Protecting against nonrandomly missing data in longitudinal studies

Nonrandomly missing data can pose serious problems in longitudinal studies. We generally have little knowledge about how missingness is related to the data values, and longitudinal studies are often far from complete. Two approaches that have been used to handle missing data--use of maximum likelihood with an ignorable mechanism and direct modeling of the missing data mechanism--have the disadvantage of not giving consistent estimates under important classes of nonrandom mechanisms. We introduce two protective estimators, that is, estimators that retain their consistency over a wide range of nonrandom mechanisms. We compare these protective estimators using longitudinal data from a mental health panel study. We also investigate their robustness to certain departures from normality.