A SEMIPARAMETRIC BAYESIAN APPROACH TO MULTIVARIATE LONGITUDINAL DATA

We extend the standard multivariate mixed model by incorporating a smooth time effect and relaxing distributional assumptions. We propose a semiparametric Bayesian approach to multivariate longitudinal data using a mixture of Polya trees prior distribution. Usually, the distribution of random effects in a longitudinal data model is assumed to be Gaussian. However, the normality assumption may be suspect, particularly if the estimated longitudinal trajectory parameters exhibit multimodality and skewness. In this paper we propose a mixture of Polya trees prior density to address the limitations of the parametric random effects distribution. We illustrate the methodology by analyzing data from a recent HIV-AIDS study.

[1]  J. Ibrahim,et al.  A Flexible B‐Spline Model for Multiple Longitudinal Biomarkers and Survival , 2005, Biometrics.

[2]  C. G. Khatri,et al.  A note on a manova model applied to problems in growth curve , 1966 .

[3]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[4]  Marie Davidian,et al.  A Semiparametric Likelihood Approach to Joint Modeling of Longitudinal and Time‐to‐Event Data , 2002, Biometrics.

[5]  M. Lavine.  More Aspects of Polya Tree Distributions for Statistical Modelling , 1992 .

[6]  J. Berger,et al.  Bayesian and Conditional Frequentist Testing of a Parametric Model Versus Nonparametric Alternatives , 2001 .

[7]  P. Diggle,et al.  Semiparametric models for longitudinal data with application to CD4 cell numbers in HIV seroconverters. , 1994, Biometrics.

[8]  W. Johnson,et al.  Modeling Regression Error With a Mixture of Polya Trees , 2002 .

[9]  Gregory C. Reinsel,et al.  Estimation and Prediction in a Multivariate Random Effects Generalized Linear Model , 1984 .

[10]  Bani K. Mallick,et al.  Hierarchical Generalized Linear Models and Frailty Models with Bayesian Nonparametric Mixing , 1997 .

[11]  J G Ibrahim,et al.  A semiparametric Bayesian approach to the random effects model. , 1998, Biometrics.

[12]  Paul H. C. Eilers,et al.  Flexible smoothing with B-splines and penalties , 1996 .

[13]  E. Lesaffre,et al.  Smooth Random Effects Distribution in a Linear Mixed Model , 2004, Biometrics.

[14]  T. Hanson.  Inference for Mixtures of Finite Polya Tree Models , 2006 .

[15]  P. O'Brien.  Procedures for comparing samples with multiple endpoints. , 1984, Biometrics.

[16]  S. Lang,et al.  Bayesian P-Splines , 2004 .

[17]  J. Ibrahim,et al.  A Bayesian semiparametric joint hierarchical model for longitudinal and survival data. , 2003, Biometrics.

[18]  S. Chib,et al.  Marginal Likelihood and Bayes Factors for Dirichlet Process Mixture Models , 2003 .

[19]  Victor DeGruttola,et al.  Dual vs single protease inhibitor therapy following antiretroviral treatment failure: a randomized trial. , 2002, JAMA.

[20]  S. Geisser,et al.  A Predictive Approach to Model Selection , 1979 .

[21]  J. Raz,et al.  Semiparametric Stochastic Mixed Models for Longitudinal Data , 1998 .

[22]  J. Ware,et al.  Random-effects models for longitudinal data. , 1982, Biometrics.

[23]  R. Potthoff,et al.  A generalized multivariate analysis of variance model useful especially for growth curve problems , 1964 .

[24]  N. Lazar,et al.  Methods and Criteria for Model Selection , 2004 .

[25]  M Davidian,et al.  Linear Mixed Models with Flexible Distributions of Random Effects for Longitudinal Data , 2001, Biometrics.

[26]  D. M. Allen,et al.  Analysis of growth and dose response curves. , 1969, Biometrics.

[27]  B. Mallick,et al.  A Bayesian Semiparametric Accelerated Failure Time Model , 1999, Biometrics.

[28]  Geert Verbeke,et al.  Pairwise Fitting of Mixed Models for the Joint Modeling of Multivariate Longitudinal Profiles , 2006, Biometrics.

[29]  David A. Schoenfeld,et al.  A Random-Effects Model for Multiple Characteristics with Possibly Missing Data , 1997 .

[30]  Jason Roy,et al.  Analysis of Multivariate Longitudinal Outcomes With Nonignorable Dropouts and Missing Covariates , 2002 .