Statnote 32 : the partial correlation coefficient

In previous statnotes, the application of correlation and regression methods to the analysis of two variables (X,Y) was described. The most important statistic used to measure the degree of correlation between two variables is Pearson’s ‘product moment correlation coefficient’ (‘r’). The correlation between two variables may be due to their common relation to other variables. Hence, investigators using correlation studies need to be alert to the possibilities of spurious correlation and the methods of ‘partial correlation’ are one method of taking this into account. This statnote applies the methods of partial correlation to three scenarios. First, to a fairly obvious example of a spurious correlation resulting from the ‘size effect’ involving the relationship between the number of general practitioners (GP) and the number of deaths of patients in a town. Second, to the relationship between the abundance of the nitrogen-fixing bacterium Azotobacter in soil and three soil variables, and finally, to a more complex scenario, first introduced in Statnote 24involving the relationship between the growth of lichens in the field and climate.

A new rapidly absorbed paracetamol tablet containing sodium bicarbonate. II. Dissolution studies and in vitro/in vivo correlation

The objective of this study was to compare the in vitro dissolution profile of a new rapidly absorbed paracetamol tablet containing sodium bicarbonate (PS) with that of a conventional paracetamol tablet (P), and to relate these by deconvolution and mapping to in vivo release. The dissolution methods used include the standard procedure described in the USP monograph for paracetamol tablets, employing buffer at pH5.8 or 0.05 M HCl at stirrer speeds between 10 and 50 rpm. The mapping process was developed and implemented in Microsoft Excel® worksheets that iteratively calculated the optimal values of scale and shape factors which linked in vivo time to in vitro time. The in vitro-in vivo correlation (IVIVC) was carried out simultaneously for both formulations to produce common mapping factors. The USP method, using buffer at pH5.8, demonstrated no difference between the two products. However, using an acidic medium the rate of dissolution of P but not of PS decreased with decreasing stirrer speed. A significant correlation (r=0.773; p<.00001) was established between in vivo release and in vitro dissolution using the profiles obtained with 0.05 M HCl and a stirrer speed of 30 rpm. The scale factor for optimal simultaneous IVIVC in the fasting state was 2.54 and the shape factor was 0.16; corresponding values for mapping in the fed state were 3.37 and 0.13 (implying a larger in vitro-in vivo time difference but reduced shape difference in the fed state). The current IVIVC explains, in part, the observed in vivo variability of the two products. The approach to mapping may also be extended to different batches of these products, to predict the impact of any changes of in vitro dissolution on in vivo release and plasma drug concentration-time profiles.

Lipoplexes formulation and optimisation:in vitro transfection studies reveal no correlation with in vivo vaccination studies

The aim of these studies was to compare the effect of liposome composition on physico-chemical characteristics and transfection efficacy of cationic liposomes both in vitro and in vivo. Comparison between 4 popularly used cationic lipids, showed 3b-N-(dimethylaminoethyl)carbamate (DC-Chol) to promote the highest transfect levels in cells in vitro with levels being at least 6 times higher than those of 1,2-di-O-octadecenyl-3-trimethylammonium propane (DOTMA). 1,2-dioleoyl-3-trimethylammonium-propane (DOTAP), and dimethyldioctadecylammonium (DDA) and approximately twice as efficient as dipalmitoyl-trimethylammonium-propane (DPTAP). To establish the role of the helper lipid, DC-Chol liposomes were formulated in combination with either 1,2-dioleoyl-sn-glycero-3-phosphatidylethanolamine (DOPE) or cholesterol (Chol) (1:1 molar ratio) with and without the addition of phosphatidyl choline. The choice of helper lipid incorporated within the bilayer was found to influence the formation of complexes, their resultant structure and their transfection efficiency in vitro, with SUV-DNA complexes containing optimum levels of DOPE giving higher transfection than those containing cholesterol. The inclusion of PC within the formulation also reduced transfection efficiency in vitro. However, when administered in vivo, SUV-DNA complexes composed of PC:Chol:DC-Chol at a molar ratio of 16:8:4 micromole/ml were the most effective at inducing splenocyte proliferation upon exposure to antigen in comparison to control spleens. These results demonstrate that there is no in vitro/in vivo correlation between the transfection efficacy of these liposome formulations and in vitro transfection in the above cell model cannot be taken as a reliable indicator for in vivo efficacy of DNA vaccines.

The use of correlation and regression methods in optometry

Correlation and regression are two of the statistical procedures most widely used by optometrists. However, these tests are often misused or interpreted incorrectly, leading to erroneous conclusions from clinical experiments. This review examines the major statistical tests concerned with correlation and regression that are most likely to arise in clinical investigations in optometry. First, the use, interpretation and limitations of Pearson's product moment correlation coefficient are described. Second, the least squares method of fitting a linear regression to data and for testing how well a regression line fits the data are described. Third, the problems of using linear regression methods in observational studies, if there are errors associated in measuring the independent variable and for predicting a new value of Y for a given X, are discussed. Finally, methods for testing whether a non-linear relationship provides a better fit to the data and for comparing two or more regression lines are considered.

Explaining volatility and serial correlation in opening and closing returns:a study of the FT-30 components

In this paper the performance of opening and closing returns, for the components of the FT-30 will be studied. It will be shown that for these stocks opening returns have higher volatility and a greater tendency towards negative serial correlation than closing returns. Unlike previous studies this contrasting performance cannot solely be attributed to differences in the trading mechanism across the trading day. All the stocks used in our sample trade thought the day using a uniform trading mechanism. In this paper, we suggest that it is differences in the speed that closing and opening returns adjust to new information that causes differences in return performance. By estimating the Amihud and Mendelson (1987) [Amihud, Yakov, & Mendelson, Haim (1987). Trading mechanisms and stock returns: An empirical investigation, Journal of Finance, 62 533-553.] partial adjustment model with noise, we show that opening returns have a tendency towards over-reaction, while closing returns have a tendency towards under-reaction. We suggest that it is these differences that cause a substantial proportion (although not all) of the asymmetric return patterns associated with opening and closing returns. © 2005 Elsevier Inc. All rights reserved.

Studies of the drying of particulate slurries

The literature relating to the drying characteristics of pure liquid drops and particulate slurry drops has been reviewed. The experimental investigation was, therefore, divided into three parts: Pure water drops, Aqueous sodium sulphate decahydrate drops, and, Slurry drops from nine detergent formulations. The value of the constant,'Ψ, reported by Ranz and Marshall, was found to be temperature dependent. In the temperature range o 26.5≤T≤118.5°C,Ψ , for pure water drops, varied between 0.38 and 0.47. A revised correlation of the mass transfer coefficients is therefore proposed.  A mathematical model for estimating the variation of crust thickness, for aqueous sodium sulphate drops, with time is proposed: β = R _ {R3 - ( 1.5G/πCo ) ( ΔHD - ΔHU) Δ} 1/3 Experimental crust thickness evaluated from stereoscan micrographs showed good agreement with theoretical prediction. It has been shown that drying characteristics of detergent drops can be evaluated from the porosity:thickness ratio, {ε/\β}. Formulations having large {ε/β I-ratios dry better than those with smaller values. The agreement between the experimental and theoretical mass transfer coefficients shows, in addition to the above correlation, that the overall mass transfer coefficient can be predicted from the expression1/K = 1/K + β/DMε 1.5 The crust is the controlling resistance to transfer in particulate slurry drops. For aqueous sodium sulphate drops, the crust provides 64.2% of the total resistance while for detergents with thicker, but less porous crusts, the value is 97.5%.

Statnote 14: the correlation of two variables (Pearson's 'r')

Pearson's correlation coefficient (‘r’) is one of the most widely used of all statistics. Nevertheless, care needs to be used in interpreting the results because with large numbers of observations, quite small values of ‘r’ become significant and the X variable may only account for a small proportion of the variance in Y. Hence, ‘r squared’ should always be calculated and included in a discussion of the significance of ‘r’. The use of ‘r’ also assumes that the data follow a bivariate normal distribution (see Statnote 17) and this assumption should be examined prior to the study. If the data do not conform to such a distribution, the use of a non-parametric correlation coefficient should be considered. A significant correlation should not be interpreted as indicating ‘causation’ especially in observational studies, in which the two variables may be correlated because of their mutual correlations with other confounding variables.

Data analysis methods in optometry. Part 5: correlation

1. Pearson's correlation coefficient only tests whether the data fit a linear model. With large numbers of observations, quite small values of r become significant and the X variable may only account for a minute proportion of the variance in Y. Hence, the value of r squared should always be calculated and included in a discussion of the significance of r. 2. The use of r assumes that a bivariate normal distribution is present and this assumption should be examined prior to the study. If Pearson's r is not appropriate, then a non-parametric correlation coefficient such as Spearman's rs may be used. 3. A significant correlation should not be interpreted as indicating causation especially in observational studies in which there is a high probability that the two variables are correlated because of their mutual correlations with other variables. 4. In studies of measurement error, there are problems in using r as a test of reliability and the ‘intra-class correlation coefficient’ should be used as an alternative. A correlation test provides only limited information as to the relationship between two variables. Fitting a regression line to the data using the method known as ‘least square’ provides much more information and the methods of regression and their application in optometry will be discussed in the next article.

Some studies relating to the design of shallow, fluidized bed boilers

The concept of shallow fluidized bed boilers is defined and a preliminary working design for a gas-fired package boiler has been produced. Those areas of the design requiring further study have been specified. Experimental investigations concerning these areas have been carried out. A two-dimensional, conducting paper analog has been developed for the specific purpose of evaluating sheet fins. The analog has been generalised and is presented as a simple means of simulating the general, two-dimensional Helmholtz equation. By recording the transient response of spherical, calorimetric probes when plunged into heated air-fluidized beds, heat transfer coefficients have been measured at bed temperatures up to 1 100°C. A correlation fitting all the data to within ±10% has been obtained. A model of heat transfer to surfaces immersed in high temperature beds has been proposed. The model solutions are, however, only in qualitative agreement with the experimental data. A simple experimental investigation has revealed that the effective, radial, thermal conductivities of shallow fluidized beds are an order of magnitude lower than the axial conductivities. These must, consequently, be taken into account when considering heat transfer to surfaces immersed within fluidized beds. Preliminary work on pre-mixed gas combustion and some further qualitative experiments have been used as the basis for discussing the feasibility of combusting heavy fuel oils within shallow beds. The use of binary beds, within which the fuel could be both gasified and subsequently burnt, is proposed. Finally, the consequences of the experimental studies on the initial design are considered, and suggestions for further work are made.

Studies of the effects of molecular encounters on N.M.R. spin-lattice relaxation times

This thesis is concerned with investigations of the effects of molecular encounters on nuclear magnetic resonance spin-lattice relaxation times, with particular reference to mesitylene in mixtures with cyclohexane and TMS. The purpose of the work was to establish the best theoretical description of T1 and assess whether a recently identified mechanism (buffeting), that influences n.m.r. chemical shifts, governs Tl also. A set of experimental conditions are presented that allow reliable measurements of Tl and the N. O. E. for 1H and 13C using both C. W. and F.T. n.m.r. spectroscopy. Literature data for benzene, cyclohexane and chlorobenzene diluted by CC14 and CS2 are used to show that the Hill theory affords the best estimation of their correlation times but appears to be mass dependent. Evaluation of the T1 of the mesitylene protons indicates that a combined Hill-Bloembergen-Purcell-Pound model gives an accurate estimation of T1; subsequently this was shown to be due to cancellation of errors in the calculated intra and intemolecular components. Three experimental methods for the separation of the intra and intermolecular relaxation times are described. The relaxation times of the 13C proton satellite of neat bezene, 1,4 dioxane and mesitylene were measured. Theoretical analyses of the data allow the calculation of Tl intra. Studies of intermolecular NOE's were found to afford a general method of separating observed T1's into their intra and intermolecular components. The aryl 1H and corresponding 13C T1 values and the NOE for the ring carbon of mesitylene in CC14 and C6H12-TMS have been used in combination to determine T1intra and T1inter. The Hill and B.P.P. models are shown to predict similarly inaccurate values for T1linter. A buffeting contribution to T1inter is proposed which when applied to the BPP model and to the Gutowsky-Woessner expression for T1inter gives an inaccuracy of 12% and 6% respectively with respect to theexperimentally based T1inter.

Similarity between class A and class B G-protein-coupled receptors exemplified through calcitonin gene-related peptide receptor modelling and mutagenesis studies

Modelling class B G-protein-coupled receptors (GPCRs) using class A GPCR structural templates is difficult due to lack of homology. The plant GPCR, GCR1, has homology to both class A and class B GPCRs. We have used this to generate a class A-class B alignment, and by incorporating maximum lagged correlation of entropy and hydrophobicity into a consensus score, we have been able to align receptor transmembrane regions. We have applied this analysis to generate active and inactive homology models of the class B calcitonin gene-related peptide (CGRP) receptor, and have supported it with site-directed mutagenesis data using 122 CGRP receptor residues and 144 published mutagenesis results on other class B GPCRs. The variation of sequence variability with structure, the analysis of polarity violations, the alignment of group-conserved residues and the mutagenesis results at 27 key positions were particularly informative in distinguishing between the proposed and plausible alternative alignments. Furthermore, we have been able to associate the key molecular features of the class B GPCR signalling machinery with their class A counterparts for the first time. These include the [K/R]KLH motif in intracellular loop 1, [I/L]xxxL and KxxK at the intracellular end of TM5 and TM6, the NPXXY/VAVLY motif on TM7 and small group-conserved residues in TM1, TM2, TM3 and TM7. The equivalent of the class A DRY motif is proposed to involve Arg(2.39), His(2.43) and Glu(3.46), which makes a polar lock with T(6.37). These alignments and models provide useful tools for understanding class B GPCR function.

Statnote 33:the intra-class correlation coefficient

The intra-class correlation coefficient (ICC or ri) is a method of measuring correlation when the data are paired and therefore, should be used when experimental units are organised into groups. A useful analogy is with the unpaired or paired ‘t’ test to compare the differences between the means of two groups. In studies of reproducibility, there may actually be little difference between the ICC and Pearson’s ‘r’ for ‘true’ repeated measurements. If, however, there is a systematic change in the measurements made on the first compared with the second occasion, then the ICC will be significantly less than ‘r’, and less confidence would be placed in the reproducibility of the results.

Exploring the correlation between lipid packaging in lipoplexes and their transfection efficacy

Whilst there is a large body of evidence looking at the design of cationic liposomes as transfection agents, correlates of formulation to function remain elusive. In this research, we investigate if lipid packaging can give further insights into transfection efficacy. DNA lipoplexes composed of 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE) or 1,2-distearoyl-sn-glycero-3-phosphoethanolamine (DSPE) in combination with 1,2-dioleoyl-3-trimethylammonium-propane (DOTAP) or 1,2-stearoyl-3-trimethylammonium-propane (DSTAP) were prepared by the lipid hydration method. Each of the formulations was prepared by hydration in dH2O or phosphate buffer saline (PBS) to investigate the effect of buffer salts on lipoplex physicochemical characteristics and in vitro transfection. In addition, Langmuir monolayer studies were performed to investigate any possible correlation between lipid packaging and liposome attributes. Using PBS, rather than dH2O, to prepare the lipoplexes increased the size of vesicles in most of formulations and resulted in variation in transfection efficacies. However, one combination of lipids (DSPE:DOTAP) could not form liposomes in PBS, whilst the DSPE:DSTAP combination could not form liposomes in either aqueous media. Monolayer studies demonstrated saturated lipid combinations offered dramatically closer molecular packing compared to the other combinations which could suggest why this lipid combination could not form vesicles. Of the lipoplexes prepared, those formulated with DSTAP showed higher transfection efficacy, however, the effect of buffer on transfection efficiency was formulation dependent. © 2011 by the authors; licensee MDPI, Basel, Switzerland.

Saccharomyces Cerevisiae as a biotechnological tool for ageing research:studies on translation and metabolism

The yeast Saccharomyces cerevisiae is an important model organism for the study of cell biology. The similarity between yeast and human genes and the conservation of fundamental pathways means it can be used to investigate characteristics of healthy and diseased cells throughout the lifespan. Yeast is an equally important biotechnological tool that has long been the organism of choice for the production of alcoholic beverages, bread and a large variety of industrial products. For example, yeast is used to manufacture biofuels, lubricants, detergents, industrial enzymes, food additives and pharmaceuticals such as anti-parasitics, anti-cancer compounds, hormones (including insulin), vaccines and nutraceuticals. Its function as a cell factory is possible because of the speed with which it can be grown to high cell yields, the knowledge that it is generally recognized as safe (GRAS) and the ease with which metabolism and cellular pathways, such as translation can be manipulated. In this thesis, these two pathways are explored in the context of their biotechnological application to ageing research: (i) understanding translational processes during the high-yielding production of membrane protein drug targets and (ii) the manipulation of yeast metabolism to study the molecule, L-carnosine, which has been proposed to have anti-ageing properties. In the first of these themes, the yeast strains, spt3?, srb5?, gcn5? and yTHCBMS1, were examined since they have been previously demonstrated to dramatically increase the yields of a target membrane protein (the aquaporin, Fps1) compared to wild-type cells. The mechanisms underlying this discovery were therefore investigated. All high yielding strains were shown to have an altered translational state (mostly characterised by an initiation block) and constitutive phosphorylation of the translational initiation factor, eIF2a. The relevance of the initiation block was further supported by the finding that other strains, with known initiation blocks, are also high yielding for Fps1. A correlation in all strains between increased Fps1 yields and increased production of the transcriptional activator protein, Gcn4, suggested that yields are subject to translational control. Analysis of the 5´ untranslated region (UTR) of FPS1 revealed two upstream open reading frames (uORFs). Mutagenesis data suggest that high yielding strains may circumvent these control elements through either a leaky scanning or a re-initiation mechanism. In the second theme, the dipeptide L-carnosine (ß-alanyl-L-histidine) was investigated: it has previously been shown to inhibit the growth of cancer cells but delay senescence in cultured human fibroblasts and extend the lifespan of male fruit flies. To understand these apparently contradictory properties, the effects of L-carnosine on yeast were studied. S. cerevisiae can respire aerobically when grown on a non-fermentable carbon source as a substrate but has a respiro-fermentative metabolism when grown on a fermentable carbon source; these metabolisms mimic normal cell and cancerous cell metabolisms, respectively. When yeast were grown on fermentable carbon sources, in the presence of L-carnosine, a reduction in cell growth and viability was observed, which was not apparent for cells grown on a non-fermentable carbon source. The metabolism-dependent mechanism was confirmed in the respiratory yeast species Pichia pastoris. Further analysis of S. cerevisiae yeast strains with deletions in their nutrient-sensing pathway, which result in an increase in respiratory metabolism, confirmed the metabolism-dependent effects of L-carnosine.

On the interpretation of synchronization in EEG hyperscanning studies:a cautionary note

EEG Hyperscanning is a method for studying two or more individuals simultaneously with the objective of elucidating how co-variations in their neural activity (i.e., hyperconnectivity) are influenced by their behavioral and social interactions. The aim of this study was to compare the performance of different hyper-connectivity measures using (i) simulated data, where the degree of coupling could be systematically manipulated, and (ii) individually recorded human EEG combined into pseudo-pairs of participants where no hyper-connections could exist. With simulated data we found that each of the most widely used measures of hyperconnectivity were biased and detected hyper-connections where none existed. With pseudo-pairs of human data we found spurious hyper-connections that arose because there were genuine similarities between the EEG recorded from different people independently but under the same experimental conditions. Specifically, there were systematic differences between experimental conditions in terms of the rhythmicity of the EEG that were common across participants. As any imbalance between experimental conditions in terms of stimulus presentation or movement may affect the rhythmicity of the EEG, this problem could apply in many hyperscanning contexts. Furthermore, as these spurious hyper-connections reflected real similarities between the EEGs, they were not Type-1 errors that could be overcome by some appropriate statistical control. However, some measures that have not previously been used in hyperconnectivity studies, notably the circular correlation co-efficient (CCorr), were less susceptible to detecting spurious hyper-connections of this type. The reason for this advantage in performance is discussed and the use of the CCorr as an alternative measure of hyperconnectivity is advocated. © 2013 Burgess.