Modeling a Repeated Ordered Categorical Response with Penalized Splines Using MCEM

• Activity Number: 499
• Type: Topic Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Sue Welham*+ and James Carpenter and Tu Ho
• Companies: Rothamsted Research and London School of Hygiene and Tropical Medicine and London School of Hygiene and Tropical Medicine
• Keywords: penalised spline ; ordinal data ; Monte-Carlo EM ; simulated maximum likelihood ; longitudinal data

Abstract

Longitudinal ordinal data occurs frequently in practice in many different contexts, such as clinical or agricultural trials where scores are used to summarise several aspects of patient/plant disease. The generic aim of analysis is to model and evaluate the treatment.time interaction. We use the proportional odds model, extended so that progress over time can be described using penalised splines to account for the correlation between the observations. In this representation, the smoothing parameter can be shown to be computationally equivalent to a variance component in the model. To avoid the use of approximations known to give bias in the variance components, we use a Monte-Carlo EM (MCEM) algorithm to obtain provisional parameter estimates. We then refine these provisional estimates using simulated maximum likelihood (SML) to obtain an estimate of the log-likelihood at the maximum.