Nonparametric Gaussian Process Models for Censored Longitudinal Data

• Activity Number: 38
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Sujit Ghosh*+ and Liwei Wang
• Companies: North Carolina State University and North Carolina State University
• Keywords: Censored data ; Gaussian process ; Longitudinal data ; Model selection ; Nonparametric Bayes ; Posterior inference

Abstract

In longitudinal studies, repeated measurements may be censored due to various reasons such as detection limits and irregularly observed subject-specific time points. Ignoring censored and missing values often lead to biased inference. Many parametric and semi-parametric methods have been developed over the past decades to analyze irregularly observed censored data. However, often such models are built on an assumed class of Gaussian process with mean and covariance functions that may not be able to approximate the complex relationship between the response and predictors. Within a Gaussian process framework, a flexible non-parametric model is developed that is shown to approximate both the mean and the covariance functions simultaneously using a nested sequence of basis functions. Censored and missing data are properly imputed using the posterior predictive distributions. In order to determine the optimal order of approximation a newly proposed Bayesian model selection criterion for the censored longitudinal model is evaluated in a simulation study, showing a superior performance to other existing criteria. An application to a real data set is provided for illustration.