Every Missing Not at Random Model for Incomplete Data Has a Missing at Random Counterpart with Equal Fit

• Activity Number: 136
• Type: Invited
• Date/Time: Monday, August 3, 2009 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Geert Molenberghs*+ and Michael G. Kenward and Geert Verbeke and Caroline Beunckens and Cristina Sotto
• Companies: Hasselt University/Katholieke Universiteit Leuven and London School of Hygiene and Tropical Medicine and Katholieke Universiteit Leuven and Hasselt University and Hasselt University
• Keywords: missing data ; sensitivity analysis ; selection model ; missing at random ; missing not at random

Abstract

Many models for incomplete data allow for MNAR. The sensitivity to unverifiable modeling assumptions, has led to several sensitivity analysis proposals. Sensitivity arises because MNAR models are not fully verifiable from the data, rendering the empirical distinction between MNAR MAR impossible, unless one is prepared to accept the posited MNAR model. We show that the empirical distinction between MAR and MNAR is not possible, in the sense that each MNAR model fit to a set of observed data can be reproduced exactly by an MAR counterpart. Such a pair will produce different predictions of the unobserved outcomes. This is true for selection, pattern-mixture, and shared-parameters alike. Specific attention will also be given to the SPM case, since we are able to provide a formal definition of MAR in this case. Methods are illustrated and implications for practice are discussed.