Covariance, analysis

T Ichiye, M Karplus. Collective motions m proteins A covariance analysis of atomic fluctuations m molecular dynamics and normal mode simulations. Proteins Stiaict Eunct Genet 11 205-217, 1991. 

We also use a linearized covariance analysis [34, 36] to evaluate the accuracy of estimates and take the measurement errors to be normally distributed with a zero mean and covariance matrix Assuming that the mathematical model is correct and that our selected partitions can represent the true multiphase flow functions, the mean of the error in the estimates is zero and the parameter covariance matrix of the errors in the parameter estimates is ... 

Results of the covariance analysis for the accuracy of estimates of the relative permeability of water and capillary pressure functions, along with the specified true functions, are shown in Figures 4.1.9 and 4.1.10 (the results for the relative permeability of oil are not included here). The accuracy measures are presented as 95 % confidence intervals. 

The covariance analysis was inspired by work of Halbritter et al. [143]. The covariance provides a measure of the strength of a correlation between different parts of the ID logarithmic conductance histograms. In other words, the covariance analysis enables evaluating whether different parts of a histogram are correlated to... 

Lenzenweger, M. F. (1999). Deeper into the schizotypy taxon On the robust nature of maximum covariance analysis. Journal of Abnormal Psychology, 108, 182-187. 

Covariance analysis a technique for separating the treatment effects on a given variate from those due to relationship with another variate which in turn is related to the treatments. 

We can now do a covariance analysis on the data and find the direction in which the spread is largest. Let M be a 2 x nm size matrix of the data points. 

A LTF rating of 1 ( very low level of effects or no effects observed ) to 5 ( severe level of effects ) was assigned to the fish survey based on the percentage of potentially effluent-related effects relative to all the endpoints measured. Statistically significant differences at a = 0.05 between reference and exposed white sucker (Catastomus commersoni) collected for the Provincial Papers study, including significant interactions from covariate analysis, in either sentinel species and in either sex, were considered to be possibly effluent-related effects (PERE). 

In summary, the pharmacostatistical model developed in the population PK analysis provided an excellent basis for the description of the cetuximab concentration data, and demonstrated that the PK of cetuximab are not likely to be influenced by intrinsic or extrinsic factors, as indicated by the results of the covariate analysis. 

The covariate analysis identified weight, sex, creatinine clearance, body mass index (BMI), and age as having an influence on PK parameters of NS2330 and/or Ml, respectively. The overall clearance of NS2330 is reduced by 20.5% in females compared to males and the NS2330 clearance which accounted for any elimination pathways except the formation of Ml from NS2330 (CLnon.met/F) is reduced in patients with a creatinine clearance lower than 62.5 ml/min ( 1.2% reduction per 1 ml/min reduction). The volume of distribution of NS2330 is influenced by body... 

The covariate analysis revealed physiologically plausible covariate effects, partly explaining the variability observed in the pharmacokinetic parameters. A high interindividual variability on the CL/F not responsible for the generation of Ml still remained even after the incorporation of the covariates sex and creatinine clearance. This indicates that there still might be yet undiscovered covariates additionally influencing the elimination of NS2330. 

The right-hand value Uf, is used when GREGPLUS is called with LEVEL = 20, whereas (n + mb + 1) is used when LEVEL = 22. LEVEL 20 requires fuller data and gives a fuller covariance analysis it gives expectation estimates of the covariance elements for each data block. LEVEL 22 gives maximum-density (most probable) covariance estimates these are smaller than the expectation values, which are averages over the posterior probability distribution. 

Alternatively, instead of using the EBE of the parameter of interest as the dependent variable, an estimate of the random effect (t ) can be used as the dependent variable, similar to how partial residuals are used in stepwise linear regression. Early population pharmacokinetic methodology advocated multiple linear regression using either forward, backwards, or stepwise models. A modification of this is to use multiple simple linear models, one for each covariate. For categorical covariates, analysis of variance is used instead. If the p-value for the omnibus F-test or p-value for the T-test is less than some cut-off value, usually 0.05, the covariate is moved forward for further examination. Many reports in the literature use this approach. 

De Alwis, D.P., Aarons, L., and Palmer, J.L. Population pharmacokinetics of ondansetron A covariate analysis. British Journal of Clinical Pharmacology 1998 46 117-125. 

Results of a covariance analysis on five internal coordinates conclusion are practically the same if more variables are introduced... 

In view of the difficulties in determining gas transfer coefficients accurately, direct methods for CO2 flux measurements aboard the ship are desirable. Sea-air CO2 flux was measured directly by means of the shipboard eddy-covariance method over the North Atlantic Ocean by Wanninkhof and McGillis in 1999. The net flux of CO2 across the sea surface was determined by a covariance analysis of the tri-axial motion of air with CO2 concentrations in the moving air measured in short time intervals ( ms) as a ship moved over the ocean. The results obtained over awind speed range of 2-13.5 m s are consistent with eqn [3] within about +20%. If the data obtainedin wind speeds up to 15 m s are taken into consideration, they indicate that the gas transfer piston velocity tends to increase as a cubeof wind speed. However, because of a large scatter ( + 35%) ofthe flux values at high wind speeds, further work is needed to confirm the cubic dependence. 

Koch GG, Tangen CM, Jung JW, Amara lA (1998) Issues for covariance analysis of dichotomous and ordered categorical data from randomized clinical trials and non-parametric strategies for addressing them. Statistics in Medicine 17 1863-1892. 

Note that Fc for treatment 27.91 is the same as determined from the covariance analysis. 

Chapter 11 introduces covariance analysis, which combines regression and analysis of variance into one model. 

Structural model definition Comparison of all potential model representations based on available data and parameter identifiability, sensitivity analysis to determine data elements that may affect parameter identifiability (missing values, data collection errors, etc.), and simulations to estimate predictive performance prior to covariate analysis. 

In the above analyses, we were able to investigate the rotational dynamics of only a limited number of large-amplitude modes due to the problem of resonance. In order to avoid the difficulty in analyzing the rotation of a single mode, we tried to analyze the rotational dynamics of a subset of normal modes by using canonical covariance analysis. 

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