Bayesian Generalized Linear Mixed Model And Its Applications In Medical

Repeated measures data are usually obtained from multiple measurements or observation of a response variable, Such multiple measurements are carried out for each experimental unit over time or under multiple conditions, they are famous for saving sample size, easier to collect and effective which are very popular in medical fields. However, as the measurements obtained from the same individual at different times are correlated, we encounter new problems in Statistics.When the response is normal distribution, Linear Mixed Models is used and its theory is mature;When the response is categories , such as the drug efficacy divided into effective and ineffective,or count data such as the number of hypertensives'treatments within a month and so on,we can use Generalized Linear Mixed Models(GLMMs), General Linear Models is the special case of GLMMs.As the likelihood of GLMMs contains N integrals over the q-dimensional random effects,in some special cases ,such as continuous outcomes with normal identify link function, these integrals can be worked out analytically.In general,no analytic expressions are available for the high dimensional integrals and numerical approximations are needed. Currently,the approximate estimation used in GLMMs is Penalized Quasi-Likelihood(PQL)and Marginal Quasi-Likelihood (MQL), However, neither of these parameter estimation methods expose some shortage in practical applications: although MQL is fast,but only consider fixed effect, When the variance of high level is larger and the number of low level is smaller, MQL tends to underestimate the fixed parameters and random parameter; PQL method is able to use the residual of high level and the bias of calculation is smaller,But the algorithm is not stable enough and the convergence is not easy to reach sometimes,and the estimation of high level variance may be biased.To resolve the estimation of GLMMs,we use Bayesian approach which is different from Classical frequency statistics, prior information + sample information is the joint posterior parameter distribution, taking into account the uncertainty of the variance components ,taking the random effects and fixed effects parameters as random variables, drawing samples from the posterior distribution with Markov Monte Carlo method(MCMC), Calculating the estimated parameters of interest.In chapterâ… ,we systematically expound the basic principles of PQL and Bayesian methods in GLMM. In chapterâ…¡, considering GLMMs data which the number of high units is different and the number of low units is small and unbalanced, we Conduct a series of simulations, the simulations show that regardless of the number of the level 2 units,the Bayesian estimate of random effects residual variance is more precise than PQL and the PQL estimation deviates from the true value seriously; In terms of the fixed effects estimates, When the number of level 2 units is 20, The mean and median of the Bayesian estimate is more precise than PQL,But With the number of level 2 units increase,the estimate of two methods is similar. Thus, in practical applications, we recommend the use of Bayesian method. In Chapterâ…¢,with the binary and count repeated measures data which is very common in medical research, we write the programs of Bayesian GLMMs in WinBUGS, describe the Bayesian GLMMs application for repeated measures data and provide a new way for medical research.