How to use analysis of variance correctly——an analysis of variance for the univariate quantitative data collected from the nested design / 四川精神卫生

The purpose of this paper was to introduce the nested design and its quantitative data analysis of variance and the SAS implementation. If one of the following two characteristics existed in a specific experimental study， a nested design could be considered to arrange the experiment. Firstly， there was a nested relationship between factors in natural attributes. Secondly， with professional knowledge as the basis， the impact of each factor on the quantitative observation results was divided into primary and secondary. The first feature mentioned above meant that the factors related to the subjects had the conditions for grouping and regrouping. The second feature mentioned above meant that the status of each factor was unequal. In the variance analysis of quantitative data， the calculation formulas of variable error mean square was required to use. Based on four examples and with the help of the SAS software， this paper implemented the univariate analysis of variance for the quantitative data of the nested design， and gave the detailed explanations for the output results of SAS software.

Characterization of circadian blood pressure patterns using non-linear mixed effects modeling

Characterizing the time course of baseline or pre-drug blood pressure is important in acquiring unbiased estimates of antihypertensive drug effect. In this study, we recruited 23 healthy male volunteers and measured systolic (SBP) and diastolic blood pressure (DBP) over 24 hours on an hourly basis. Using a non-linear mixed effects model, circadian rhythm observed in blood pressure measurements was described by incorporating two cosine functions with periods 24 and 12 hours. A mixture model was applied to identify subgroups exhibiting qualitatively different circadian rhythms. Our results suggested that 78% of the study population, defined as ‘dippers’, demonstrated a typical circadian profile with a morning rise and a nocturnal dip. The remaining 22% of the subjects defined as ‘non-dippers’, however, were not adequately described using the typical profile and demonstrated an elevation of blood pressure during night-time. Covariate search identified weight as being positively correlated with mesor of SBP. Visual predictive checks using 1,000 simulated datasets were performed for model validation. Observations were in agreement with predicted values in ‘dippers’, but deviated slightly in ‘non-dippers’. Our work is expected to serve as a useful reference in assessing systematic intra-day blood pressure fluctuations and antihypertensive effects as well as assessing drug safety of incrementally modified drugs.

Lower clearance of sodium tanshinone IIA sulfonate in coronary heart disease patients and the effect of total bilirubin: a population pharmacokinetics analysis / 中国天然药物

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 was 48.7 L(h with inter individual variability of 27.4%, whereas that in healthy volunteers with the same TBIL level was 63.1 L(h. 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.

Association between 7-year Changes in Intraocular Pressure and Systemic Factors in Koreans: A Longitudinal Study

PURPOSE: To investigate the changes in intraocular pressure (IOP) and associated systemic factors over 7 years in a healthy Korean population. METHODS: This longitudinal study included healthy subjects with no history of ocular disease and who had been receiving health examinations seven years apart at the Konkuk University Medical Center, Healthcare Center. The participants completed lifestyle questionnaires and underwent general health examinations (blood pressure, height and weight, and blood biochemical tests) and ocular examinations including noncontact tonometry and fundus photography. Subjects with abnormal fundus photography findings and ocular hypertension were excluded. Changes in IOP and systemic factors over 7 years were analyzed. RESULTS: Of 524 possible subjects, 469 were enrolled (55 subjects were excluded: 50 due to abnormal fundus photography and 5 for missing data). The left eye was analyzed in all patients. In all subjects, initial IOP (mean 14.50 ± 3.14 mmHg) was not significantly different from final IOP (14.72 ± 3.38 mmHg) (paired t-test, p = 0.074). In male patients, the final IOP was significantly higher than the initial IOP (paired t-test, p = 0.035). Lifestyle questionnaire variables were associated with a final IOP that was significantly higher than the initial IOP (smokers, alcohol drinkers and less exercisers, paired t-test; p = 0.014, 0.010 and 0.024, respectively). A linear mixed-effects model analysis showed that the change in IOP was negatively associated with age, but this was not statistically significant. Changes in systolic blood pressure (SBP), body mass index (BMI), total cholesterol (T.Chol) and low density lipoprotein (LDL) were positively correlated with change in IOP. CONCLUSIONS: A linear mixed-model analysis showed IOP decreased with age but this was not statistically significant. Changes in SBP, BMI, T.Chol and LDL were significantly positively correlated with change in IOP.

Bioequivalence data analysis for the case of separate hospitalization

A bioequivalence study is usually conducted with the same-day drug administration. However, hospitalization is occasionally separated for logistical, operational, or other reasons. Recently, there was a case of separate hospitalization because of difficulties in subject recruitment. This article suggests a better way of bioequivalence data analysis for the case of separate hospitalization. The key features are (1) considering the hospitalization date as a random effect than a fixed effect and 2) using “PROC MIXED” instead of “PROC GLM” to include incomplete subject data.

Population Pharmacokinetics of Isoniazid in Chinese Tuberculosis Patients / 中国药学杂志

OBJECTIVE: To characterize the population pharmacokinetics of isoniazid in Chinese tuberculosis patients. METHODS: A total of 321 serum samples were obtained from 201 patients receiving oral doses of isoniazid. The effects of 16 covariates including demographics and blood tests to isoniazid's pharmacokinetics were evaluated. Data analysis was performed using non-linear mixed effects modeling (NONMEM). Prediction-corrected visual prediction check was performed for model evaluation. RESULTS: A two-compartment model with first-order absorption and linear elimination can well fit the isoniazid concentration-time data. A "MIXTURE" model was used to separate the subpopulation of 'subgroup A' and 'subgroup B'. Typical clearance of the two subpopulations were 82.7 and 19.3 L·h-1, respectively. CONCLUSION: Model validation shows the final model is reliable, which could be used for individualized treatment.

Joint Modeling of Multivariate Longitudinal Data and Its Application / 世界科学技术-中医药现代化

Multiple outcomes measured repeatedly for the same subject are common in longitudinal observation.If we use the approach by analyzing each outcome separately,it may lead to wrong conclusions due to the failure of accounting for joint evolution of different outcomes.To adequately capture the interdependence among multiple outcomes,we proposed a joint modeling for multivariate longitudinal data by constructing a linear mixed-effects model for each outcome and accommodating the relationship among multiple outcomes through correlation in random effects.Maximum likelihood method was adopted to estimate parameters in this model.The application of this method was demonstrated through the analysis of stroke data.

ROC Curve Based on Generalized Linear Mixed Effects Models in Repeated Diagnostic Tests / 中国卫生统计

Objective To investigate the impact of covariates on diagnostic test and assess the correlation between re-peated measurement data,this paper explores innovative modeling techniques of ROC curve.Methods We introduce the new ROC curve method based on generalized linear mixed effects model and apply Bayesian techniques to parameters estimation with Winbugs Software.Further,areas under the ROC curve(AUC)with different values of covariates could be calculated in terms of assessment.Results Cases analysis results indicate the proposed method efficiently explores the repeated measurement data and provides parameters with practical significance,serving as a golden reference.Conclusion The ROC curve based on generalized linear mixed effects models can be effectively used to solve the test accuracy evaluation problem of the repeated diagnostic trials.

Population pharmacokinetics and inter-laboratory variability of sildenafil and its metabolite after oral administration in Korean healthy male volunteers

This study was to clarify population pharmacokinetics (PK) of sildenafil and its metabolite, N-desmethyl sildenafil (NDS) in Korean healthy male population using a pooled data from multiple clinical trials in consideration of inter-institution and inter-laboratory difference. A population PK analysis was performed with data of 243 healthy volunteers from five single-center (4 centers) comparative PK trials. The dataset included 7,376 sildenafil and NDS concentration (3,688 for each analyte) observed during 24 hours after the single dose of original sildenafil (either 50 mg or 100 mg of Viagra®). The plasma concentration was assayed in two laboratories. Various model structure was tested and the final model was evaluated using visual predictive checks. Demographic and clinical variables were assessed as potential covariates for PK parameters. A one-compartment first-order elimination model with proportional error was selected for the dispositional characteristics of sildenafil, and two-compartment model was chosen for NDS. Three transit compartments with Erlang-type absorption for fast absorption pathway and one compartment for slow absorption pathway constructed overall absorption model. The first-pass effect was rejected since it does not improve the model. The difference of NDS level by the bioanalysis laboratory was selected as the only covariate. Even though a direct comparison was difficult, the general trend in PK of sildenafil and NDS for Korean healthy male was considered similar to that of the other populations reported previously. It is recommended that the laboratory effect should be explored and evaluated when dataset is built using results from several laboratories.

Modeling of the Parathyroid Hormone Response after Calcium Intake in Healthy Subjects

Plasma ionized calcium (Ca2+) concentrations are tightly regulated in the body and maintained within a narrow range; thus it is challenging to quantify calcium absorption under normal physiologic conditions. This study aimed to develop a mechanistic model for the parathyroid hormone (PTH) response after calcium intake and indirectly compare the difference in oral calcium absorption from PTH responses. PTH and Ca2+ concentrations were collected from 24 subjects from a clinical trial performed to evaluate the safety and calcium absorption of Geumjin Thermal Water in comparison with calcium carbonate tablets in healthy subjects. Indirect response models (NONMEM Ver. 7.2.0) were fitted to observed Ca2+ and PTH data, respectively, in a manner that absorbed but unobserved Ca2+ inhibits the secretion of PTH. Without notable changes in Ca2+ levels, PTH responses were modeled and used as a marker for the extent of calcium absorption.

Standard Error of Empirical Bayes Estimate in NONMEM(R) VI

The pharmacokinetics/pharmacodynamics analysis software NONMEM(R) output provides model parameter estimates and associated standard errors. However, the standard error of empirical Bayes estimates of inter-subject variability is not available. A simple and direct method for estimating standard error of the empirical Bayes estimates of inter-subject variability using the NONMEM(R) VI internal matrix POSTV is developed and applied to several pharmacokinetic models using intensively or sparsely sampled data for demonstration and to evaluate performance. The computed standard error is in general similar to the results from other post-processing methods and the degree of difference, if any, depends on the employed estimation options.

La modelación jerárquica y los efectos de grupo en la predicción del rendimiento académico / The hierarchical modelling and the group effects in the prediction of academic performance

El presente trabajo se realizó con el propósito de mostrar que el grupo es un modificador de la relación entre el rendimiento académico y sus predictores y con ello, fundamentar la necesidad de recurrir a la modelación jerárquica para la predicción del rendimiento. Se aplicaron modelos con coeficientes aleatorios, especialmente apropiados para la circunstancia frecuente de casos agrupados, en la que los supuestos usuales de los modelos lineales ordinarios dejan de ser válidos y los modelos clásicos, inaplicables. Se constató que algunos de los predictores tradicionales tenían relevancia condicionada al grupo, aunque no parecían tener relevancia marginal. Se demostró así que el grupo es un modulador de la relación entre el rendimiento académico y algunos de sus predictores. La consecuencia de mayor trascedencia fue que la asignación de un estudiante a un grupo podía influir considerablemente en su rendimiento académico, independientemente de sus condiciones iniciales

The present paper was aimed at demonstrating that the group acts as a modifier of the relation between the academic performance and its predictors, and at founding the need of resorting to hierarchical modelling to predict this performance. Models with randomized coefficients, specially appropriate for the frequent circumstance of grouped cases, where the suppossed ordinary lineal models are not valid anymore and the classical models are unapplicable, were applied. It was proved that some of the traditonal predictors were relevant according to the group, though they did not seem to have marginal relevancy. This way, it was demonstrated that the group was a modullator of the relation between academic performance and some of its predictors. The most significant consequence was that the assignation of a student to a group may influence considerably on his academic performance, independently of its initial conditions.