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PubMed1990

An empirical demonstration of the problem of cluster dissimilarity from different clustering methods in a single sample.

This study utilized the four most commonly employed clustering techniques (CLINK, SLINK, UPGMA, and Ward's) to illustrate the dissimilarity of cluster group membership (based upon short-form MMPI scale scores and a measure of alcohol dependency) between partitions in a sample of 113 impaired driving offenders. Results, examined with the Rand index of cluster comparison, demonstrated that cluster group membership can be so different between alternative clustering methods as to equal chance assignment. Cautions are given with regard to the use of cluster analysis for other than exploratory work. In particular, psychologists are cautioned against attempting to use cluster analysis based upon personality inventory scores (which can never be wholly reliable or discrete) for patient classification.

Adult↗

PubMed2004

Comparing completely and stratified randomized designs in cluster randomized trials when the stratifying factor is cluster size: a simulation study.

Stratified randomized designs are popular in cluster randomized trials (CRTs) because they increase the chance of the intervention groups being well balanced in terms of identified prognostic factors at baseline and may increase statistical power. The objective of this paper is to assess the gains in power obtained by stratifying randomization by cluster size, when cluster size is associated with an important cluster level factor which is otherwise unaccounted for in data analysis. A simulation study was carried out using a CRT where UK general practices were the randomized units as a template. The results show that when cluster size is strongly associated with a cluster level factor which is predictive of outcome, the stratified randomized design has superior power results to the completely randomized design and that the superiority is related to the number of clusters.

Cluster Analysis↗

PubMed2006

The geography of power: statistical performance of tests of clusters and clustering in heterogeneous populations.

Heterogeneous population densities complicate comparisons of statistical power between hypothesis tests evaluating spatial clusters or clustering of disease. Specifically, the location of a cluster within a heterogeneously distributed population at risk impacts power properties, complicating comparisons of tests, and allowing one to map spatial variations in statistical power for different tests. Such maps provide insight into the overall power of a particular test, and also indicate areas within the study area where tests are more or less likely to detect the same local increase in relative risk. While such maps are largely driven by local sample size, we also find differences due to features of the statistics themselves. We illustrate these concepts using two tests: Tango's index of clustering and the spatial scan statistic. Furthermore, assessments of the accuracy of the 'most likely cluster' involve not only statistical power, but also spatial accuracy in identifying the location of a true underlying cluster. We illustrate these concepts via induction of artificial clusters within the observed incidence of severe cardiac birth defects in Santa Clara County, CA in 1981.

California↗

PubMed2007

Properties of analysis methods that account for clustering in volume-outcome studies when the primary predictor is cluster size.

In recent years health services researchers have conducted 'volume-outcome' studies to evaluate whether providers (hospitals or surgeons) who treat many patients for a specialized condition have better outcomes than those that treat few patients. These studies and the inherent clustering of events by provider present an unusual statistical problem. The volume-outcome setting is unique in that 'volume' reflects both the primary factor under study and also the cluster size. Consequently, the assumptions inherent in the use of available methods that correct for clustering might be violated in this setting. To address this issue, we investigate via simulation the properties of three estimation procedures for the analysis of cluster correlated data, specifically in the context of volume-outcome studies. We examine and compare the validity and efficiency of widely-available statistical techniques that have been used in the context of volume-outcome studies: generalized estimating equations (GEE) using both the independence and exchangeable correlation structures; random effects models; and the weighted GEE approach proposed by Williamson et al. (Biometrics 2003; 59:36-42) to account for informative clustering. Using data generated either from an underlying true random effects model or a cluster correlated model we show that both the random effects and the GEE with an exchangeable correlation structure have generally good properties, with relatively low bias for estimating the volume parameter and its variance. By contrast, the cluster weighted GEE method is inefficient.

Aged↗

PubMed2025

Benchmarking methods for measuring biosynthetic gene cluster similarity and determination of gene cluster families.

MOTIVATION: Natural products are often produced by a set of biosynthetic enzymes that are encoded by genes clustered together in the producer's genome, referred to as a biosynthetic gene cluster (BGC). The ability to compare and cluster BGCs is essential for several applications, including predicting which bacteria will make a known product and assessing the potential diversity of natural products produced by a set of bacteria. There are multiple methods for comparing and clustering BGCs based on their similarity, but there has been a lack of investigation into how strongly BGC similarity relates to product structural similarity and how these methods perform relative to each other. RESULTS: Using publicly available databases, we developed a benchmark dataset to assess how well different BGC similarity metrics correlate with the structural similarity of their products and how well these methods cluster BGCs. We found that all methods showed moderate correlation between BGC and structural similarity, with correlations improving for more similar BGCs and varying significantly by BGC biosynthetic class. Analysis of outliers revealed some outliers were due to mistakes or omissions in public datasets, while others represented deviation between BGC similarity and product structural similarity. All methods generally performed better on clustering metrics, with BiG-SCAPE performing the best after errors in the public datasets had been corrected. AVAILABILITY AND IMPLEMENTATION: Scripts and data required to reproduce the results are available at https://github.com/aswalker-lab/BGC-clustering-benchmark and processed similarity, clusters, and scaffolds are also available at https://huggingface.co/datasets/allie-walker/BGC-clustering-benchmark. Code is also available at Zenodo: 10.5281/zenodo.17373546.

Multigene Family↗

PubMed2006

Dynamic characterization of cluster structures for robust and inductive support vector clustering.

A topological and dynamical characterization of the cluster structures described by the support vector clustering is developed. It is shown that each cluster can be decomposed into its constituent basin level cells and can be naturally extended to an enlarged clustered domain, which serves as a basis for inductive clustering. A simplified weighted graph preserving the topological structure of the clusters is also constructed and is employed to develop a robust and inductive clustering algorithm. Simulation results are given to illustrate the robustness and effectiveness of the proposed method.

Algorithms↗

PubMed2002

Advanced statistics: statistical methods for analyzing cluster and cluster-randomized data.

Sometimes interventions in randomized clinical trials are not allocated to individual patients, but rather to patients in groups. This is called cluster allocation, or cluster randomization, and is particularly common in health services research. Similarly, in some types of observational studies, patients (or observations) are found in naturally occurring groups, such as neighborhoods. In either situation, observations within a cluster tend to be more alike than observations selected entirely at random. This violates the assumption of independence that is at the heart of common methods of statistical estimation and hypothesis testing. Failure to account for the dependence between individual observations and the cluster to which they belong can have profound implications on the design and analysis of such studies. Their p-values will be too small, confidence intervals too narrow, and sample size estimates too small, sometimes to a dramatic degree. This problem is similar to that caused by the more familiar "unit of analysis error" seen when observations are repeated on the same subjects, but are treated as independent. The purpose of this paper is to provide an introduction to the problem of clustered data in clinical research. It provides guidance and examples of methods for analyzing clustered data and calculating sample sizes when planning studies. The article concludes with some general comments on statistical software for cluster data and principles for planning, analyzing, and presenting such studies.

Cluster Analysis↗

PubMed2004

Deviations from the population-averaged versus cluster-specific relationship for clustered binary data.

There has been much debate about the relative merits of mixed effects and population-averaged logistic models. We present a different perspective on this issue by noting that the investigation of the relationship between these models for a given dataset offers a type of sensitivity analysis that may reveal problems with assumptions of the mixed effects and/or population-averaged models for clustered binary response data in general and longitudinal binary outcomes in particular. We present several datasets in which the following violations of assumptions are associated with departures from the expected theoretical relationship between these two models: 1) negative intra-cluster correlations; 2) confounding of the response-covariate relationship by cluster effects; and 3) confounding of autoregressive relationships by the link between baseline outcomes and subject effects. Under each of these conditions, the expected theoretical attenuation of the population-averaged odds ratio relative to the cluster-specific odds ratio does not necessarily occur. In all cases, the naive fitting of a random intercept logistic model appears to lead to bias. In response, the random intercept model is modified to accommodate negative intra-cluster correlations, confounding due to clusters, or baseline correlations with random effects. Comparisons are made with GEE estimation of population-averaged models and conditional likelihood estimation of cluster-specific models. Several examples, including a cross-over trial, a multicentre nonrandomized treatment study, and a longitudinal observational study are used to illustrate these modifications.

Animals↗

PubMedDate not supplied

Cluster analysis: significance, empty space, clustering tendency, non-uniformity. II--Empty Space index.

The here presented Empty Space index (ES) evaluates the fraction of the information space without experimental points, i.e. the space where the distance from an experimental point is significantly larger than the mean distance between the experimental points themselves. ES can be used to eliminate the ambiguity of the some clustering indexes, that aim to evaluate the separation of the data set in clusters, but these clustering indexes are really a mixed measure of clustering, of empty space (the empty space does not necessarily correspond to the break between clusters) and of the degree of uniformity of the objects. The ES index can be used also to correct the MST index, the clustering index based on the distribution of edge lengths in the minimum spanning tree connecting the objects. The corrected MST index seems to be a reliable measure of the clustering degree.

Chemistry Techniques, Analytical↗

PubMed2003

Tuberculosis contact investigation and DNA fingerprint surveillance in The Netherlands: 6 years' experience with nation-wide cluster feedback and cluster monitoring.

SETTING: The Netherlands, 1995-2000. OBJECTIVES: To describe the contribution of 6 years of nationwide DNA fingerprint surveillance to tuberculosis control in general and to conventional contact investigations in particular. DESIGN: All Mycobacterium tuberculosis cultures are subjected to standardised IS6110-based RFLP typing, and clustered cases are systematically reported to the regional TB services involved (cluster feedback). Standardised questionnaires are used to collect information on contact investigations and epidemiological links (epi links) at regional level. Revision of the questionnaires for the period 1997-2000 allows comparison of epi linking before and after cluster feedback. RESULTS: Among 2206 clustered cases, 462 (21%) epi links were expected before the RFLP result, whereas an additional 540 (24%) epi links were established after cluster feedback. Epi links based on documented exposure increased by 35%, from 357 to 550 (P < 0.001). Only 1% of contact investigations were extended, however, and relatively few additional persons with active or latent tuberculosis were diagnosed. Reasons for the limited impact on contact investigation outcome were 1) contact took place 1-7 years previously (51%), 2) documented contact involved a subsequent case in the cluster (21%), 3) casual contact (15.5%) and 4) different region (9%). Five per cent of epi links established by contact investigation were contradicted by RFLP data. Epi links were more frequently documented in Dutch (41%) than non-Dutch cases (19%, OR 3.0; 95%CI 1.41-1.91). Cluster monitoring permitted: 1) identification of transmission chains that could not be detected by contact investigations, 2) development and evaluation of targeted interventions, and 3) identification of professional failures and poor programme performance. CONCLUSIONS: RFLP surveillance forms the bridge between conventional contact investigation and other forms of targeted active case finding. Combining both complementary strategies in a comprehensive approach to systematic outbreak monitoring and management allows countries in the elimination phase of the disease to better target and evaluate TB control interventions.

Cluster Analysis↗

PubMed2002

An adaptive meta-clustering approach: combining the information from different clustering results.

With the development of microarray techniques, there is an increasing need of information processing methods to analyze the high throughput data. Clustering is one of the most promising candidates because of its simplicity, flexibility and robustness. However, there is no "perfect" clustering approach outperforming its counterparts, and it is hard to evaluate and combine the results from different techniques, especially in a field without much prior knowledge, such as bioinformatics. This paper proposes a meta-clustering approach to extract the information from results of different clustering techniques, so that a better interpretation of the data distribution can be obtained. A special distance measure is defined to represent the statistical "signal" of each cluster produced by various clustering techniques. The algorithm is applied on both artificial and real data Simulations show that the proposed approach is able to extract the information efficiently and accurately from the input clustering structure.

Algorithms↗

PubMed2005

Efficient determination of cluster boundaries for analysis of gene expression profile data using hierarchical clustering and wavelet transform.

The existing methods for clustering of gene expression profile data either require manual inspection and other biological knowledge or require some cut-off value which can not be directly calculated from the given data set. Thus, the problem of systematic and efficient determination of cluster boundaries of clusters in gene expression profile data still remains demanding. In this context, we have developed a procedure for automatic and systematic determination of the boundaries of clusters in the hierarchical clustering of gene expression data based on the ratio of with-in class variance and between-class variance, which can be fully calculated from the given expression data. After the determination of dendrogram based on agglomerative hierarchical clustering, this ratio is used to determine the cluster boundary. Except this ratio which can be completely calculated from the given expression profile data, unlike other existing approaches, our approach does not require any manual inspection or biological knowledge. Our results are favorably comparable and in some of cases better than existing method which does not utilize prior information or manual inspection. Moreover, gene expression profile data are often contaminated with various type of noise and in order to reduce this noise content, we have also applied image enhancing technique called discrete wavelet transform. We tested a number of mother wavelet functions to smooth the noise in the gene expression data set and obtained some improvements in the quality of the results.

Algorithms↗

PubMed2006

Characterization of E. coli O24 and O56 O antigen gene clusters reveals a complex evolutionary history of the O24 gene cluster.

O antigen is part of the lipopolysaccharide present in the outer membrane of Gram-negative bacteria. It has many different forms, which are almost entirely due to genetic variations of O antigen gene clusters. In this study, the O antigen gene clusters of E. coli O24 and O56 were sequenced, and all genes were assigned functions on the basis of homology. Comparison of O antigen gene clusters indicated that E. coli O24 O antigen gene cluster has possibly arisen from the E. coli O56 gene cluster, through inactivation of two glycosyltransferase genes and acquisition of two new genes from E. coli O157 and O152, respectively. The insertion sequence elements seemed to play important roles for the assembly of the O24 O antigen gene cluster. This is the first time that the evolutionary history of a multi-origin O antigen gene cluster is clearly demonstrated. Genes specific to E. coli O24 and O56 were also identified, which may be used for development of DNA-based serotyping schemes.

Base Sequence↗

PubMed1993

Characterization of the [3Fe-4S] and [4Fe-4S] clusters in unbound PsaC mutants C14D and C51D. Midpoint potentials of the single [4Fe-4S] clusters are identical to FA and FB in bound PsaC of photosystem I.

In a previous paper we showed that the C51D mutant of PsaC contains a [3Fe-4S] cluster in the FA site and a [4Fe-4S] cluster in the FB site and that the C14D mutant contains an uncharacterized cluster in the FB site and a [4Fe-4S] cluster in the FA site [Zhao, J. D., Li, N., Warren, P. V., Golbeck, J. H., & Bryant, D. A. (1992) Biochemistry 31, 5093-5099]. In this paper we describe the electrochemical and electron spin resonance properties of the recombinant C14D and C51D holoproteins after in vitro reinsertion of the iron-sulfur clusters. Unbound PsaC shows no significant resonances in the oxidized state, but the unbound C14D and C51D mutant proteins show an intense set of resonances at g approximately 2.02 and 1.99 characteristic of an oxidized [3Fe-4S]1+/0 cluster. The Em' values for the [3Fe-4S]1+/0 clusters in C14D (FB*) and C51D (FA*) are -98 mV, and both represent one-electron transfers. After reduction with dithionite at pH 10.0, wild-type PsaC shows a broad set of resonances resulting from the superposition of FA- and FB- characterized by a low-field peak at an apparent g value of 2.051 and a high-field trough at an apparent g value of 1.898. The FB resonances in C51D were slightly narrower, with a low-field peak at an apparent g value of 2.039 and high-field trough at an apparent g value of 1.908.(ABSTRACT TRUNCATED AT 250 WORDS)

Bacterial Proteins↗

PubMed2001

Synthesis and characterization of an Al(69)(3-) cluster with 51 naked Al atoms: analogies and differences to the previously characterized Al(77)(2-) cluster.

A disproportionation process of a metastable AlCl solution with a simultaneous ligand exchange-Cl is substituted by N(SiMe(3))(2)-leads to a [Al(69)[N(SiMe(3))(2)](18)](3-) cluster compound that can be regarded as an intermediate on the way to bulk metal formation. The cluster was characterized by an X-ray crystal structural analysis. Regarding its structure and the packing within the crystal, this metalloid cluster with 4 times more Al atoms than ligands is compared to the [Al(77)N(SiMe(3))(2)](20)](2-) cluster that has been published four years ago. Although there is a similar packing density of the Al atoms in both clusters as well as in Al metal, the X-ray structural analysis shows significant differences in topology and distance proportions. The differences between these-at a first glance almost identical-Al clusters demonstrate that results of physical measuring, e.g., of nanostructured surfaces which carry supposedly identical cluster species, have to be interpreted with great caution.

Journal Article↗

PubMed2002

High nuclearity ruthenium-tin clusters from the reactions of triphenylstannane with pentaruthenium carbonyl carbido cluster complexes.

The reaction of Ru(5)(CO)(15)(mu(5)-C), 1, with Ph(3)SnH in the presence of UV irradiation has yielded the Ph(3)SnH adduct Ru(5)(CO)(15)(SnPh(3))(mu(5)-C)(mu-H), 3, by SnH bond activation and cleavage of one Ru-Ru bond in the cluster of 1. The reaction of 1 with Ph(3)SnH at 127 degrees C yielded the high nuclearity cluster compound Ru(5)(CO)(10)(SnPh(3))(mu-SnPh(2))(4)(&mu(5)-C)(mu-H), 4, that contains five tin ligands. Four of these are SnPh(2) groups that bridge each edge of the base of the Ru(5) square pyramidal cluster. The reaction of Ph(3)SnH with the benzene-substituted cluster Ru(5)(CO)(12)(C(6)H(6))(mu(5)-C), 2, at 68 degrees C yielded two products: Ru(5)(CO)(11)(SnPh(3))(C(6)H(6))(mu(5)-C)(mu-H), 5, and Ru(5)(CO)(10)(SnPh(3))(2)(C(6)H(6))(mu(5)-C)(mu-H)(2), 6. Both contain square pyramidal Ru(5) clusters with one and two SnPh(3) groups, respectively. At 127 degrees C, the reaction of 2 with an excess of Ph(3)SnH has led to the formation of two new high-nuclearity cluster complexes: Ru(5)(CO)(8)(mu-SnPh(2))(4)(C(6)H(6))(mu(5)-C), 7, and Ru(5)(CO)(7)(mu-SnPh(2))(4)(SnPh(3))(C(6)H(6))(mu-H), 8. Both compounds contain square pyramidal Ru(5) clusters with SnPh(2) groups bridging each edge of the square base. Compound 8 contains a SnPh(3) group analogous to that of compound 4. When treated with CO, compound 8 is converted to 4. When heated to 68 degrees C, compound 5 was converted to the new compound Ru(5)(CO)(11)(C(6)H(6))(mu(4)-SnPh)(mu(3)-CPh), 9, by loss of benzene and the shift of a phenyl group from the tin ligand to the carbido carbon atom to form a triply bridging benzylidyne ligand and a novel quadruply bridging stannylyne ligand.

Journal Article↗

PubMed2006

Metal clusters as ligands. Substitution of fe ions in Fe/Mo/S clusters by thiophilic CuI ions.

The reactivity of Fe/S and Fe/Mo/S clusters, similar or analogous to those occurring in biological systems, with thiophilic metal ions has not been explored. In this Communication, we demonstrate that synthesis of heteropolynuclear clusters with different coordination geometries for different metals at different sites is possible by metal substitution or by metal addition reactions. The two clusters we report herein ([(Cl4-cat)2Mo2Cu5Fe4S9(PnPr3)7(SPnPr3)2]PF6 and [(Cl4-cat)2Mo2Cu6Fe4S10(PnPr3)8]) contain Fe, Mo, and Cu, which display pseudotetrahedral, pseudooctahedral, and pseudotrigonal geometries, respectively. The synthesis of these clusters is achieved by the addition of appropriate amounts of [Cu(CH3CN)4]+ to [(Cl4-cat)2Mo2Fe8(PnPr3)6]. The formation of the different products is temperature- and solvent-dependent. The Cu(I) units incorporated into the metal cluster framework, either bind to available lone pairs of the already bridging S ligands or displace the less thiophilic Fe atoms. Among the essential features of these new molecules are recognizable Fe/S fragments including an Fe6S9 core in the first cluster and the pentlandite Fe4Cu4S6 core in the second cluster.

Cations↗

PubMed2002

An anchoring role for FeS clusters: chelation of the amino acid moiety of S-adenosylmethionine to the unique iron site of the [4Fe-4S] cluster of pyruvate formate-lyase activating enzyme.

Pyruvate formate-lyase activating enzyme (PFL-AE) generates the catalytically essential glycyl radical on pyruvate formate-lyase via the interaction of the catalytically active [4Fe-4S]+ cluster with S-adenosylmethionine (AdoMet). Like other members of the Fe-S/AdoMet family of enzymes, PFL-AE is thought to function via generation of an AdoMet-derived 5'-deoxyadenosyl radical intermediate; however, the mechanistic steps by which this radical is generated remain to be elucidated. While all of the members of the Fe-S/AdoMet family of enzymes appear to have a unique iron site in the [4Fe-4S] cluster, based on the presence of a conserved three-cysteine cluster binding motif, the role of this unique site has been elusive. Here we utilize 35-GHz pulsed electron nuclear double resonance (ENDOR) studies of the [4Fe-4S]+ cluster of PFL-AE in complex with isotopically labeled AdoMet (denoted [1+/AdoMet]) to show that the unique iron serves to anchor the AdoMet for catalysis. AdoMet labeled with 17O at the carboxylate shows a coupling of A = 12.2 MHz, consistent with direct coordination of the carboxylate to the unique iron of the cluster. This is supported by 13C-ENDOR with the carboxylato carbon labeled with 13C, which shows a hyperfine coupling of 0.71 MHz. AdoMet enriched with 15N at the amino position gives rise to a spectrum with A(15N) = 5.8 MHz, consistent with direct coordination of the amino group to a unique iron of the cluster. Together, the results demonstrate that the unique iron of the [4Fe-4S] cluster anchors AdoMet by forming a classical N/O chelate with the amino and carboxylato groups of the methionine fragment.

Acetyltransferases↗