Meta-analysis: a unifying meta-likelihood approach framing unobserved heterogeneity, study covariates, publication bias, and study quality

OBJECTIVES: This contribution provides a unifying concept for meta-analysis integrating the handling of unobserved heterogeneity, study covariates, publication bias and study quality. It is important to consider these issues simultaneously to avoid the occurrence of artifacts, and a method for doing so is suggested here. METHODS: The approach is based upon the meta-likelihood in combination with a general linear nonparametric mixed model, which lays the ground for all inferential conclusions suggested here. RESULTS: The concept is illustrated at hand of a meta-analysis investigating the relationship of hormone replacement therapy and breast cancer. The phenomenon of interest has been investigated in many studies for a considerable time and different results were reported. In 1992 a meta-analysis by Sillero-Arenas et al. concluded a small, but significant overall effect of 1.06 on the relative risk scale. Using the meta-likelihood approach it is demonstrated here that this meta-analysis is due to considerable unobserved heterogeneity. Furthermore, it is shown that new methods are available to model this heterogeneity successfully. It is argued further to include available study covariates to explain this heterogeneity in the meta-analysis at hand. CONCLUSIONS: The topic of HRT and breast cancer has again very recently become an issue of public debate, when results of a large trial investigating the health effects of hormone replacement therapy were published indicating an increased risk for breast cancer (risk ratio of 1.26). Using an adequate regression model in the previously published meta-analysis an adjusted estimate of effect of 1.14 can be given which is considerably higher than the one published in the meta-analysis of Sillero-Arenas et al. In summary, it is hoped that the method suggested here contributes further to a good meta-analytic practice in public health and clinical disciplines.

The effects of spatial and temporal heterogeneity on the population dynamics of four animal species in a Danish landscape

Background: Variation in carrying capacity and population return rates is generally ignored in traditional studies of population dynamics. Variation is hard to study in the field because of difficulties controlling the environment in order to obtain statistical replicates, and because of the scale and expense of experimenting on populations. There may also be ethical issues. To circumvent these problems we used detailed simulations of the simultaneous behaviours of interacting animals in an accurate facsimile of a real Danish landscape. The models incorporate as much as possible of the behaviour and ecology of skylarks Alauda arvensis, voles Microtus agrestis, a ground beetle Bembidion lampros and a linyphiid spider Erigone atra. This allows us to quantify and evaluate the importance of spatial and temporal heterogeneity on the population dynamics of the four species. Results: Both spatial and temporal heterogeneity affected the relationship between population growth rate and population density in all four species. Spatial heterogeneity accounted for 23–30% of the variance in population growth rate after accounting for the effects of density, reflecting big differences in local carrying capacity associated with the landscape features important to individual species. Temporal heterogeneity accounted for 3–13% of the variance in vole, skylark and spider, but 43% in beetles. The associated temporal variation in carrying capacity would be problematic in traditional analyses of density dependence. Return rates were less than one in all species and essentially invariant in skylarks, spiders and beetles. Return rates varied over the landscape in voles, being slower where there were larger fluctuations in local population sizes. Conclusion: Our analyses estimated the traditional parameters of carrying capacities and return rates, but these are now seen as varying continuously over the landscape depending on habitat quality and the mechanisms of density dependence. The importance of our results lies in our demonstration that the effects of spatial and temporal heterogeneity must be accounted for if we are to have accurate predictive models for use in management and conservation. This is an area which until now has lacked an adequate theoretical framework and methodology.

Estimating the hidden number of scrapie affected holdings in great Britain using a simple, truncated count model allowing for heterogeneity

None of the current surveillance streams monitoring the presence of scrapie in Great Britain provide a comprehensive and unbiased estimate of the prevalence of the disease at the holding level. Previous work to estimate the under-ascertainment adjusted prevalence of scrapie in Great Britain applied multiple-list capture-recapture methods. The enforcement of new control measures on scrapie-affected holdings in 2004 has stopped the overlapping between surveillance sources and, hence, the application of multiple-list capture-recapture models. Alternative methods, still under the capture-recapture methodology, relying on repeated entries in one single list have been suggested in these situations. In this article, we apply one-list capture-recapture approaches to data held on the Scrapie Notifications Database to estimate the undetected population of scrapie-affected holdings with clinical disease in Great Britain for the years 2002, 2003, and 2004. For doing so, we develop a new diagnostic tool for indication of heterogeneity as well as a new understanding of the Zelterman and Chao's lower bound estimators to account for potential unobserved heterogeneity. We demonstrate that the Zelterman estimator can be viewed as a maximum likelihood estimator for a special, locally truncated Poisson likelihood equivalent to a binomial likelihood. This understanding allows the extension of the Zelterman approach by means of logistic regression to include observed heterogeneity in the form of covariates-in case studied here, the holding size and country of origin. Our results confirm the presence of substantial unobserved heterogeneity supporting the application of our two estimators. The total scrapie-affected holding population in Great Britain is around 300 holdings per year. None of the covariates appear to inform the model significantly.

Electrochemical determination of plant-derived leuco-indigo after chemical reduction by glucose

Electrochemical determination of redox active dye species is demonstrated in indigo samples contaminated with high levels of organic and inorganic impurities. The use of a hydrodynamic electrode system based on a vibrating probe (250 Hz, 200 mu m lateral amplitude) allows time-independent diffusion controlled signals to be enhanced and reliable concentration data to be obtained under steady state conditions at relatively fast scan rates up to 4 V s-1In this work the indigo content of a complex plant-derived indigo sample (dye content typically 30%) is determined after indigo is reduced by addition of glucose in aqueous 0.2 M NaOH. The soluble leuco-indigo is measured by its oxidation response at a vibrating electrode. The vibrating electrode, which consisted of a laterally vibrating 500 mu m diameter gold disc, is calibrated with Fe(CN)(6) 3-/4- in 0.1 M KCl and employed for indigo determination at 55, 65, and 75 C in 0.2 M NaOH. Determinations of the indigo content of 25 different samples of plant-derived indigo are compared with those obtained by conventional spectrophotometry. This comparison suggests a significant improvement by the electrochemical method, which appears to be less sensitive to impurities.

Electrochemical and sonoelectrochemical monitoring of indigo reduction by glucose

The reduction of indigo (dispersed in water) to leuco-indigo (dissolved in water) is an important industrial process and investigated here for the case of glucose as an environmentally benign reducing agent. In order to quantitatively follow the formation of leuco-indigo two approaches based on (i) rotating disk voltammetry and (ii) sonovoltammetry are developed. Leuco-indigo, once formed in alkaline solution, is readily monitored at a glassy carbon electrode in the mass transport limit employing hydrodynamic voltammetry. The presence of power ultrasound further improves the leuco-indigo determination due to additional agitation and homogenization effects. While inactive at room temperature, glucose readily reduces indigo in alkaline media at 65 degrees C. In the presence of excess glucose, a surface dissolution kinetics limited process is proposed following the rate law d eta(leuco-indigo)/dt = k x c(OH-) x S-indigo where eta(leuco-indigo) is the amount of leuco-indigo formed, k = 4.1 x 10(-9) m s(-1) (at 65 degrees C, assuming spherical particles of I gm diameter) is the heterogeneous dissolution rate constant,c(OH-) is the concentration of hydroxide, and Sindigo is the reactive surface area. The activation energy for this process in aqueous 0.2 M NaOH is E-A = 64 U mol(-1) consistent with a considerable temperature effects. The redox mediator 1,8-dihydroxyanthraquinone is shown to significantly enhance the reaction rate by catalysing the electron transfer between glucose and solid indigo particles. (c) 2006 Elsevier Ltd. All fights reserved.

A comparison of three different models for estimating relative risk in meta-analysis of clinical trials under unobserved heterogeneity

We focus on the comparison of three statistical models used to estimate the treatment effect in metaanalysis when individually pooled data are available. The models are two conventional models, namely a multi-level and a model based upon an approximate likelihood, and a newly developed model, the profile likelihood model which might be viewed as an extension of the Mantel-Haenszel approach. To exemplify these methods, we use results from a meta-analysis of 22 trials to prevent respiratory tract infections. We show that by using the multi-level approach, in the case of baseline heterogeneity, the number of clusters or components is considerably over-estimated. The approximate and profile likelihood method showed nearly the same pattern for the treatment effect distribution. To provide more evidence two simulation studies are accomplished. The profile likelihood can be considered as a clear alternative to the approximate likelihood model. In the case of strong baseline heterogeneity, the profile likelihood method shows superior behaviour when compared with the multi-level model. Copyright (C) 2006 John Wiley & Sons, Ltd.

A phylogenetic mixture model for detecting pattern-heterogeneity in gene sequence or character-state data

We describe a general likelihood-based 'mixture model' for inferring phylogenetic trees from gene-sequence or other character-state data. The model accommodates cases in which different sites in the alignment evolve in qualitatively distinct ways, but does not require prior knowledge of these patterns or partitioning of the data. We call this qualitative variability in the pattern of evolution across sites "pattern-heterogeneity" to distinguish it from both a homogenous process of evolution and from one characterized principally by differences in rates of evolution. We present studies to show that the model correctly retrieves the signals of pattern-heterogeneity from simulated gene-sequence data, and we apply the method to protein-coding genes and to a ribosomal 12S data set. The mixture model outperforms conventional partitioning in both these data sets. We implement the mixture model such that it can simultaneously detect rate- and pattern-heterogeneity. The model simplifies to a homogeneous model or a rate- variability model as special cases, and therefore always performs at least as well as these two approaches, and often considerably improves upon them. We make the model available within a Bayesian Markov-chain Monte Carlo framework for phylogenetic inference, as an easy-to-use computer program.

Rhodium assisted C-H activation of N-(2 '-hydroxyphenyl)benzaldimines. Synthesis, structure and electrochemical properties of a group of organorhodium complexes

Reaction of a group of N-(2'-hydroxyphenyl)benzaldimines, derived from 2-aminophenol and five para-substituted benzaldehydes (the para substituents are OCH3, CH3, H, Cl and NO2), with [Rh(PPh3)(3)Cl] in refluxing toluene in the presence of a base (NEW afforded a family of organometallic complexes of rhodium(III). The crystal structure of one complex has been determined by X-ray crystallography. In these complexes the benzaldimine ligands are coordinated to the metal center, via dissociation of the phenolic proton and the phenyl proton at the ortho position of the phenyl ring in the imine fragment, as dianionic tridentate C,N,O-donors, and the two PPh3 ligands are trans. The complexes are diamagnetic (low-spin d(6), S = 0) and show intense MLCT transitions in the visible region. Cyclic voltammetry shows a Rh(III)-Rh(IV) oxidation within 0.63-0.93 V vs SCE followed by an oxidation of the coordinated benzaldimine ligand. A reduction of the coordinated benzaldimine is also observed within -0.96 to -1.04 V vs SCE. Potential of the Rh(Ill)-Rh(IV) oxidation is found to be sensitive to the nature of the para-substituent. (c) 2006 Elsevier B.V. All rights reserved.

Oxorhenium(V) complexes with tetradentate NSNO pyridylthioazophenolates: syntheses, spectral and electrochemical studies

A family of oxorhenium (V) complexes of newly designed pyridylthioazophenolate ligands has been synthesized and isolated in pure form. The solid state structure of an organic compound (HL1) has been established by X-ray crystallography. The molecular structure observed in the solid state is that the two molecules of the ligand (HL1) in the asymmetric unit have similar geometries, except for the orientation of the pyridine ring. This series of organic moieties acts as tetradentate monobasic NSNO donor chelators in oxorhenium(V) complexes which has been characterized by elemental analyses, IR, H-1-NMR, UV-Vis. The complexes are 1: 1 electrolytes in nature in MeOH solution, the counter anion being ClO4). The electrochemical studies of the [(ReO)-O-V(L)Cl]ClO4 complexes in MeCN using TBAP as supporting electrolyte exhibit quasi-reversible voltammogram showing one-electron couple for [(ReO)-O-VI(L)Cl](2+)-[(ReO)-O-V(L)Cl](+) in the 1.11-1.29 V vs SCE range.

The synthesis of novel 3-substituted polypyrroles bearing crown-ether moieties and a study of their electrochemical properties

A series of fourteen novel pyrrole monomers substituted at the 3-position with aliphatic and aromatic crown-ether moieties have been synthesised in good yield and characterised extensively. Several of these compounds were electropolymerised successfully in acetonitrile, using both potentiostatic and galvanostatic modes and the electrochemical properties of those systems were studied via cyclic voltammetry in aqueous and organic media. Novel crown-ether substituted polypyrrole derivatives revealed reversible redox couples in LiClO4/CH3CN (0.1 M). The morphology of these novel crown-ether substituted polypyrrole derivatives was characterised by scanning electron microscopy. These polymers exhibited an open porous structure and half the charge was required when compared to polypyrrole to afford films of equal thickness. The mass change during polymerisation was followed by electrochemical quartz crystal microbalance measurement, and the rate of polymer growth was found to be nonlinear when compared to polypyrrole. (c) 2005 Elsevier B.V. All rights reserved.

Tris-(1,3-diaryltriazenide) complexes of rhodium: synthesis, structure and, spectral and electrochemical properties

Reaction of 1,3-diaryltriazenes (abbreviated in general as HL-R, where R stands for the para-substituent in the aryl fragment and H stands for the dissociable hydrogen atom, R = OCH3, CH3, H, Cl, NO2) with [Rh(PPh3)(2)(CO)Cl] in ethanol in the presence of NEt3 produces a series of tris-diaryltriazenide complexes of rhodium of type [Rh(L-R)(3)], where the triazenes are coordinated to rhodium as monoanionic, bidentate N,N-donors. Structure of the [Rh(L-OCH3)(3)] complex has been determined by X-ray crystallography. The complexes are diamagnetic, and show characteristic H-1 NMR signals and intense MLCT transitions in the visible region. They also fluoresce in the visible region under ambient condition while excited at around 400 nm. Cyclic voltammetry on these complexes shows a Rh(III)-Rh(IV) oxidation (within 0.84-1.67 V vs SCE), followed by an oxidation of the coordinated tri- and azene ligand (except the R = NO2 complex). An irreversible reduction of the coordinated triazene is also observed for all the complexes below -1.03 V vs SCE.

Conformational heterogeneity of tripeptides containing Boc-Leu-Aib as corner residues in the solid state

A critical analysis of single crystal X-ray diffraction studies on a series of terminally protected tripeptides containing a centrally positioned Aib (alpha-aminoisobutyric acid) residue has been reported. For the tripeptide series containing Boc-Ala-Aib as corner residues, all the reported peptides formed distorted type II beta-turn structures. Moreover, a series of Phe substituted analogues ( tripeptides with Boc-Phe-Aib) have also shown different beta-turn conformations. However, the Leu-modified analogues (tripeptides with Boc-Leu-Aib) disrupt the concept of beta-turn formation and adopt various conformations in the solid state. X-ray crystallography sheds some light on the conformational heterogeneity at atomic resolution. (c) 2007 Elsevier Ltd. All rights reserved.

Synthesis, structure, and electrochemical properties of a family of 2-(arylazo)phenolate complexes of ruthenium with unusual C-C coupling and N=Ncleavage

Reaction of 2-(4'-R-phenylazo)-4-methylphenols (R = OCH3, CH3, H, Cl, and NO2) with [Ru(dmso)(4)Cl-2] affords a family of five ruthenium(III) complexes, containing a 2-(arylazo)phenolate ligand forming a six-membered chelate ring and a tetradentate ligand formed from two 2-(arylazo) phenols via an unusual C-C coupling linki.ng the two ortho carbons of the phenyl rings in the arylazo fragment. A similar reaction with 2-(2'-methylphenylazo)-4-methylphenol with [Ru(dmso)(4)Cl-2] has afforded a similar complex, in which one 2-(2'-methylphenylazo)-4-methylphenolate ligand is coordinated forming a six-membered chelate ring, and the other two ligands have undergone the C-C coupling reaction, and the coupled species is coordinated as a tetradentate ligand forming a five-membered N,O-chelate ring, a nine-membered N,N-chelate ring, and another five-membered chelate ring. Reaction of 2-(2',6'-dimethylphenylazo)-4-methylphenol with [Ru(dmso)(4)Cl-2] has afforded a complex in which two 2-(2',6'-dimethylphenylazo)-4-methylphenols are coordinated as bidentate N,O-donors forming five- and six-membered chelate rings, while the third one has undergone cleavage across the N=N bond, and the phenolate fragment, thus generated, remains coordinated to the metal center in the iminosemiquinonate form. Structures of four selected complexes have been determined by X-ray crystallography. The first six complexes are one-electron paramagnetic and show rhombic ESR spectra. The last complex is diamagnetic and shows characteristic H-1 NMR signals. All the complexes show intense charge-transfer transitions in the visible region and a Ru(III)-Ru(IV) oxidation on the positive side of SCE and a Ru(III)-Ru(II) reduction on the negative side.

An electrochemical study of 4-aminothiophenol/pt nanoparticle multilayers on gold electrodes

Quartz crystal microbalance (QCM) measurements of the formation of a 4-aminothiophenol (4-ATP)self-assembled monolayer (SAM) at a gold electrode showed that a surface coverage of 118 ng cm(-2) was obtained after a 3 h exposure period, indicating that good surface coverage was achieved. Cyclic voltammetry of the ferricyanide redox couple across this SAM modified surface produced similar results to those of a bare electrode; however, the electroreduction of oxygen was found to be impaired. The 4-ATP SAM layer was not stable to repeated electrochemical oxidation and reduction; it is believed that the 4-ATP SAM layer was first converted to a 4'-mercapto-N-phenylquinone diimine (NPQD) layer followed by subsequent formation of a 4'-mercapto-N-phenylquinone monoimine (NPQM) layer. We also report a quartz crystal microbalance study of the attachment of platinum nanoparticles to such SAM modified electrodes. We show that five times the amount of platinum nanoparticles can be attached to a 4-ATP modified electrode surface (observed frequency change - 187 Hz) compared with an NPQD modified electrode surface (observed frequency change -35 Hz). The presence of the platinum particles was confirmed electrochemically by their surface electrochemical properties, which were different from those of the underlying gold electrode. It is believed that this is the first time that such direct evidence of electrochemical communication between platinum nanoparticles and a SAM modified electrode surface has been obtained. It was also shown to be possible to build up multilayer SAM/nanoparticle modified surfaces while maintaining efficient electrochemical communication. Up to three SAM/nanoparticle sandwich layers were constructed.

Electrochemical characterisation and anodic stripping voltammetry at mesoporous platinum rotating disc electrodes

Using the technique of liquid crystal templating a rotating disc electrode (RDE) was modified with a high surface area mesoporous platinum film. The surface area of the electrode was characterised by acid voltammetry, and found to be very high (ca. 86 cm(2)). Acid characterisation of the electrode produced distorted voltammograms was interpreted as being due to the extremely large surface area which produced a combination of effects such as localised pH change within the pore environment and also ohmic drop effects. Acid voltammetry in the presence of two different types of surfactant, namely Tween 20 and Triton X-100, suggested antifouling properties associated with the mesoporous deposit. Further analysis of the modified electrode using a redox couple in solution showed typical RDE behaviour although extra capacitive currents were observed due to the large surface area of the electrode. The phenomenon of underpotential deposition was exploited for the purpose of anodic stripping voltammetry and results were compared with data collected for microelectrodes. Underpotential deposition of metal ions at the mesoporous RDE was found to be similar to that at conventional platinum electrodes and mesoporous microelectrodes although the rate of surface coverage was found to be slower at a mesoporous RDE. It was found that a mesoporous RDE forms a suitable system for quantification of silver ions in solution.