A bidimensional finite mixture model for longitudinal data subject to dropout

• Published in: Statistics in medicine Vol. 37; no. 20; pp. 2998 - 3011
• Main Authors: Spagnoli, Alessandra, Marino, Maria Francesca, Alfò, Marco
• Format: Journal Article
• Language: English
• Published: England Wiley Subscription Services, Inc 10.09.2018
• Subjects: Aged, 80 and over; Algorithms; Cognition Disorders - genetics; Female; Humans; informative missingness; latent variables; Longitudinal Studies; Lost to Follow-Up; Male; Medical research; Mental Status and Dementia Tests; Models, Statistical; Netherlands; nonparametric maximum likelihood; Nonparametric statistics; sensitivity to nonignorability; Netherlands; nonparametric maximum likelihood; sensitivity to nonignorability; latent variables; informative missingness
• ISSN: 0277-6715; 1097-0258; 1097-0258
• DOI: 10.1002/sim.7698

In longitudinal studies, subjects may be lost to follow up and, thus, present incomplete response sequences. When the mechanism underlying the dropout is nonignorable, we need to account for dependence between the longitudinal and the dropout process. We propose to model such a dependence through discrete latent effects, which are outcome‐specific and account for heterogeneity in the univariate profiles. Dependence between profiles is introduced by using a probability matrix to describe the corresponding joint distribution. In this way, we separately model dependence within each outcome and dependence between outcomes. The major feature of this proposal, when compared with standard finite mixture models, is that it allows the nonignorable dropout model to properly nest its ignorable counterpart. We also discuss the use of an index of (local) sensitivity to nonignorability to investigate the effects that assumptions about the dropout process may have on model parameter estimates. The proposal is illustrated via the analysis of data from a longitudinal study on the dynamics of cognitive functioning in the elderly.