Pseudo likelihood selection models for nonrandomly missing data.

Abstract

Many standard statistical techniques require balanced data. However, missing data may arise by design or attrition during data collection. Several approaches have been proposed for this problem. Complete-case analysis uses only the cases with all variables observed. This approach is simple but inefficient and generally requires the strong assumption that the complete cases are a random subsample of all cases. Imputation methods impute missing values and then analyze the filled-in data. Many imputation methods require that missingess only depends on the observed data, or the data are missing at random (MAR). Another approach is maximum likelihood, based on a model for the complete data and the conditional distribution of the missing-data mechanism given the complete data. If the missing data are not MAR, the functional form of the mechanism has to be specified, and misspecification of the mechanism often leads to biased estimates. Missing data for longitudinal studies with attrition often have monotone pattern, where the variables can be arranged so that any variable is always equally or less observed than previous variables. In this dissertation, I investigate statistical methods for monotone missing data that provide consistent estimates of the complete-data model parameters for a class of non-MAR mechanisms without specifying the functional form of the mechanism. Within the framework of selection models, a pseudo likelihood method is proposed and illustrated on bivariate incomplete monotone data. This method in turn is extended to general multivariate incomplete monotone data. Statistical properties of this method are developed by theory and simulation, and the application of the method is illustrated on the data set from a Schizophrenia trial.