Research On Several Issues Of Experimental Design Of Generalized Linear Mixed Effects Model

Discrete response data is often occurred in public health,medicine,sociology,economics and other fields,such as in the Clinical medicine experiment,the response of whether the medicine is effective,whether it is toxic,and the times of vomiting after taking the medicine is binary or counting type,which is usually modeled by the generalized linear mixed effect models.The generalized linear mixed effects model is generated from the fixed effects model by introducing random effect,which makes the model not only can depicts average trend of the data,but also can describes its structure.In most existing work,given the mixed effects,the responses are assumed to be conditionally independent with each other,then the correlation between the responses will be completely described by the mixed effects.But in fact,when the mixed effects is given for a given individual,there still exist correlation over time.Taking the drug clinical trial for example,in order to study the metabolic process of drugs in the human body,the concentration of the drug in an individual's blood is repeatedly measured for several times,so the responses of these measurements should be correlated.Such data is called longitudinal data,and it is not enough to describe the correlation only by the mixed effects.Compared with mixed effects models,the problem of optimal design under longitudinal data is more complicated.Firstly,expect the random effects,how to model the correlation between repeated measurements,there will be more correlation structure involved in the model.Secondly,the design criterion is related with the fixed effects parameters,as well as the variation components in the mixed effects,and the parameter in the correlation structure.Thirdly,the times of the experiment and the value of the covariate of each individual may be the same or not.Lastly,in the case of multiresponse,the design schedual of each kind of response may be the same or not.The aim of this paper is how to model the longitudinal discrete response data,and how to arrange the experiment scientifically,such that several times of experiment can bring as much statistic information as it can.This paper studies the optimal design and robust design for generalized linear mixed effects models,based on the modeling and analytical method of linear mixed effects models.In addition,an improving method is put forward for the Maximin design criterion and hypercube design criterion based on the num-ber theory,and Poisson mixed effects models are used to illustrate the new method.This paper focuses on investigating the optimal design and robust design of generalized linear models,which includes five respects:?.Optimal designs for Poisson mixed effects models with longitudinal data.The Pseudo-Bayesian D-optimal designs for an one-variable first-order Poisson mixed effect-s model with longitudinal data is considered,which generalizes the results of Niaparast(2010).AR(1)structure is used to model the correlation of longitudinal data,and a standard approximate covariance matrix of the parameter estimations is obtained based on the quasi-likelihood method.To overcome the problem of dependence of Pseudo-Bayesian designs on the choice of prior mean,a hierarchical Pseudo-Bayesian D-optimal designs based on the hierarchical prior distribution of the unknown parameter is proposed.The results show that the optimal number of time points depends both on the interclass autoregressive coefficients and different cost constraints.The relative efficiency of equidistant designs with equally spaced time points is also compared with the hierarchical Pseudo-Bayesian D-optimal designs.?.Opti,mal designs for,multi-response linear,mixed effects,models with longitudinal dataThe problem of the optimal selection and allocation of time points for a multiresponse linear mixed effects model in repeated measures experiments is considered.D-optimal designs for the linear regression model with a random intercept and first order autoregressive serial correlations are computed numerically and compared with designs having equally spaced time points.When the order of the polynomial is known,the D-optimal design is hardly affected by the autocorre-lation coefficient,especially when the serial correlation is large.Under the cost limitation,the difference between the equidistant design and the D-optimal design becomes smaller and smaller,with the increase of number of design points and autocorrelation coefficient.When there is no prior knowledge about the order of the underlying polynomial,if the autocorrelation coefficient is very small,the best choice in terms of efficiency is a D-optimal design for the highest possible relevant order of the polynomial,a design with equally-spaced time points is the second best choice.However,if the autocorrelation coefficient is very large(close to 1),the equidistant design is almost as efficient as the D-optimal design for any assumption of the order of the regression polynomial(expect when the order of regression function is 3).?.Optimal designs for multivariate Logistic mixed models with longitudinal dataThe optimal design problem for multivariate mixed-effects Logistic models with longitudinal data is considered.A decomposition method of the binary outcome and the penalized quasi-likelihood are used to obtain the information matrix.The D-optimality criterion based on the approximate information matrix is minimized under different cost constraints.The results show that the autocorrelation coefficient plays a significant role in the design.To overcome the depen-dence of the D-optimal designs on the unknown fixed-effects parameters,the Pseudo-Bayesian D-optimality criterion is proposed.The relative efficiencies of designs reveal that both the cost ratio and autocorrelation coefficient play an important role in the optimal designs.?,Unbalanced optimal designs for multivariate generalized linear mixed effects models with longitudinal dataThe optimal design problem for multivariate generalized mixed effects models with longitu-dinal data is considered.The response data is a mixed discrete-continuous case,such as the re-sponse data collected in the Aged Related Macular Degeneration Trail.A decomposition method of the binary outcome and the penalized quasi-likelihood are also used to obtain the information matrix.The unbalanced D-optimal design is obtained by the simulated annealing algorithm and two simulation study are carried out to show the effectiveness of our method.The linear cost is also defined for unbalanced design,as well as the D-efficiency.?.A modified,methods on robust design criterion for Poisson mixed effects,modelsThe Maximin optimum design(MMD)and Hypercube design(HClnD)are two robust designs which overcome the problem of design dependence on the unknown parameters.Given the prior knowledge of the fixed effects parameter,a modification of the two robust design criterions for a mixed-effects Poisson regression model is proposed,based on the idea of Number-theoretic methods(NTM).The simulated annealing algorithm is used to find exact designs for the experi-ments,the optimal design is assessed in a more timely manner and efficient using our methodology,compared to locally optimal designs over a space of possible value of fixed parameters.The mean and standard error of the parameter estimations under the optimal designs are also demon-strated.