A Bayesian Approach of Testing for Serial Homogeneity in the Correlation of Longitudinally Measured Biomarkers

• Activity Number: 341
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Su Chen*+ and Timothy D. Johnson and Thomas M Braun
• Companies: University of Michigan and University of Michigan and University of Michigan
• Keywords: longitudinal study ; Metropolis-Hastings ; posterior p-value ; serial correlation

Abstract

We wish to determine if the pair-wise correlations of time-adjacent longitudinal data are homogeneous and can be pooled into a single time-invariant value. Historically, this hypothesis has been addressed using an asymptotic Wald test. As an alternative, we propose to evaluate whether the correlation between two continuous biomarkers measured at several time points are equal by examining the posterior predictive p-values within the Bayesian paradigm. We decompose the variance/covariance matrix to standard deviation elements and correlation elements and run a Metropolis-Hastings with Gibbs algorithm. A replicated dataset is generated conditional on each draw of parameters, and a "test statistic" is calculated for both the original and replicated dataset, by which the posterior predictive p-value is determined. The performance of our method is examined via simulation studies. We demonstrate our method on a periodontal longitudinal data set.