The application of robust calibration to radioimmunoassay.

The minute concentrations of many biochemically and clinically important substances are currently estimated by radioimmunoassay (RIA). Traditionally, the most popular approaches to the statistical analysis of RIA data have been to linearize the data through transformation and fit the calibration curve using least squares or to directly fit a nonlinear calibration curve using least squares. Estimates of the hormone concentration in patients are then obtained using this curve. Unfortunately, the transformation is frequently unsuccessful in linearizing the data. Furthermore, the least squares fit can lead to erroneous results in both approaches since the many sources of error which exist in the RIA process often result in outlier observations. In this paper, an approach to the analysis of RIA data which incorporates robust estimation methods is described. An algorithm is presented for obtaining the M-estimates of nonlinear calibration curves. The curves to be fitted are modified hyperbolae based on 12 to 16 observations. A procedure, based on the application of the Bonferroni Inequality, is presented for obtaining tolerance-like interval estimates of the concentration of the hormone of interest in the patients. Results of simulations are cited to support the method of construction of confidence bands for the fitted calibration curve. Data obtained from the Veteran's Hospital, Buffalo, New York are used to illustrate the application of the algorithm which is presented.     

Order-restricted inference for clustered ROC data with application to fingerprint matching accuracy

Receiver operating characteristic (ROC) curve is commonly used to evaluate and compare the accuracy of classification methods or markers. Estimating ROC curves has been an important problem in various fields including biometric recognition and diagnostic medicine. In real applications, classification markers are often developed under two or more ordered conditions, such that a natural stochastic ordering exists among the observations. Incorporating such a stochastic ordering into estimation can improve statistical efficiency (Davidov and Herman, 2012). In addition, clustered and correlated data arise when multiple measurements are gleaned from the same subject, making estimation of ROC curves complicated due to within-cluster correlations. In this article, we propose to model the ROC curve using a weighted empirical process to jointly account for the order constraint and within-cluster correlation structure. The algebraic properties of resulting summary statistics of the ROC curve such as its area and partial area are also studied. The algebraic expressions reduce to the ones by Davidov and Herman (2012) for independent observations. We derive asymptotic properties of the proposed order-restricted estimators and show that they have smaller mean-squared errors than the existing estimators. Simulation studies also demonstrate better performance of the newly proposed estimators over existing methods for finite samples. The proposed method is further exemplified with the fingerprint matching data from the National Institute of Standards and Technology Special Database 4.     

Quantification of riboflavin in human urine using high performance liquid chromatography-tandem mass spectrometry

We developed a selective method to measure riboflavin in human urine. Sample preparation involved solid phase extraction and concentration of the target analyte in urine. The urine concentrate was analyzed using high performance liquid chromatography-tandem mass spectrometry. Riboflavin concentrations were quantified using an isotopically labeled internal standard. The limit of detection was 11 ng/mL, and the linear range was 4.4-20,000 ng/mL. The relative standard deviation at 100, 1000, and 5000 ng/mL was 17%, 17%, and 12%, respectively. The accuracy was 90%. On average, 100 samples, including calibration standards and quality control samples, were prepared per day. Using our method, we measured concentrations of riboflavin in human urine samples that were collected from participants in a study where riboflavin was used as a surrogate chemical to simulate exposure to an environmental toxicant.     

Evaluation of absolute peptide quantitation strategies using selected reaction monitoring

The use of internal peptide standards in selected reaction monitoring experiments enables absolute quantitation. Here, we describe three approaches addressing calibration of peptide concentrations in complex matrices and assess their performance in terms of trueness and precision. The simplest approach described is single reference point quantitation where a heavy peptide is spiked into test samples and the endogenous analyte quantified relative to the heavy peptide internal standard. We refer to the second approach as normal curve quantitation. Here, a constant amount of heavy peptide and a varying amount of light peptide are spiked into matrix to construct a calibration curve. This accounts for matrix effects but due to the presence of endogenous analyte, it is usually not possible to determine the lower LOQ. We refer to the third method as reverse curve quantitation. Here, a constant amount of light peptide and a varying amount of heavy peptide are spiked into matrix to construct a calibration curve. Because there is no contribution to the heavy peptide signal from endogenous analyte, it is possible to measure the equivalent of a blank sample and determine LOQ. These approaches are applied to human plasma samples and used to assay peptides of a set of apolipoproteins.     

Statistical survey of “saturation analysis” calibration curve data for prednisolone,prednisone and digoxin

An extensive survey of radioimmunoassay calibration data for prednisolone, prednisone and digoxin indicated that the common practice of preparing calibration curves with individual subject's pre-dose plasma or serum, and using this to estimate unknown concentrations for the same subject, is not supported by statistical considerations. Preparation of calibration plots from pooled data is better because this introduces less bias in estimated concentrations. Such a method also saves a great deal of time, since it is not necessary to repeat the calibration procedure each time “unknowns” are being assayed. The data suggest that there is no optimum calibration plot for all radioimmunoassays. Rather, each antibody-drug combination should be investigated thoroughly to determine the best calibration plot for the particular combination. We found that the best calibration plots are; the logistic-logarithmic plot for prednisolone; nonlinear least squares fit to a polyexponential equation for prednisone; and a weighted least squares regression of normalized % bound $\text{versus}$ concentration for digoxin. The error in the radioimmunoassay is usually concentration-dependent, and, in certain regions of the standard curve, is larger than the literature indicates, since, frequently, the error has been gauged from % bound values, but should be gauged from inversely-estimated concentrations.     

Dexamethasone quantification in dried blood spot samples using LC-MS: The potential for application to neonatal pharmacokinetic studies

A high-performance liquid chromatography (LC-MS) method has been developed and validated for the determination of dexamethasone in dried blood spot (DBS) samples. For the preparation of DBS samples whole blood spiked with analyte was used to produce 30μl blood spots on specimen collection cards. An 8mm disc was cut from the DBS sample and extracted using a combination of methanol: water (70:30, v/v) containing the internal standard, triamcinolone acetonide. Extracts were centrifuged and chromatographic separation was achieved using a Zorbax Eclipse Plus C18 column using gradient elution with a mobile phase of acetonitrile and water with formic acid at a flow rate of 0.2ml/min. LC-MS detection was conducted with single ion monitoring using target ions at m/z 393.1 for dexamethasone and 435.1 for the internal standard. The developed method was linear within the tested calibration range of 15-800ng/ml. The overall extraction recovery of dexamethasone from DBS samples was 99.3% (94.3-105.7%). The accuracy (relative error) and precision (coefficient of variation) values were within the pre-defined limits of ≤15% at all concentrations. Factors with potential to affect drug quantification measurements such as blood haematocrit, the volume of blood applied onto the collection card and spotting device were investigated. Although a haematocrit related effect was apparent, the assay accuracy and precision values remained within the 15% variability limit with fluctuations in haematocrit of ±5%. Variations in the volume of blood spotted did not appear to affect the performance of the developed assay. Similar observations were made regarding the spotting device used. The methodology has been applied to determine levels of dexamethasone in DBS samples collected from premature neonates. The measured concentrations were successfully evaluated using a simple 1-compartment pharmacokinetic model. Requiring only a microvolume (30μl) blood sample for analysis, the developed assay is particularly suited to pharmacokinetic studies involving paediatric populations.     

Dose-response curve estimation: a semiparametric mixture approach

In the estimation of a dose-response curve, parametric models are straightforward and efficient but subject to model misspecifications; nonparametric methods are robust but less efficient. As a compromise, we propose a semiparametric approach that combines the advantages of parametric and nonparametric curve estimates. In a mixture form, our estimator takes a weighted average of the parametric and nonparametric curve estimates, in which a higher weight is assigned to the estimate with a better model fit. When the parametric model assumption holds, the semiparametric curve estimate converges to the parametric estimate and thus achieves high efficiency; when the parametric model is misspecified, the semiparametric estimate converges to the nonparametric estimate and remains consistent. We also consider an adaptive weighting scheme to allow the weight to vary according to the local fit of the models. We conduct extensive simulation studies to investigate the performance of the proposed methods and illustrate them with two real examples.     

A Bayesian method for calculating real-time quantitative PCR calibration curves using absolute plasmid DNA standards

Background  

In real-time quantitative PCR studies using absolute plasmid DNA standards, a calibration curve is developed to estimate an unknown DNA concentration. However, potential differences in the amplification performance of plasmid DNA compared to genomic DNA standards are often ignored in calibration calculations and in some cases impossible to characterize. A flexible statistical method that can account for uncertainty between plasmid and genomic DNA targets, replicate testing, and experiment-to-experiment variability is needed to estimate calibration curve parameters such as intercept and slope. Here we report the use of a Bayesian approach to generate calibration curves for the enumeration of target DNA from genomic DNA samples using absolute plasmid DNA standards.     

Bayesian analysis of serial dilution assays

In a serial dilution assay, the concentration of a compound is estimated by combining measurements of several different dilutions of an unknown sample. The relation between concentration and measurement is nonlinear and heteroscedastic, and so it is not appropriate to weight these measurements equally. In the standard existing approach for analysis of these data, a large proportion of the measurements are discarded as being above or below detection limits. We present a Bayesian method for jointly estimating the calibration curve and the unknown concentrations using all the data. Compared to the existing method, our estimates have much lower standard errors and give estimates even when all the measurements are outside the "detection limits." We evaluate our method empirically using laboratory data on cockroach allergens measured in house dust samples. Our estimates are much more accurate than those obtained using the usual approach. In addition, we develop a method for determining the "effective weight" attached to each measurement, based on a local linearization of the estimated model. The effective weight can give insight into the information conveyed by each data point and suggests potential improvements in design of serial dilution experiments.     

Environmental factors influencing the relationship between optical density and cell count for Listeria monocytogenes

AIMS: The effect of temperature (2-30 degrees C), pH (4.8-7.4) and water activity (0.946-0.995) on the relationship between optical density (OD) at 600 nm and the plate count (CFU ml(-1)) was investigated for Listeria monocytogenes. METHODS AND RESULTS: Calibration curves, relating OD with plate counts, were collected by measuring the OD of consecutive one-half dilution series, before determining the cell density by classic plate count methods. The calibration curves were observed to be shifting in a parallel way, with increasing stress levels. Especially pH influenced the curve in a great extent, while the other variables were showing more synergetic effects. The reason for the shift was investigated by a microscopic viability test, showing a viability decrease with increasing stress levels, causing the shift of the calibration curve. In a last step a model was made describing the effect of environmental factors on the calibration curve, with different data transformations being tested. A polynomial equation was fitted to the data, taking into account a set of constraints to incorporate microbiological knowledge in the black box model. Hence, illogical interpolation results and overfitting of the data could be avoided. CONCLUSIONS: Different stress factors are affecting the relationship between the OD and the cell count of L. monocytogenes by lowering the cell viability. These effects could be modelled using a constrained polynomial model. SIGNIFICANCE AND IMPACT OF THE STUDY: The observed phenomena are important when calculating growth parameters, like growth rate and lag phase, based on OD data.     

Error in oxygen measurements in open systems owing to oxygen consumption in unstirred layer

When a steady-state oxygen concentration is measured with a membrane-covered probe in an open system, the oxygen consumption in the unstirred layer gives rise to an error of measurement whose seriousness depends on the kinetics of the oxygen-consuming process. First-order oxygen consumption in the sample causes a proportional reduction in the signal so that the calibration in curve remains linear. A zeroth-order process causes the calibration curve to be offset from the origin, but it remains linear. Oxygen consumption according to the Michaelis–Menten equation causes the calibration curve to become nonlinear with the maximum deviation at the lower end of the scale. The error determines a lower limit for usefulness of membrane-covered probes. Steady-state kinetics at oxygen concentrations in the order of K_M cannot be determined with a membrane-covered probe for enzyes with K_M for oxygen lower than 0.01μM. In a dense culture of respiring microorganisms, no oxygen will reach the probe when the bulk concentration of oxygen is in the order of K_M.     

Analysis of longitudinal count data with serial correlation

We propose a state space model for analyzing equally or unequally spaced longitudinal count data with serial correlation. With a log link function, the mean of the Poisson response variable is a nonlinear function of the fixed and random effects. The random effects are assumed to be generated from a Gaussian first order autoregression (AR(1)). In this case, the mean of the observations has a log normal distribution. We use a combination of linear and nonlinear methods to take advantage of the Gaussian process embedded in a nonlinear function. The state space model uses a modified Kalman filter recursion to estimate the mean and variance of the AR(1) random error given the previous observations. The marginal likelihood is approximated by numerically integrating out the AR(1) random error. Simulation studies with different sets of parameters show that the state space model performs well. The model is applied to Epileptic Seizure data and Primary Care Visits Data. Missing and unequally spaced observations are handled naturally with this model.     

三次设计结合模矢法拟合Logistic曲线的研究

Ｌｏｇｉｓｔｉｃ曲线是种群动态的一个经典模型,针对传统拟合方法存在的缺陷和三次设计的优点,以及拟合过程是离差平方和最小──可看作是运筹学中无约束极值问题──的优化原则,本文提出新的方法－三次设计结合模大法的组合方法来拟合,结果表明该法能取长补短,拟合效果最佳,因此在一般非线性模型参数求解中具有普遍意义．     

Compact optical microfluidic uric acid analysis system

We designed, fabricated and tested a novel compact fluorescence analysis system for quantification of uric acid (UA) in clinical samples at the point-of-care. To perform an analysis, diluted saliva, urine or blood samples are simply placed in a disposable thin-film sample holder using a dropper. A new enzyme immobilization technique was developed to retain within the sample holder two enzymes and a molecule, which transforms into a fluorescer in amounts depending on the UA concentration. The small instrument (7.5 cm × 5 cm × 5 cm) into which the sample holder is placed for analysis contains an LED, a narrow-band filter and an amplified photodiode. The analysis time is 30s, and the dynamic range of the system is 4-400 μM of UA. The calibration curve for transparent saliva and urine was made using solutions of UA. The calibration curve for opaque blood was obtained with spiked samples of blood. The three different types of clinical samples were collected from three subjects and simply diluted before their measurements. Analysis with our instrument yielded UA concentrations within the expected concentration ranges. Development of instruments based on the current laboratory prototype is expected to result in products for clinical trials and point-of-care.     

废水中类固醇物质的LCMSMS检测方法优化及其在养殖废水检测中的应用

以固相萃取为预处理手段,用高效液相色谱 串联四极杆质谱联用技术,针对澳大利亚南威尔士州畜牧业废水中的丙酸睾酮等13种类固醇化合物含量建立了分析方法.采用大气压化学电离源,在正离子模式下,对色谱条件和质谱条件进行优化,其中,丙酸睾酮等7种化合物以质子化的准分子离子峰［M+H］⁺、另6种化合物以产生了脱去水的离子峰［M+H-H₂O］⁺为母离子进行二级质谱扫描,以最大丰度确定定量离子对.结果表明：该方法所建立的13种化合物的9点标准曲线的线性相关范围为1～1000 ng·ml^-1,在该范围内,相关系数均>0.9990;各化合物的平均回收率在83.75%～111.50%,相对标准差2.02%～14.21%;除美雌醇和雌三醇的灵敏度相对较低,检测限高于15 ng·ml^-1外,其余物质的检测限均低于5 ng·ml^-1;实际样品测定时,不同处理流程中各化合物的浓度均能得到较好体现,该方法能满足检测要求.     

Validation of chemometric models for the determination of deoxynivalenol on maize by mid-infrared spectroscopy

Validation methods for chemometric models are presented, which are a necessity for the evaluation of model performance and prediction ability. Reference methods with known performance can be employed for comparison studies. Other validation methods include test set and cross validation, where some samples are set aside for testing purposes. The choice of the testing method mainly depends on the size of the original dataset. Test set validation is suitable for large datasets (>50), whereas cross validation is the best method for medium to small datasets (<50). In this study the K-nearest neighbour algorithm (KNN) was used as a reference method for the classification of contaminated and blank corn samples. A Partial least squares (PLS) regression model was evaluated using full cross validation. Mid-Infrared spectra were collected using the attenuated total reflection (ATR) technique and the fingerprint range (800–1800 cm⁻¹) of 21 maize samples that were contaminated with 300 – 2600 μg/kg deoxynivalenol (DON) was investigated. Separation efficiency after principal component analysis/cluster analysis (PCA/CA) classification was 100%. Cross validation of the PLS model revealed a correlation coefficient of r=0.9926 with a root mean square error of calibration (RMSEC) of 95.01. Validation results gave an r=0.8111 and a root mean square error of cross validation (RMSECV) of 494.5 was calculated. No outliers were reported. Presented at the 25^th Mykotoxin Workshop in Giessen, Germany, May 19–21, 2003     

Nondestructive near-infrared spectroscopic measurement of multiple analytes in undiluted samples of serum-based cell culture media.

An adaptive calibration procedure is used to build selective multivariate calibration models for the measurement of glucose, lactate, glutamine, and ammonia in undiluted serum-based cell culture media. This adaptive procedure removes metabolism-induced covariance between these analytes in a series of calibration samples collected during the cultivation of PC-3 human prostate cancer cells. Partial least-squares calibration models are generated from single-beam near-infrared (NIR) spectra collected over the 4800- to 4200-cm(-1) combination spectral range. Calibration models were generated with both the full spectral range and optimized spectral ranges. In both cases, the number of model factors was optimized and model validity was determined by comparing analyte concentrations predicted from a series of independent and unaltered samples that were obtained during a subsequent cultivation of the PC-3 cells. Similar analytical performance was achieved with fewer model factors when the optimized spectral range was used. The lowest standard errors of prediction were 0.82, 0.94, 0.55, and 0.76 mM for glucose, lactate, glutamine, and ammonia, respectively. Different spectral ranges were optimal for each analyte and the optimized spectral range coincided with the distinguishing spectral features of the analyte. The results of this study demonstrate that NIR spectroscopy can be used effectively in the off-line measurement of important nutrients (glucose and glutamine) and byproducts (lactate and ammonia) in a serum-based animal cell culture medium.     

Youden Index and optimal cut-point estimated from observations affected by a lower limit of detection

The receiver operating characteristic (ROC) curve is used to evaluate a biomarker's ability for classifying disease status. The Youden Index (J), the maximum potential effectiveness of a biomarker, is a common summary measure of the ROC curve. In biomarker development, levels may be unquantifiable below a limit of detection (LOD) and missing from the overall dataset. Disregarding these observations may negatively bias the ROC curve and thus J. Several correction methods have been suggested for mean estimation and testing; however, little has been written about the ROC curve or its summary measures. We adapt non-parametric (empirical) and semi-parametric (ROC-GLM [generalized linear model]) methods and propose parametric methods (maximum likelihood (ML)) to estimate J and the optimal cut-point (c *) for a biomarker affected by a LOD. We develop unbiased estimators of J and c * via ML for normally and gamma distributed biomarkers. Alpha level confidence intervals are proposed using delta and bootstrap methods for the ML, semi-parametric, and non-parametric approaches respectively. Simulation studies are conducted over a range of distributional scenarios and sample sizes evaluating estimators' bias, root-mean square error, and coverage probability; the average bias was less than one percent for ML and GLM methods across scenarios and decreases with increased sample size. An example using polychlorinated biphenyl levels to classify women with and without endometriosis illustrates the potential benefits of these methods. We address the limitations and usefulness of each method in order to give researchers guidance in constructing appropriate estimates of biomarkers' true discriminating capabilities.     

Regression analysis when covariates are regression parameters of a random effects model for observed longitudinal measurements

We consider regression analysis when covariate variables are the underlying regression coefficients of another linear mixed model. A naive approach is to use each subject's repeated measurements, which are assumed to follow a linear mixed model, and obtain subject-specific estimated coefficients to replace the covariate variables. However, directly replacing the unobserved covariates in the primary regression by these estimated coefficients may result in a significantly biased estimator. The aforementioned problem can be evaluated as a generalization of the classical additive error model where repeated measures are considered as replicates. To correct for these biases, we investigate a pseudo-expected estimating equation (EEE) estimator, a regression calibration (RC) estimator, and a refined version of the RC estimator. For linear regression, the first two estimators are identical under certain conditions. However, when the primary regression model is a nonlinear model, the RC estimator is usually biased. We thus consider a refined regression calibration estimator whose performance is close to that of the pseudo-EEE estimator but does not require numerical integration. The RC estimator is also extended to the proportional hazards regression model. In addition to the distribution theory, we evaluate the methods through simulation studies. The methods are applied to analyze a real dataset from a child growth study.     

High-throughput analysis of animal cell cultures using two-dimensional fluorometry

We report a new method which combines fluorescence spectroscopy at microtiter plate scale with multivariate statistical analysis for rapid and high-throughput analysis of secreted recombinant protein and viable cell growth in animal cell cultures. The potential of the method is demonstrated by application to cultures of three Chinese Hamster Ovary (CHO) cell clones with distinct IgG₄ antibody yields. Supernatant samples collected throughout culture time were analysed by two-dimensional fluorometry; significant changes were observed in the regions of tryptophan, metabolic cofactors and vitamins. Partial least squares regression was then used to correlate the entire fluorescence map with measured concentrations of antibody and viable cells. For both target variables, a model was calibrated with representative data from the two less productive clones and validated with data from the best producer clone; this allowed viable cell density to be predicted for the validation clone with an average error of 10%; even better, the secreted antibody could be predicted with an average error of 7%, proving the predictive capacity of the model beyond the calibration region. All the main spectral regions were required to establish the best correlations for both targeted variables. In conclusion, this method effectively analyzes cellular productivity in 96-well plate format, shortening the time spent in early phases of bioprocess development.