A Mallows Mixture Model for Event Sequences: Application to Partially Ranked Data

• Activity Number: 253
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Laurel Beckett*+ and Erik Gregory
• Companies: University of California at Davis and University of California at Davis
• Keywords: Mallows model ; cross-sectional data ; event sequence ; Alzheimer's disease ; partially ranked data

Abstract

We consider a situation where k events occur over time in a person-specific sequence, R. Mallows (1957) proposed a parametric model for the distribution of the vector R on the set of all possible permutations. We have previously developed methods for fitting Mallows's model to partially ranked sequences (Smith 1991); such sequences arise in cross-sectional studies where all that is known is whether an event has already occurred or not. Mallows's model has also been extended to a finite mixture model (Murphy 2003). We combine these ideas to estimate finite mixture models with partially-ranked data. We apply our model to data from the Alzheimer's Disease Neuroimaging Initiative (Mueller 2005) to examine consistency with the event sequence proposed by Jack (2010) for onset of Alzheimer's disease, compared with an alternative model that dementia onset may have a mixture of time course sequences.