Mixed-effects models,also called random-effects models,are a regression type of analysis which enables the analyst to not only describe the trend over time within each subject,but also to describe the variation among ...Mixed-effects models,also called random-effects models,are a regression type of analysis which enables the analyst to not only describe the trend over time within each subject,but also to describe the variation among different subjects.Nonlinear mixed-effects models provide a powerful and flexible tool for handling the unbalanced count data.In this paper,nonlinear mixed-effects models are used to analyze the failure data from a repairable system with multiple copies.By using this type of models,statistical inferences about the population and all copies can be made when accounting for copy-to-copy variance.Results of fitting nonlinear mixed-effects models to nine failure-data sets show that the nonlinear mixed-effects models provide a useful tool for analyzing the failure data from multi-copy repairable systems.展开更多
Modelling tree height-diameter relationships in complex tropical rain forest ecosystems remains a challenge because of characteristics of multi-species, multi-layers, and indeterminate age composition. Effective model...Modelling tree height-diameter relationships in complex tropical rain forest ecosystems remains a challenge because of characteristics of multi-species, multi-layers, and indeterminate age composition. Effective modelling of such complex systems required innovative techniques to improve prediction of tree heights for use for aboveground biomass estimations. Therefore, in this study, deep learning algorithm (DLA) models based on artificial intelligence were trained for predicting tree heights in a tropical rain forest of Nigeria. The data consisted of 1736 individual trees representing 116 species, and measured from 52 0.25 ha sample plots. A K-means clustering was used to classify the species into three groups based on height-diameter ratios. The DLA models were trained for each species-group in which diameter at beast height, quadratic mean diameter and number of trees per ha were used as input variables. Predictions by the DLA models were compared with those developed by nonlinear least squares (NLS) and nonlinear mixed-effects (NLME) using different evaluation statistics and equivalence test. In addition, the predicted heights by the models were used to estimate aboveground biomass. The results showed that the DLA models with 100 neurons in 6 hidden layers, 100 neurons in 9 hidden layers and 100 neurons in 7 hidden layers for groups 1, 2, and 3, respectively, outperformed the NLS and NLME models. The root mean square error for the DLA models ranged from 1.939 to 3.887 m. The results also showed that using height predicted by the DLA models for aboveground biomass estimation brought about more than 30% reduction in error relative to NLS and NLME. Consequently, minimal errors were created in aboveground biomass estimation compared to those of the classical methods.展开更多
Ecoregion-based height-diameter models were developed in the present study for Scots pine(Pinus sylves-tris L.)stands in Turkiye and included several ecological factors derived from a pre-existing ecoregional classifi...Ecoregion-based height-diameter models were developed in the present study for Scots pine(Pinus sylves-tris L.)stands in Turkiye and included several ecological factors derived from a pre-existing ecoregional classification system.The data were obtained from 2831 sample trees in 292 sample plots.Ten generalized height–diameter models were developed,and the best model(HD10)was selected according to statistical criteria.Then,nonlinear mixed-effects modeling was applied to the best model.The R2 for the generalized height‒diameter model(Richards function)modified by Sharma and Parton is 0.951,and the final model included number of trees,dominant height,and diameter at breast height,with a random parameter associated with each ecoregion attached to the inverse of the mean basal area.The full model predictions using the nonlinear mixed-effects model and the reduced model(HD10)predictions were compared using the nonlinear sum of extra squares test,which revealed significant differences between ecore-gions;ecoregion-based height–diameter models were thus found to be suitable to use.In addition,using these models in appropriate ecoregions was very important for achieving reliable predictions with low prediction errors.展开更多
A Bayesian analysis of the minimal model was proposed where both glucose and insulin were analyzed simultaneously under the insulin-modified intravenous glucose tolerance test (IVGTT). The resulting model was implemen...A Bayesian analysis of the minimal model was proposed where both glucose and insulin were analyzed simultaneously under the insulin-modified intravenous glucose tolerance test (IVGTT). The resulting model was implemented with a nonlinear mixed-effects modeling setup using ordinary differential equations (ODEs), which leads to precise estimation of population parameters by separating the inter- and intra-individual variability. The results indicated that the Bayesian method applied to the glucose-insulin minimal model provided a satisfactory solution with accurate parameter estimates which were numerically stable since the Bayesian method did not require approximation by linearization.展开更多
Nonlinear mixed-eirects (NLME) modek have become popular in various disciplines over the past several decades.However,the existing methods for parameter estimation imple-mented in standard statistical packages such as...Nonlinear mixed-eirects (NLME) modek have become popular in various disciplines over the past several decades.However,the existing methods for parameter estimation imple-mented in standard statistical packages such as SAS and R/S-Plus are generally limited k) single-or multi-level NLME models that only allow nested random effects and are unable to cope with crossed random effects within the framework of NLME modeling.In t his study,wc propose a general formulation of NLME models that can accommodate both nested and crassed random effects,and then develop a computational algorit hm for parameter estimation based on normal assumptions.The maximum likelihood estimation is carried out using the first-order conditional expansion (FOCE) for NLME model linearization and sequential quadratic programming (SCJP) for computational optimization while ensuring positive-definiteness of the estimated variance-covariance matrices of both random effects and error terms.The FOCE-SQP algorithm is evaluated using the height and diameter data measured on trees from Korean larch (L.olgeiisis var,Chang-paienA.b) experimental plots aa well as simulation studies.We show that the FOCE-SQP method converges fast with high accuracy.Applications of the general formulation of NLME models are illustrated with an analysis of the Korean larch data.展开更多
Nonlinear mixed effects model(NLMEM) is built on the relationship of the fixed and random effects in the regression function.The NLMEM has an obvious comparative advantage in analyzing the longitudinal data,repeated m...Nonlinear mixed effects model(NLMEM) is built on the relationship of the fixed and random effects in the regression function.The NLMEM has an obvious comparative advantage in analyzing the longitudinal data,repeated measures data and multilevel data.Two-level NLMEM is used to analyze the dominant height for Chinese fir (Cunninghamia lanceolata).The authors outline the two-level NLMEM and introduce the parameters estimation method of the model.Based on five common Richard and Logistic models,the mixed model is built.The modeling data are used to calculate and compare with 19 models derived from each based model,and 5 optimal mixed models are built.Compared the 5 optimal mixed models with traditional regression models,it is showed that the two-level NLMEM has a better fitting effect than the regression model.展开更多
This study developed a population pharmacokinetic model for sodium tanshinone IIA sulfonate(STS) in healthy volunteers and coronary heart disease(CHD) patients in order to identify significant covariates for the pharm...This study developed a population pharmacokinetic model for sodium tanshinone IIA sulfonate(STS) in healthy volunteers and coronary heart disease(CHD) patients in order to identify significant covariates for the pharmacokinetics of STS. Blood samples were obtained by intense sampling approach from 10 healthy volunteers and sparse sampling from 25 CHD patients, and a population pharmacokinetic analysis was performed by nonlinear mixed-effect modeling. The final model was evaluated by bootstrap and visual predictive check. A total of 230 plasma concentrations were included, 137 from healthy volunteers and 93 from CHD patients. It was a two-compartment model with first-order elimination. The typical value of the apparent clearance(CL) of STS in CHD patients with total bilirubin(TBIL) level of 10 μmol×L^(–1) was 48.7 L×h^(–1) with inter individual variability of 27.4%, whereas that in healthy volunteers with the same TBIL level was 63.1 L×h^(–1). Residual variability was described by a proportional error model and estimated at 5.2%. The CL of STS in CHD patients was lower than that in healthy volunteers and decreased when TBIL levels increased. The bootstrap and visual predictive check confirmed the stability and validity of the final model. These results suggested that STS dosage adjustment might be considered based on TBIL levels in CHD patients.展开更多
In this article,a partially nonlinear model with random effects is proposed and its new estimation procession is provided.In order to estimate the link function,we propose generalised leastsquare estimate and B-spline...In this article,a partially nonlinear model with random effects is proposed and its new estimation procession is provided.In order to estimate the link function,we propose generalised leastsquare estimate and B-splines estimate methods.Further,we also use the Gauss–Newton methodto construct the estimates of unknown parameters.Finally,we also consider the estimation forthe variance components.The consistency and the asymptotic normality of the estimator will beproved.Simulated and real examples are given to illustrate our proposed methodology,whichshows that our methods give effective estimation.展开更多
Nonlinear mixed effects model（NLMEM） is based on the relationship between the fixed and random effects in the regression function.The NLMEM has a competitive advantage in analyzing repeated measures data,the longitu...Nonlinear mixed effects model（NLMEM） is based on the relationship between the fixed and random effects in the regression function.The NLMEM has a competitive advantage in analyzing repeated measures data,the longitudinal data and multilevel data.This paper chose two kinds of two-level nonlinear mixed model to analyze basal area growth for Chinese Fir（Cunninghamia lanceolata）. Model 1 is a general two-level NLMEM and Model 2 is based on Model 1 to further consider the fixed effects parameters changes with a specific factor. Firstly,through the analysis of these two models, this paper defined the basic model to build the two-level NLMEM.Secondly,665 kinds of models derived from Model 1 and 2 703 kinds of models derived from Model 2 were calculated and compared. The results showed that:for Model 1,there were 57 kinds of models converging,and when the formal parameter b<sub>0</sub> considered the block effects and plot effects,b<sub>1</sub> and b<sub>4</sub> only considered the block effects, the model fitted the best;and for Model 2,there were 24 kinds of model converging,and when the formal parameter bs considered the block effects and plot effects,b<sub>1</sub> only considered block effects and the fixed effects b<sub>0</sub> changed with any level of block level, Model 2 fitted the best.Finally,by comparing the traditional nonlinear regression model,Model 1 and Model 2,the results showed that Model 1 and Model 2 fitted better than the traditional nonlinear regression, and Model 2 was best fitting model.展开更多
文摘Mixed-effects models,also called random-effects models,are a regression type of analysis which enables the analyst to not only describe the trend over time within each subject,but also to describe the variation among different subjects.Nonlinear mixed-effects models provide a powerful and flexible tool for handling the unbalanced count data.In this paper,nonlinear mixed-effects models are used to analyze the failure data from a repairable system with multiple copies.By using this type of models,statistical inferences about the population and all copies can be made when accounting for copy-to-copy variance.Results of fitting nonlinear mixed-effects models to nine failure-data sets show that the nonlinear mixed-effects models provide a useful tool for analyzing the failure data from multi-copy repairable systems.
文摘Modelling tree height-diameter relationships in complex tropical rain forest ecosystems remains a challenge because of characteristics of multi-species, multi-layers, and indeterminate age composition. Effective modelling of such complex systems required innovative techniques to improve prediction of tree heights for use for aboveground biomass estimations. Therefore, in this study, deep learning algorithm (DLA) models based on artificial intelligence were trained for predicting tree heights in a tropical rain forest of Nigeria. The data consisted of 1736 individual trees representing 116 species, and measured from 52 0.25 ha sample plots. A K-means clustering was used to classify the species into three groups based on height-diameter ratios. The DLA models were trained for each species-group in which diameter at beast height, quadratic mean diameter and number of trees per ha were used as input variables. Predictions by the DLA models were compared with those developed by nonlinear least squares (NLS) and nonlinear mixed-effects (NLME) using different evaluation statistics and equivalence test. In addition, the predicted heights by the models were used to estimate aboveground biomass. The results showed that the DLA models with 100 neurons in 6 hidden layers, 100 neurons in 9 hidden layers and 100 neurons in 7 hidden layers for groups 1, 2, and 3, respectively, outperformed the NLS and NLME models. The root mean square error for the DLA models ranged from 1.939 to 3.887 m. The results also showed that using height predicted by the DLA models for aboveground biomass estimation brought about more than 30% reduction in error relative to NLS and NLME. Consequently, minimal errors were created in aboveground biomass estimation compared to those of the classical methods.
基金supported by Scientific Research Projects Management Coordinator of Kastamonu University,under grant number KÜ-BAP01/2019-41.
文摘Ecoregion-based height-diameter models were developed in the present study for Scots pine(Pinus sylves-tris L.)stands in Turkiye and included several ecological factors derived from a pre-existing ecoregional classification system.The data were obtained from 2831 sample trees in 292 sample plots.Ten generalized height–diameter models were developed,and the best model(HD10)was selected according to statistical criteria.Then,nonlinear mixed-effects modeling was applied to the best model.The R2 for the generalized height‒diameter model(Richards function)modified by Sharma and Parton is 0.951,and the final model included number of trees,dominant height,and diameter at breast height,with a random parameter associated with each ecoregion attached to the inverse of the mean basal area.The full model predictions using the nonlinear mixed-effects model and the reduced model(HD10)predictions were compared using the nonlinear sum of extra squares test,which revealed significant differences between ecore-gions;ecoregion-based height–diameter models were thus found to be suitable to use.In addition,using these models in appropriate ecoregions was very important for achieving reliable predictions with low prediction errors.
文摘A Bayesian analysis of the minimal model was proposed where both glucose and insulin were analyzed simultaneously under the insulin-modified intravenous glucose tolerance test (IVGTT). The resulting model was implemented with a nonlinear mixed-effects modeling setup using ordinary differential equations (ODEs), which leads to precise estimation of population parameters by separating the inter- and intra-individual variability. The results indicated that the Bayesian method applied to the glucose-insulin minimal model provided a satisfactory solution with accurate parameter estimates which were numerically stable since the Bayesian method did not require approximation by linearization.
基金The authors would like to thank the Thirteenth Five-year Plan Pioneering project of High Technology Plan of the National Department of Technology (No. 2017YFC0504101)the National Natural Science Foundations of China (Nos. 31470641, 31300534 and 31570628) for the financial support of this study.
文摘Nonlinear mixed-eirects (NLME) modek have become popular in various disciplines over the past several decades.However,the existing methods for parameter estimation imple-mented in standard statistical packages such as SAS and R/S-Plus are generally limited k) single-or multi-level NLME models that only allow nested random effects and are unable to cope with crossed random effects within the framework of NLME modeling.In t his study,wc propose a general formulation of NLME models that can accommodate both nested and crassed random effects,and then develop a computational algorit hm for parameter estimation based on normal assumptions.The maximum likelihood estimation is carried out using the first-order conditional expansion (FOCE) for NLME model linearization and sequential quadratic programming (SCJP) for computational optimization while ensuring positive-definiteness of the estimated variance-covariance matrices of both random effects and error terms.The FOCE-SQP algorithm is evaluated using the height and diameter data measured on trees from Korean larch (L.olgeiisis var,Chang-paienA.b) experimental plots aa well as simulation studies.We show that the FOCE-SQP method converges fast with high accuracy.Applications of the general formulation of NLME models are illustrated with an analysis of the Korean larch data.
文摘Nonlinear mixed effects model(NLMEM) is built on the relationship of the fixed and random effects in the regression function.The NLMEM has an obvious comparative advantage in analyzing the longitudinal data,repeated measures data and multilevel data.Two-level NLMEM is used to analyze the dominant height for Chinese fir (Cunninghamia lanceolata).The authors outline the two-level NLMEM and introduce the parameters estimation method of the model.Based on five common Richard and Logistic models,the mixed model is built.The modeling data are used to calculate and compare with 19 models derived from each based model,and 5 optimal mixed models are built.Compared the 5 optimal mixed models with traditional regression models,it is showed that the two-level NLMEM has a better fitting effect than the regression model.
基金supported by the Science and Technology Commission of Shanghai Municipality(12DZ1930300,12DZ1930302,12DZ1930303)the Weak Discipline Construction Project(No.2016ZB0301–01)the 2016 Key Clinical Program of Clinical Pharmacy of Shanghai Municipal Commission of Health and Family Planning.cdh3
文摘This study developed a population pharmacokinetic model for sodium tanshinone IIA sulfonate(STS) in healthy volunteers and coronary heart disease(CHD) patients in order to identify significant covariates for the pharmacokinetics of STS. Blood samples were obtained by intense sampling approach from 10 healthy volunteers and sparse sampling from 25 CHD patients, and a population pharmacokinetic analysis was performed by nonlinear mixed-effect modeling. The final model was evaluated by bootstrap and visual predictive check. A total of 230 plasma concentrations were included, 137 from healthy volunteers and 93 from CHD patients. It was a two-compartment model with first-order elimination. The typical value of the apparent clearance(CL) of STS in CHD patients with total bilirubin(TBIL) level of 10 μmol×L^(–1) was 48.7 L×h^(–1) with inter individual variability of 27.4%, whereas that in healthy volunteers with the same TBIL level was 63.1 L×h^(–1). Residual variability was described by a proportional error model and estimated at 5.2%. The CL of STS in CHD patients was lower than that in healthy volunteers and decreased when TBIL levels increased. The bootstrap and visual predictive check confirmed the stability and validity of the final model. These results suggested that STS dosage adjustment might be considered based on TBIL levels in CHD patients.
基金This research was supported by the National Natural Science Foundation of China[grant number 11471160],[grant number 11101114],[grant number 11571112]the National Statistical Science Research Key Program of China[grant number 2013LZ45]+1 种基金the Fundamental Research Funds for the Central Universities[grant number 30920130111015]the Jiangsu Provincial Basic Research Program(Natural Science Foundation)[grant number BK20131345]and sponsored by Qing Lan Project.
文摘In this article,a partially nonlinear model with random effects is proposed and its new estimation procession is provided.In order to estimate the link function,we propose generalised leastsquare estimate and B-splines estimate methods.Further,we also use the Gauss–Newton methodto construct the estimates of unknown parameters.Finally,we also consider the estimation forthe variance components.The consistency and the asymptotic normality of the estimator will beproved.Simulated and real examples are given to illustrate our proposed methodology,whichshows that our methods give effective estimation.
文摘Nonlinear mixed effects model（NLMEM） is based on the relationship between the fixed and random effects in the regression function.The NLMEM has a competitive advantage in analyzing repeated measures data,the longitudinal data and multilevel data.This paper chose two kinds of two-level nonlinear mixed model to analyze basal area growth for Chinese Fir（Cunninghamia lanceolata）. Model 1 is a general two-level NLMEM and Model 2 is based on Model 1 to further consider the fixed effects parameters changes with a specific factor. Firstly,through the analysis of these two models, this paper defined the basic model to build the two-level NLMEM.Secondly,665 kinds of models derived from Model 1 and 2 703 kinds of models derived from Model 2 were calculated and compared. The results showed that:for Model 1,there were 57 kinds of models converging,and when the formal parameter b<sub>0</sub> considered the block effects and plot effects,b<sub>1</sub> and b<sub>4</sub> only considered the block effects, the model fitted the best;and for Model 2,there were 24 kinds of model converging,and when the formal parameter bs considered the block effects and plot effects,b<sub>1</sub> only considered block effects and the fixed effects b<sub>0</sub> changed with any level of block level, Model 2 fitted the best.Finally,by comparing the traditional nonlinear regression model,Model 1 and Model 2,the results showed that Model 1 and Model 2 fitted better than the traditional nonlinear regression, and Model 2 was best fitting model.
