Pseudo-Bayesian D-optimal designs for longitudinal Poisson mixed models with correlated errors

This paper is concerned with the problem of pseudo-Bayesian D-optimal designs for the first-order Poisson mixed model for longitudinal data with time-dependent correlated errors. A standard approximate covariance matrix of the parameter estimation is obtained based on the quasi-likelihood method. Furthermore, to overcome the dependence of pseudo-Bayesian D-optimal designs on the choice of the prior mean, a hierarchical pseudo-Bayesian D-optimal designs based on the hierarchical prior distribution of unknown parameters is proposed. The results show that the optimal number of time points depends on both the interclass autoregressive coefficients and different cost constraints. The relative efficiency of equidistant designs compared with the hierarchical pseudo-Bayesian D-optimal designs is also discussed.

[1]  Tsung-I Lin,et al.  Multivariate skew-normal at linear mixed models for multi-outcome longitudinal data , 2013 .

[2]  Martijn P. F. Berger,et al.  OPTIMAL ALLOCATION OF TIME POINTS FOR THE RANDOM EFFECTS MODEL , 1999 .

[3]  Anuradha Roy,et al.  Estimating Correlation Coefficient between Two Variables with Repeated Observations using Mixed Effects Model , 2006, Biometrical journal. Biometrische Zeitschrift.

[4]  M. Ghosh,et al.  Design Issues for Generalized Linear Models: A Review , 2006, math/0701088.

[5]  Anthony N. Pettitt,et al.  Simulation-based fully Bayesian experimental design for mixed effects models , 2015, Comput. Stat. Data Anal..

[6]  F. Tekle.  D-optimal designs for prospective cohort studies , 2008 .

[7]  P. McCullagh,et al.  Generalized Linear Models , 1984 .

[8]  S. Zeger,et al.  Longitudinal data analysis using generalized linear models , 1986 .

[9]  Martijn P. F. Berger,et al.  Maximin D-optimal designs for binary longitudinal responses , 2008, Comput. Stat. Data Anal..

[10]  Valerii V. Fedorov,et al.  Optimal Design for Nonlinear Response Models , 2013 .

[11]  William Li,et al.  Model-Robust Factorial Designs , 2000, Technometrics.

[12]  Martijn P. F. Berger,et al.  Bayesian D-optimal designs for the two parameter logistic mixed effects model , 2014, Comput. Stat. Data Anal..

[13]  Keying Ye,et al.  D-optimal designs for Poisson regression models , 2006 .

[14]  G. Molenberghs,et al.  Models for Discrete Longitudinal Data , 2005 .

[15]  R. W. Wedderburn.  Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method , 1974 .

[16]  James M. McGree,et al.  Robust Designs for Poisson Regression Models , 2012, Technometrics.

[17]  Martijn P. F. Berger,et al.  A maximin criterion for the logistic random intercept model with covariates , 2006 .

[18]  I. Ford,et al.  The Use of a Canonical Form in the Construction of Locally Optimal Designs for Non‐Linear Problems , 1992 .

[19]  Rainer Schwabe,et al.  Optimal design for quasi-likelihood estimation in Poisson regression with random coefficients , 2013 .

[20]  Tsai-Hung Fan,et al.  ECM-based maximum likelihood inference for multivariate linear mixed models with autoregressive errors , 2010, Comput. Stat. Data Anal..

[21]  G. Casella,et al.  Statistical Inference , 2003, Encyclopedia of Social Network Analysis and Mining.

[22]  Susan M. Lewis,et al.  D-OPTIMAL DESIGNS FOR POISSON REGRESSION MODELS , 2009 .

[23]  G. Reinsel,et al.  Models for Longitudinal Data with Random Effects and AR(1) Errors , 1989 .

[24]  L C Ward,et al.  Optimal designs for studying bioimpedance , 2007, Physiological measurement.

[25]  K. Fang,et al.  Number-theoretic methods in statistics , 1993 .