后向变量选择偏最小二乘法用于近红外光谱定量校正模型的建立

目的:对小麦中蛋白质含量以及橘叶中的橙皮苷含量建立定量校正模型。方法:将原始数据分为校正集、停止集和测试集,考察不同的停止集样本量对删除变量数的影响,并以相关系数与采用传统的偏最小二乘法(PLS)所建立的模型进行对比。结果:使用于建模的变量数分别减少了79%和89%,同时相关系数分别从0.9016和0.7730提高到了0.9306和0.8657。结论:较之于传统的偏最小二乘法,该方法所需用于建模的变量数大大减少,提高了模型的运行速度和预测能力,并且使所建立的模型更富于解释性。     

多变量表征化,设计与分析在分析优化中的应用

本文利用多变量法及偏最小二乘法将化合物化学性质的定量信息与柱子和流动相的定量指标结合起来，建成了可以预测相关的新化合物保留时间的回归模型。     

代谢组学数据处理方法——主成分分析

代谢组学在生命科学领域得到了越来越广泛的应用并展现出良好的前景。代谢组学分析产生的含有大量变量的数据难以用常规方法进行分析,如何正确分析和解释代谢组学的数据是研究的关键。本文主要介绍了在代谢组学数据分析中占主导地位的主成分分析基本方法,旨在加强代谢组学数据分析的基础知识并规范数据分析的方法。     

基于最小二乘支持向量机的大肠癌K-ras基因突变预测

目的探讨利用最小二乘支持向量机模型对大肠癌K-ras基因突变进行预测的可行性。方法首先采用测序法检测90例大肠癌患者癌组织K-ras基因突变情况,继而选取特征变量用最小二乘支持向量机模型进行预测并与测序结果进行比较。结果重复100次的最小二乘支持向量机模型预测发现,训练集的准确率为100%,方差为0;检验集的准确率为79.4%,方差为4.51。结论应用最小二乘支持向量机预测模型预测大肠癌K-ras基因突变是可行的,有助于指导临床诊断、治疗和评价预后。     

基于偏最小二乘回归的红外光谱波段筛选用于甘露醇-氯化钙共晶的定量分析

甘露醇-氯化钙金属有机骨架(MOF)共晶显著改善了β-甘露醇的可压片性,可开发作为新型片剂填充剂,但研究者在该辅料放大生产过程中发现产物中含有甘露醇单体,显著影响辅料的功能特性。本研究拟对甘露醇-氯化钙共晶体系的多组分进行定量研究。实验以MOF共晶辅料甘露醇-氯化钙共晶为模型化合物,采集红外光谱,以偏最小二乘回归(PLSR)为基础,采用去除异常波段、归一化进行光谱预处理,采用遗传算法(GA)和竞争性自适应重加权算法(CARS) 2种不同变量筛选方法筛选关键变量,建立并比较了共晶辅料制备产物中甘露醇-氯化钙MOF共晶含量的定量校正模型。采用GA法和CARS法2种不同变量筛选方法分别筛选出160、14个变量,CARS-PLSR法建立的甘露醇-氯化钙共晶模型具有最佳性能,模型的平均相对误差(MRE)和校正均方根误差(RMSEC)分别为0.008 8和0.892 5,与全光谱模型相比,模型的决定系数(R2)由0.978 3提升为0.994 4。本研究建立的共晶体系定量方法预测精度高、检测速度快、稳定性好,对优化此类共晶辅料制备工艺条件及质量控制方法的研究具有重要意义。     

量化参数在抗HIV黄酮类化合物毒性的构效关系中的应用

目的　定量描述具有抗艾滋病毒HIV活性的33种黄酮类化合物的结构与毒性的构效关系。方法　在B3LYP/ 6 -31G 的水平上计算了该类化合物1 4个量子化学参数,并通过逐步回归分析(SRA)进行变量筛选,得到5个重要的量子化学参数,分别是分子最低空轨道能量(ELUMO)、分子硬度(η)、分子极化率(α)、偶极距(μ)和7号碳原子上的净电荷Q7。然后分别采用主成分回归(PCR)和偏最小二乘回归(PLS)方法,通过留一法交叉验证选择潜变量个数,建立具有较好预测能力的定量构效关系(QSAR)模型。结果　两个模型均具有较好的预测能力,但PLS方法得到的模型优于PCR方法,具有更强的预测能力。结论　从建立的QSAR模型可看出各个参数对其毒性的影响,通过改变取代基可降低其毒性,并指导抗HIV低毒性药物的结构设计和研究开发。     

季节性时间序列资料预测的线性方法

在季节性时间序列资料分析的加法原理基础上，提出了几个线性模型，并指出这些线性模型的适用范围     

常用非线性模型参数估计新方法及应用

提出了非线性模型 y=a· e- kx ,y=k1+a· e- bt两种模型参数估计的简便方法 ,对于基层工作者具有参考价值     

偏最小二乘回归与主成分回归的比较

多元回归的建模与分析中 ,变量间存在多元共线性的现象十分普遍。另外 ,实际工作中由于种种原因会造成自变量个数 p较多而观察时点数 n并不多 ,甚至出现 n相似文献   

回归直线的稳健求法及模拟研究

经典最小二乘法是求直线回归方程的常用方法,但当数据中存在异常值时,这种方法较敏感,本文给出了二类求稳健回归直线的方法,并将它们统一在迭代再加权最小二乘统一算法之下,模拟结果及实例分析表明这些方法在抗异常值方面较最小二乘法为优。     

基于谱-效相关黄芩提取物抑菌药效物质基础及质量评价系统的研究

目的： 建立黄芩提取物抑菌谱-效相关质量评价系统,对其药效物质基础进行分析。方法： 自制黄芩提取物,建立HPLC指纹图谱检测方法;采用微量稀释法测定黄芩提取物样品水提液的抑菌率。利用灰色关联分析、相关分析及偏最小二乘回归分析对谱-效数据进行关联分析,挖掘药效物质基础;同时采用最小二乘支持向量机（LS-SVM）方法建立数学模型。结果： 成分4,7,8,9,10与抑菌率呈正相关关系;相关分析显示,成分3,7,4,5,6,9与抑菌率药效呈（非常）显著的相关关系;偏最小二乘回归分析显示,成分3,4,5,6,7,9的标准化回归系数绝对值较大,VIP值大于或接近于1,对抑菌率贡献率较大;数学模型预测值与实测值相对误差在6%以下。结论： 初步确定黄芩提取物抑菌药效物质基础主要为汉黄芩苷、汉黄芩素以及白杨素-7-O-葡萄糖醛酸苷;数学模型的建立,达到了从抑菌作用评价黄芩提取物质量的目的,并为中药谱-效相关质量评价系统的建立提供了详细的数据支撑。     

Nonlinear perpendicular least-squares regression in pharmacodynamics

Currently available software for nonlinear regression does not account for errors in both the independent and the dependent variables. In pharmacodynamics, measurement errors are involved in the drug concentrations as well as in the effects. Instead of minimizing the sum of squared vertical errors (OLS), a Fortran program was written to find the closest distance from a measured data point to the tangent line of an estimated nonlinear curve and to minimize the sum of squared perpendicular distances (PLS). A Monte Carlo simulation was conducted with the sigmoidal E_max model to compare the OLS and PLS methods. The area between the true pharmacodynamic relationship and the fitted curve was compared as a measure of goodness of fit. The PLS demonstrated an improvement over the OLS by 20·8% with small differences in the parameter estimates when the random noise level had a standard deviation of five for both concentration and effect. Consideration of errors in both concentrations and effects with the PLS could lead to a more rational estimation of pharmacodynamic parameters. © 1997 John Wiley & Sons, Ltd.     

Determination of hydrogen peroxide concentration in antiseptic solutions using portable near-infrared system

Hydrogen peroxide (H₂O₂) concentrations in antiseptic solutions (normally 3% H₂O₂) has been determined non-destructively using a portable near-infrared (NIR) analyzer. The spectral variation due to ---OH band around 1400 nm in the second derivative spectra has been found as H₂O₂ concentration changes. Both multiple linear regression (MLR) and partial least squares (PLS) were employed to generate calibration models over the 1100–1720 nm range. The PLS calibration model showed the better calibration performance with a standard error of prediction (SEP) of 0.16%. In order to validate the developed PLS calibration model, H₂O₂ concentrations in commercial antiseptic solutions were predicted and compared with values from a conventional redox titration method. The results showed that NIR predictions had good correlation with conventional analysis values. The rapid and non-destructive determination of H₂O₂ in the antiseptic solution was successfully performed using portable NIR analyzer without any hazardous chemical solvents.     

Revisiting thin-layer chromatography as a lipophilicity determination tool—A comparative study on several techniques with a model solute set

The lipophilicity of a compound is a fundamental property related to pharmaceutical and biomedical activity. As many approaches are mixed together in every-day published studies, the subject needs some standardization. The paper presents a comparative study on several approaches of TLC lipophilicity determination: a single TLC run, extrapolation of a retention, principal component analysis of a retention matrix, PARAFAC on a three-way array and a PLS regression. All techniques were applied to 35 model solutes with simple molecules, using nine concentrations of six modifiers: acetonitrile, acetone, dioxane, propan-2-ol, methanol and tetrahydrofurane. The elaborated comparative analysis formed several general recommendations. Methanol and dioxane were the best modifiers, while acetonitrile gave the worst and inacceptable correlation of retention with lipophilicity. Surprisingly, good correlations were obtained for the single TLC runs and this method is underestimated in the literature. The advanced chemometric processing proposed recently, such as PCA, PARAFAC and PLS did not show a visible advantage comparing to classical methods. A need to use a robust regression and robust correlation measures, due to presence of significant outliers, was also noticed and studied.     

Pharmacokinetic parameter estimates from several least squares procedures: Superiority of extended least squares

The precision of pharmacokinetic parameter estimates from several least squares parameter estimation methods are compared. The methods can be thought of as differing with respect to the way they weight data. Three standard methods, Ordinary Least Squares (OLS-equal weighting), Weighted Least Squares with reciprocal squared observation weighting [WLS(y^–2)], and log transform OLS (OLS(ln))-the log of the pharmacokinetic model is fit to the log of the observations-are compared along with two newer methods, Iteratively Reweighted Least Squares with reciprocal squared prediction weighting (IRLS,(f^–2)), and Extended Least Squares with power function weighting (ELS(f^–)-here is regarded as an unknown parameter). Tne values of the weights are more influenced by the data with the ELS(f^–) method than they are with the other methods. The methods are compared using simulated data from several pharmacokinetic models (monoexponential, Bateman, Michaelis-Menten) and several models for the observation error magnitude. For all methods, the true structural model form is assumed known. Each of the standard methods performs best when the actual observation error magnitude conforms to the assumption of the method, but OLS is generally least perturbed by wrong error models. In contrast, WLS(y^–2) is the worst of all methods for all error models violating its assumption (and even for the one that does not, it is out performed by OLS(ln). Regarding the newer methods, IRLS(f^–2) improves on OLS(ln), but is still often inferior to OLS. ELS(f^–), however, is nearly as good as OLS (OLS is only 1–2% better) when the OLS assumption obtains, and in all other cases ELS(f^–) does better than OLS. Thus, ELS(f^–.This work supported by NIH Grants GM 26676 and GM 26691.     

基于近红外光谱技术的摩罗丹水提液浓缩过程的多指标快速检测

目的 基于近红外光谱(near infrared spectroscopy,NIR)技术,以芍药内酯苷、芍药苷、密度和固含物为质量控制指标,对摩罗丹水提液的浓缩过程进行快速检测,实现摩罗丹浓缩过程在线质量控制.方法 采集摩罗丹水提液浓缩过程的在线近红外光谱,并收集样本;基于HPLC、烘干法等理化仪器分析方法,测定摩罗丹...     

基于紫外光谱和偏最小二乘回归算法的畲药地稔中浸出物和6种活性成分快速预测方法

目的 建立基于紫外光谱的畲药地稔中浸出物、没食子酸、阿魏酸、芦丁、槲皮素、木犀草素、山奈酚的快速分析方法。方法 测定地稔水提液中的浸出物和6种化合物浓度,采集紫外光谱。采用SIMCA-P+软件,分别建立浸出物、6种化合物浓度与紫外光谱的偏最小二乘回归模型。采用Visual Basic开发应用软件,将所建模型嵌套入软件,为同时快速分析待测溶液中浸出物和6种化合物浓度提供工具。结果 验证集浸出物和6种化合物浓度的预测均方根误差分别为39.1 μg/mL、0.263 μg/mL、19.0 ng/mL、93.8 ng/mL、0.894 ng/mL、0.593 ng/mL、0.896 ng/mL,预测值和真实值的相关系数均>0.9,并通过软件在10 s内得到了浸出物和6种化合物浓度的预测结果。结论 本方法可为地稔的快速质量评价提供依据。     

A note on confidence intervals with extended least squares parameter estimates

It has previously been shown that the extended least squares (ELS) method for fitting pharmacokinetic models behaves better than other methods when there is possible heteroscedasticity (unequal error variance) in the data. Confidence intervals for pharmacokinetic parameters, at the target confidence level of 95%, computed in simulations with several pharmacokinetic and error variance models, using a theoretically reasonable approximation to the asymptotic covariance matrix of the ELS parameter estimator, are found to include the true parameter values considerably less than 95% of the time. Intervals with the ordinary least squares method perform better. Two adjustments to the ELS confidence intervals, taken together, result in better performance. These are: (i) apply a bias correction to the ELS estimate of variance, which results in wider confidence intervals, and (ii) use confidence intervals with a target level of 99% to obtain confidence intervals with actual level closer to 95%. Kineticists wishing to use the ELS method may wish to use these adjustments.     

Applications of NIR in early stage formulation development. Part II. Content uniformity evaluation of low dose tablets by principal component analysis

A near infrared method based on principal component analysis (PCA) was developed for predicting content uniformity of low dose tablets manufactured by a direct compression process. The work was conducted in early stage formulation development. NIR spectra of one hundred and eighty tablets from three feasibility batches were used as the pseudo-calibration set. A correlation was established between PCA scores and a set of reference values obtained by HPLC analysis. The reference values were also used to define a concentration range for the active pharmaceutical ingredient to facilitate content uniformity prediction by PCA. Analyses of unknown samples were conducted by forming a prediction set that included the calibration and unknown samples, followed by PCA. Samples from two development batches were predicted using the PCA model and the results were consistent with the reference HPLC values. Remarkably, the model was able to predict CU for tablets that were prepared using different grades of lactose (anhydrous versus monohydrate). Additionally, during this study, the impact of spectrum pretreatments on PCA is demonstrated. A brief discussion is given to highlight the advantages of PCA over partial least squares (PLS) regression for analysis of samples generated in early stage formulation development.     

Pharmacokinetic parameter estimations by minimum relative entropy method

For estimating pharmacokinetic parameters, we introduce the minimum relative entropy (MRE) method and compare its performance with least squares methods. There are several variants of least squares, such as ordinary least squares (OLS), weighted least squares, and iteratively reweighted least squares. In addition to these traditional methods, even extended least squares (ELS), a relatively new approach to nonlinear regression analysis, can be regarded as a variant of least squares. These methods are different from each other in their manner of handling weights. It has been recognized that least squares methods with an inadequate weighting scheme may cause misleading results (the “choice of weights” problem). Although least squares with uniform weights, i.e., OLS, is rarely used in pharmacokinetic analysis, it offers the principle of least squares. The objective function of OLS can be regarded as a distance between observed and theoretical pharmacokinetic values on the Euclidean space ℝ^N, whereN is the number of observations. Thus OLS produces its estimates by minimizing the Euclidean distance. On the other hand, MRE works by minimizing the relative entropy which expresses discrepancy between two probability densities. Because pharmacokinetic functions are not density function in general, we use a particular form of the relative entropy whose domain is extended to the space of all positive functions. MRE never assumes any distribution of errors involved in observations. Thus, it can be a possible solution to the choice of weights problem. Moreover, since the mathematical form of the relative entropy, i.e., an expectation of the log-ratio of two probability density functions, is different from that of a usual Euclidean distance, the behavior of MRE may be different from those of least squares methods. To clarify the behavior of MRE, we have compared the performance of MRE with those of ELS and OLS by carrying out an intensive simulation study, where four pharmacokinetic models (mono- or biexponential, Bateman, Michaelis-Menten) and several variance models for distribution of observation errors are employed. The relative precision of each method was investigated by examining the absolute deviation of each individual parameter estimate from the known value. OLS is the best method and MRE is not a good one when the actual observation error magnitude conforms to the assumption of OLS, that is, error variance is constant, but OLS always behaves poorly with the other variance models. On the other hand, MRE performs better than ELS and OLS when the variance of observation is proportional to its mean. In contrast, ELS is superior to MRE and OLS when the standard deviation of observation is proportional to its mean. In either case the difference between MRE and ELS is relatively small. Generally, the performance of MRE is comparable to that of ELS. Thus MRE provides as reliable a method as ELS for estimating pharmacokinetic parameters.