A Robust Measurement of Correlation in Dependent Time Series

A special problem in behavioral sciences are time series where the data points of one series are dependent on the just prior values of the other series. The data structure may additionally exhibit an interdependence between the variables that changes over time. Pfanzagl's T provides a robust test of trend independence between such data sets. At the same time the applicability of Pearson's r can be extended by using the statistical considerations for T. For this purpose, the time series are transformed into binary series, consisting either of the values 1 or 0. These series may show distinct trend patterns of consecutive data points with the value 1 or with the value 0. Data points belonging to the same trend pattern are regarded as cohering values for any further mathematical operation applied. Based on the trend identifcation the T-value is derived, providing information on the coherent development of trend patterns in the two series. Additionally Pearson's r together with a modified sampling theory offers a standard measure of linear association between the time series. The procedures are described and a computer program is provided, combining Pfanzagl's T and Pearson's r with a bootstrap procedure for the statistical evaluation of the correlation coefficients.     

Electronic spreadsheet program for estimating two-compartment intravenous pharmacokinetic parameters by least squares linear regression analysis

A microcomputer program using an electronic spreadsheet program was developed to calculate pharmacokinetic values of thiacetarsamide sodium, a drug used to kill the adult heartworm (Dirofilaria immitis) parasite of the dog. A least squares, semilogarithmic regression analysis was done on data using a two compartment intravenous model. The data entered includes the time after injection and the drug concentration at that time. A graph of the points can be viewed or plotted, with the time on the x-axis, and the natural log of the drug concentration on the y-axis.The program was developed on a Televideo (512 kbytes) microcomputers⁷. The spreadsheet used was Lotus 123⁷¹     

Impact of enzyme concentration and residence time on apparent activity recovery in jump dilution analysis

Jump dilution analysis is commonly used to evaluate the reversibility of inhibition and to quantify the residence time of the inhibitor–enzyme complex. During hit and lead characterization, one sometimes observes apparently linear progress curves after jump dilution that display activity recoveries that are intermediate between those expected for fully reversible and irreversible inhibition. Computer simulations of progress curves after jump dilution indicate that seemingly linear progress curves can result when dealing with tight-binding inhibitors if substoichiometric concentrations of inhibitor are preincubated with enzyme. In this situation, the activity recovered is comparable to that expected for instantaneously reversible inhibitors. In addition, simulations demonstrate that intermediate values of activity recovery may be observed for compounds with modestly slow dissociation rates (i.e., residence times >0 min but ?20 min) when the attending curvature of the data is not accounted for. The observation of intermediate values of recovery can, thus, serve as an indication of either modest residence time or a contaminating inactivator within an inhibitor sample, in either case prompting greater scrutiny of the test compound.     

Food effects on the absorption and pharmacokinetics of cocoa flavanols

Macronutrients in food and gastric acid are known to have a pronounced effect on the metabolism of many xenobiotics, an effect that impacts their efficacy as bioactive agents. In this investigation we assessed the impact of select food treatments and the histamine H(2)-receptor antagonist Famotidine (Pepcid-AC) on flavanol absorption and metabolism. Four crossover intervention studies were conducted with 6 subjects each. Volunteers consumed sugar-free, flavanol-rich cocoa (0.125 g/kg body wt) alone, with macronutrient-rich foods (8.75 or 17.5 kJ/kg subject body wt) or Famotidine (Pepcid-AC). Blood samples were drawn at 5 time points including baseline. Plasma samples were analyzed for epicatechin and catechin flavanols by HPLC. Pharmacokinetic parameters were assessed using non-compartmental methodology. When provided at 17.5 kJ/kg subject body weight (approximately 4 kcal/kg), sugar and bread test meals increased flavanol area under the curve (AUC) values to 140% of control values (P < 0.05). A corresponding tendency for plasma antioxidant capacity to increase was observed for the cocoa treatment at 1.5 and 2.5 h (P < 0.17, P < 0.06, respectively). The ability of treatment meals to affect AUC values was positively correlated with treatment carbohydrate content (r = 0.83; P< 0.02). In contrast to carbohydrate rich meals, lipid and protein rich meals and Famotidine treatment had minimal effects on flavanol absorption. Based on C(max) and AUC values, this data suggests that the uptake of flavanols can be increased significantly by concurrent carbohydrate consumption.     

Correlation of dose-antimicrobial effect in modeling in vitro pharmacokinetic profiles of normal and impaired elimination of antibiotics

Relationships between concentration and antimicrobial effect (AME) of sisomicin (SMN) and cefotaxime (CTX) were established by simulating their pharmacokinetic profiles in an in vitro dynamic model. The AME duration (TE, time shift between the curves of bacteria heat output in the presence and absence of the antibiotics) or intensity (IE, area between the above curves) for both the antibiotics depended in the same way on the area under the concentration/time curve (AUC, mimicing of intravenous administration of the antibiotics in various doses). At low and moderate values of the AUC the dependences of IE or TE vs the AUC (the bacteriostatic phase of the AME development) were of the sigmoid shape while at high values of the AUC there was a marked increase in IE or TE (the bactericidal phase). The patterns of the IE or TE vs AUC curves in impaired antibiotic elimination were analogous. At the same time the IE or TE vs AUC curves for both the antibiotics under simulation of normal elimination (T 1/2, SMN-2.1 h, T 1/2, CTX-1.2 h) and impaired one (T 1/2, SMN-8.3 h, T 1/2, CTX-4.6 h) did not match. In the first case the AMESMN was on the whole higher and the AMECTX was lower than in the second case. Therefore, in patients with renal failure the efficient concentration of the aminoglycoside in blood can be higher and that of the cephalosporin on the contrary can be lower than the normal.     

SMOOTH: a statistical method for successful removal of genotyping errors from high-density genetic linkage data

High-density genetic linkage maps can be used for purposes such as fine-scale targeted gene cloning and anchoring of physical maps. However, their construction is significantly complicated by even relatively small amounts of scoring errors. Currently available software is not able to solve the ordering ambiguities in marker clusters, which inhibits the application of high-density maps. A statistical method named SMOOTH was developed to remove genotyping errors from genetic linkage data during the mapping process. The program SMOOTH calculates the difference between the observed and predicted values of data points based on data points of neighbouring loci in a given marker order. Highly improbable data points are removed by the program in an iterative process with a mapping algorithm that recalculates the map after cleaning. SMOOTH has been tested with simulated data and experimental mapping data from potato. The simulations prove that this method is able to detect a high amount of scoring errors and demonstrates that the program enables mapping software to successfully construct a very accurate high-density map. In potato the application of the program resulted in a reliable placement of nearly 1,000 markers in one linkage group.     

A modeling approach for mixing and reaction in wetlands with continuously varying flow

Prior investigations have examined steady-state flow in surface flow treatment wetlands, with mixing modeled as advection-dominated, and reaction calculated using flow-weighted averages over collections of stream tubes with different velocities. This work extends these concepts to non-steady flow conditions and temporally varying inlet concentrations. The essential construct that makes the approach feasible is definition of a set of reference (steady) state conditions under which the residence time distribution (RTD) and stream-tube specific rate constants are defined. Residence time in any stream tube under non-steady flow is treated as a linear function of its reference-condition residence time, and the overall wetland retention time under both mean and varying flow regimes. Outlet concentration is found by convolution of the reaction term with a varying inlet concentration function. For real-world flow and concentration data collected at discrete points in time, integration for outlet concentration is approximated using linear interpolation to generate inlet concentrations and velocities at intermediate points in time. The approach is examined using data from the literature. Vegetation density and depth distributions are seen as central in determining mixing and treatment performance.     

Numerical simulations of stochastic circulatory models

Properties of two of the stochastic circulatory models theoretically introduced by Smith et al., 1997, Bull. Math. Biol. 59, 1–22 were investigated. The models assumed the gamma distribution of the cycle time under either the geometric or Poisson elimination scheme. The reason for selecting these models was the fact that the probability density functions of the residence time of these models are formally similar to those of the Bateman and gamma-like function models, i.e., the two common deterministic models. Using published data, the analytical forms of the probability density functions of the residence time and the distributions of the simulated values of the residence time were determined on the basis of the deterministic models and the stochastic circulatory models, respectively. The Kolmogorov-Smirnov test revealed that even for 1000 xenobiotic particles, i.e., a relatively small number if the particles imply drug molecules, the probability density functions of the residence time based on the deterministic models closely matched the distributions of the simulated values of the residence time obtained on the basis of the stochastic circulatory models, provided that parameters of the latter models fulfilled selected conditions.     

Diversity matters: dynamic simulation of distributed bacterial states in suspended growth biological wastewater treatment systems

A MATLAB-based program was developed to simulate the distributions of states and behaviors of microbial storage product-accumulating bacteria in suspended growth systems. Currently available computer simulators of these systems predict dynamic behaviors by numerically solving differential biokinetic equations using average, or "lumped" system states (e.g., average microbial storage products concentrations). However, individual bacterial states are expected to diverge from average values, in part because individuals can have different hydrodynamic histories in terms of their residence times in upstream completely mixed flow reactors. The distributed state simulation program presented in this paper (DisSimulator 1.0) tracks individual bacteria as they move through a completely mixed reactor system. The program was evaluated for competition between polyphosphate-accumulating organisms (PAOs) and non-polyphosphate-accumulating heterotrophs in an enhanced biological phosphorus removal (EBPR) system for treatment of domestic wastewater. For identical systems and process conditions, simulations accounting for distributed states predicted larger anaerobic and aerobic solids residence time requirements for successful EBPR than did simulations using the lumped approach. One reason for this was that distributed simulations predicted large numbers of the PAOs were essentially inactive due to depleted or maximized storage product contents, while the lumped simulations predicted homogenous, 100% active PAO populations. Characteristic state profile shapes developed rapidly and were stable as total population numbers changed. Lumped state assumptions were demonstrated to produce large errors in predictions of EBPR system performance, and so consideration of distributed states may improve the accuracy of microbial storage products-based process simulations in systems with completely mixed hydrodynamics.     

Comparison of Dynamic and Liver-Specific Gadoxetic Acid Contrast-Enhanced MRI versus Apparent Diffusion Coefficients

Background

Hepatic lesions often present diagnostic connundrums with conventional MR techniques. Hepatobiliary phase contrast-enhanced imaging with gadoxetic acid can aid in the characterization of such lesions. However, quantitative measures describing late-phase enhancement must be assessed relative to their accuracy of hepatic lesion classification.Purpose: To compare quantitative parameters in gadoxetic acid contrast-enhanced dynamic and hepatobiliary phase imaging versus apparent diffusion coefficients in hepatic lesion characterization.

Material and Methods

57 patients with focal hepatic lesions on gadoxetic acid MR were included. Lesion enhancement at standard post-contrast time points and in the hepatobiliary phase (HB; 15 and 25 minutes post-contrast) was assessed via calculation of contrast (CR) and enhancement ratios (ER). Apparent diffusion coefficient (ADC) values were also obtained. Values for these parameters were compared among lesions and ROC analyses performed.Results: HB enhancement was greatest with FNH and adenomas. HB ER parameters but not HB CR could distinguish HCC from benign entities (0.9 ER ROC AUC versus 0.5 CR ROC AUC). There was no statistically significant difference found between the 15 and 25 minutes HB time points in detection of any lesion (p>0.4). ADC values were statistically significantly higher with hemangiomas (p<0.05) without greater accuracy in lesion detection relative to HB phase parameters.

Conclusion

Hepatobiliary phase gadoxetic acid contrast-enhanced MR characterizes focal hepatic lesions more accurately than ADC and conventional dynamic post-contrast time point enhancement parameters. ER values are generally superior to CR. No discernible benefit of 25 minute versus 15 minute delayed imaging is demonstrated.     

The Biodegradation of Zein <Emphasis Type="Italic">In Vitro</Emphasis> and <Emphasis Type="Italic">In Vivo</Emphasis> and its Application in Implants

A unique polymer-based sustained-release implant drug delivery system was prepared by using biocompatible and biodegradable Zein as the skeleton meterial. After preparing Zein colloids, the Zein-loaded implant rods were formulated by injection molding followed by evaporating the solvent, and being coated with poly(lactic-co-glycolic) acid (PLGA) solution. Drug release kinetics was examined by using Fluorouracil (5-FU) as model drug. Nearly zero-order release was achieved for the model drugs for a period of 0–25 days when the implants were incubated in distilled water at 37°C. And then the degradation kinetics of the rods in vivo and in vitro were evaluated, which indicated that Zein could be absorbed by body and has good degradation property. The effects of different ratios of Zein/5-FU and the rods’ diameter on drug release were studied, respectively. The plasma concentration of 5-FU in the implants were determined by HPLC after implanting a single dose of the implants in rats. All data were subsequently processed by using the computer program 3P97, and the values were showed as follows: the area under the plasma concentration–time curve (AUC) value was 321.88 (μg/ml) × day, and the mean residence time (MRT) value was 23.05 days. The sustained-release implants of Zein/5-FU were successfully formulated. The uniqueness of the article is that Zein has been used as a skeleton material in implant delivery system for the first time and zero-order release kinetics has been obtained successfully.     

SURFNET: A program for visualizing molecular surfaces,cavities, and intermolecular interactions

The SURFNET program generates molecular surfaces and gaps between surfaces from 3D coordinates supplied in a PDB-format file. The gap regions can correspond to the voids between two or more molecules, or to the internal cavities and surface grooves within a single molecule. The program is particularly useful in clearly delineating the regions of the active site of a protein. It can also generate 3D contour surfaces of the density distributions of any set of 3D data points. All output surfaces can be viewed interactively, along with the molecules or data points in question, using some of the best-known molecular modeling packages. In addition, PostScript output is available, and the generated surfaces can be rendered using various other graphics packages.     

Robust Estimation of Area Under ROC Curve Using Auxiliary Variables in the Presence of Missing Biomarker Values

Summary In medical research, the receiver operating characteristic (ROC) curves can be used to evaluate the performance of biomarkers for diagnosing diseases or predicting the risk of developing a disease in the future. The area under the ROC curve (ROC AUC), as a summary measure of ROC curves, is widely utilized, especially when comparing multiple ROC curves. In observational studies, the estimation of the AUC is often complicated by the presence of missing biomarker values, which means that the existing estimators of the AUC are potentially biased. In this article, we develop robust statistical methods for estimating the ROC AUC and the proposed methods use information from auxiliary variables that are potentially predictive of the missingness of the biomarkers or the missing biomarker values. We are particularly interested in auxiliary variables that are predictive of the missing biomarker values. In the case of missing at random (MAR), that is, missingness of biomarker values only depends on the observed data, our estimators have the attractive feature of being consistent if one correctly specifies, conditional on auxiliary variables and disease status, either the model for the probabilities of being missing or the model for the biomarker values. In the case of missing not at random (MNAR), that is, missingness may depend on the unobserved biomarker values, we propose a sensitivity analysis to assess the impact of MNAR on the estimation of the ROC AUC. The asymptotic properties of the proposed estimators are studied and their finite‐sample behaviors are evaluated in simulation studies. The methods are further illustrated using data from a study of maternal depression during pregnancy.     

Comparative plasma pharmacokinetics of meloxicam in sheep and goats following intravenous administration

Meloxicam, a novel cyclooxygenase-2 selective nonsteroidal anti-inflammatory drug (NSAID), has been used extensively in humans and recently in some domestic animal species. Although it is an attractive NSAID for use in small ruminants, meloxicam pharmacokinetics have not been investigated in sheep and goats and this information is essential for rational therapeutic use of the drug in these species. In this investigation, comparative pharmacokinetic properties of meloxicam were studied in sheep and goats after a single intravenous dose of 0.5 mg kg(-1) body mass. Blood samples were collected via jugular venepuncture into heparinised tubes at predetermined times after drug administration. Plasma concentrations of meloxicam were determined by reversed-phase high performance liquid chromatography. The plasma concentrations of meloxicam were detectable in sheep and goats up to 72 and 48 h, respectively. The plasma concentration versus time data of meloxicam in both sheep and goats were adequately described by a two-compartment open model. The values obtained for sheep and goats for distribution half-life, volume of distribution at steady state and volume of the central compartment were almost similar in sheep and goats. The elimination half-life (t(1/2beta)), area under the plasma concentration-time curve (AUC), mean residence time (MRT) and total systemic clearance (Cl(B)) in sheep were significantly different from those of goats. The mean+/-S.E. values of t(1/2beta), MRT, AUC and Cl(B) in sheep were 10.85+/-1.21 h, 15.13+/-1.67 h, 31.88+/-2.97 microg h mL(-1) and 0.016+/-0.002 L h(-1) kg(-1), respectively whereas the respective values in goats were 6.73+/-0.58 h, 9.37+/-0.83 h, 19.23+/-2.23 microg h mL(-1) and 0.03+/-0.01 L h(-1) kg(-1). The results indicate that elimination kinetics of meloxicam differ significantly between sheep and goats and the elimination of the drug tends to be faster in goats compared to sheep.     

Stereoselective pharmacokinetics of clausenamide enantiomers and their major metabolites after single intravenous and oral administration to rats

The pharmacokinetics of clausenamide (CLA) enantiomers and their metabolites were investigated in Wistar rat. After intravenous and oral administration at a dose of 80 and 160 mg/kg each enantiomer, plasma concentrations of (-)- or (+)-CLA and its major metabolites were simultaneously determined by reverse-phase HPLC with UV detection. Notably, stereoselective differences in pharmacokinetics were found. The mean plasma levels of (+)-CLA were higher at almost all time points than those of (-)-CLA. (+)-CLA also exhibited greater t(max), C(max), t(1/2beta), AUC(0-12h), and AUC(0--> infinity) and smaller CL (or CL/F) and V(d) (or V(d)/F), than its antipode. The (+)/(-) isomer ratios for t(1/2beta), t(max), AUC(0-12 h), and AUC(0--> infinity), which ranged from 1.26 to 2.08. The ratio for CL (or CL/F) was about 0.5, and there were significant differences in these values between CLA enantiomers (P < 0.05), implying that the absorption, distribution, and elimination of (-)-CLA were more rapid than those of (+)-CLA. Similar findings for (-)-7-OH-CLA, the major metabolite of (-)-CLA, and (+)-4-OH-CLA, the major metabolite of (+)-CLA, can be also seen in rat plasma. The contributing factors for the differences in stereoselective pharmacokinetics of CLA enantiomers appeared to be involved in their different plasma protein binding, first-pass metabolism and interaction with CYP enzymes, especially with their metabolizing enzyme CYP 3A isoforms.     

Curve fitting of germination data using the Richards function

Abstract. The fitting of the generalized Richards function to germination data by using two nested iterative and least squares regression procedures to estimate the four parameters (all of which can be associated with features of biological growth) is demonstrated. The program also involves a procedure of parallel curve analysis which makes comparisons between two curves by examining the whole process represented by the curve and not just a point or portion thereof. Excellent agreement between observed and expected values was obtained by analyzing data which defined patterns of germination exhibiting a range of rates and final percentages. The program also calculates a number of derived quantities including maximum daily rate of germination and time to 50% of final germination.     

Nonideality and protein thermal denaturation

We studied the thermal denaturation of eglin c by using CD spectropolarimetry and differential scanning calorimetry (DSC). At low protein concentrations, denaturation is consistent with the classical two-state model. At concentrations greater than several hundred microM, however, the calorimetric enthalpy and the midpoint transition temperature increase with increasing protein concentration. These observations suggested the presence of intermediates and/or native state aggregation. However, the transitions are symmetric, suggesting that intermediates are absent, the DSC data do not fit models that include aggregation, and analytical ultracentrifugation (AUC) data show that native eglin c is monomeric. Instead, the AUC data show that eglin c solutions are nonideal. Analysis of the AUC data gives a second virial coefficient that is close to values calculated from theory and the DSC data are consistent with the behavior expected for nonideal solutions. We conclude that the concentration dependence is caused by differential nonideality of the native and denatured states. The nondeality arises from the high charge of the protein at acid pH and is exacerbated by low buffer concentrations. Our conclusion may explain differences between van't Hoff and calorimetric denaturation enthalpies observed for other proteins whose behavior is otherwise consistent with the classical two-state model.     

An algol program for the computation of empiric regressions

An explanation is given about the meaning of empirical regression and on the domain of application of this biomathematical-statistical procedure. It may be helpful in data handling after the measurements and in a first stage of data processing especially if there is a large amount of datas. An empirical regression can provide the basis for a functional relationship analysis by giving hints for the choice of empirical mathematical functions. This will be useful and necessary in such cases where the measured values have a greater dispersion and one wants to get an analytical expression for the course of measured points. In the appendix a program listing of the ALGOL-program for empirical regression is presented. Detailed remarks are made in the text concerning the program structure, the data input and output resp. the program control parameters to enable the biological or medical user to adapt the program to their special problems without the help by a mathematician, and neither with deeper knowledge of mathematics nor with detailed insight to computer technical aspects of data processing.