Bayesian analysis for mixed-effects model defined by stochastic differential equations

The nonlinear mixed-effects model with stochastic differential equations （SDEs） is used to model the population pharmacokinetic （PPK） data that are extended from ordinary differential equations （ODEs） by adding a stochastic term to the state equation. Compared with the ODEs, the SDEs can model correlated residuals which are ubiquitous in actual pharmacokinetic problems. The Bayesian estimation is provided for nonlinear mixed-effects models based on stochastic differential equations. Combining the Gibbs and the Metropolis-Hastings algorithms, the population and individual parameter values are given through the parameter posterior predictive distributions. The analysis and simulation results show that the performance of the Bayesian estimation for mixed-effects SDEs model and analysis of population pharmacokinetic data is reliable. The results suggest that the proposed method is feasible for population pharmacokinetic data.

Incorporating topographic factors in nonlinear mixed-effects models for aboveground biomass of natural Simao pine in Yunnan,China

A total of 128 Simao pine trees （Pinus kesiya var. langbianensis） from three regions of Pu＇er City, Yunnan Province, People＇s Republic of China, were destructively sampled to obtain tree aboveground biomass （AGB）. Tree variables such as diameter at breast height and total height, and topographical factors such as altitude, aspect of slope, and degree of slope were recorded. We considered the region and site quality classes as the ran- dom-effects, and the topographic variables as the fixed- effects. We fitted a total of eight models as follows： least- squares nonlinear models （BM）, least-squares nonlinear models with the topographic factors （BMT）, nonlinear mixed-effects models with region as single random-effects （NLME-RE）, nonlinear mixed-effects models with site as single random-effects （NLME-SE）, nonlinear mixed-ef- fects models with the two-level nested region and site random-effects （TLNLME）, NLME-RE with the fixed-ef- fects of topographic factors （NLMET-RE）, NLME-SE with the fixed-effects of topographic factors （NLMET-SE）, and TLNLME with the fixed-effects of topographic factors （TLNLMET）. The eight models were compared by modelfitting and prediction statistics. The results showed： model fitting was improved by considering random-effects of region or site, or both. The models with the fixed-effects of topographic factors had better model fitting. According to AIC and BIC, the model fitting was ranked as TLNLME 〉 NLMET-RE 〉 NLME-RE.〉 NLMET-SE 〉 TLNLMET 〉 NLME-SE 〉 BMT 〉 BM. The differences among these models for model prediction were small. The model pre- diction was ranked as TLNLME 〉 NLME-RE 〉 NLME- SE 〉 NLMET-RE 〉 NLMET-SE 〉 TLNLMET 〉 BMT 〉 BM. However, all eight models had relatively high prediction precision （〉90 %）. Thus, the best model should be chosen based on the available data when using the model to predict individual tree AGB.

Frequentist model averaging for linear mixed-effects models

Linear mixed-effects models are a powerful tool for the analysis of longitudinal data. The aim of this paper is to study model averaging for linear mixed-effects models. The asymptotic distribution of the frequentist model average estimator is derived, and a confidence interval procedure with an actual coverage probability that tends to the nominal level in large samples is developed. The two confidence intervals based on the model averaging and based on the full model are shown to be asymptotically equivalent. A simulation study shows good finite sample performance of the model average estimators.