; ii) an outcome regression method that replaces missing outcomes of subjects who are alive with their conditional mean outcomes given past observed data; and iii) an augmented inverse probability method that combines the previous two methods and is double robust against model misspecification. These methods are described for both monotone and non-monotone missing data patterns, and are applied to a cohort of elderly adults from the Health and Retirement Study. Sensitivity analysis to departures from the assumption that missingness at some visit t is independent of the outcome at visit t given past observed data and time of death is used in the data application.