Model-based Clustering Approach Research Articles

Identifying clusters from multidimensional symptom trajectories in postpartum women.

Depressive symptoms, stress, fatigue, and lack of sleep are often experienced by women in the perinatal period and are potential contributors to adverse maternal and child health outcomes. To explore the evolution of symptoms and identify groups of women of similar severity and patterns, we utilized clustering of multidimensional symptom trajectories. In an observational study data were collected from pregnant women in the 3rd trimester (36 weeks prenatal) and in the postnatal period at weeks 1 and 2 as well as at 1-, 2-, 3-, and 6-months postpartum. Depressive symptoms and maternal stress were measured using the Edinburg Postnatal Depression Scale (EPDS) and the Perceived Stress Scale (PSS), respectively. Self-reported duration of sleep and levels of fatigue also were collected. A model-based clustering approach was used to classify women by their symptom severity. The sample included 151 pregnant women with a 6-month follow-up. Two clusters were identified. Cluster 1 (n = 43) comprised women with fewer depressive symptoms, less perceived stress, lower likelihood of being fatigued, increased sleep duration and a negative trend in EPDS (β = -0.05, CI [-0.09, -0.001]), and PSS (β = -0.09, CI [-0.17, -0.01]). Cluster 2 (n = 108) comprised women with higher EPDS and PSS scores, increased likelihood of fatigue and lower sleep duration with a positive trend in sleep hours (β = -0.02, CI [0.01, 0.03]). Pro-inflammatory markers interleukin-6 and tumor necrosis factor-α were associated with longer sleep duration and fewer depressive symptoms, respectively. Using this methodology in maternal and child health research can potentially predict women's risk of developing severe symptoms and help clinicians provide timely interventions.

A Model-based Clustering Approach for Analyzing Energy-related Financial Literacy and Its Determinants

Recent research highlights the role of consumer’s energy-related financial literacy in adoption of energy efficient household appliances in order to reduce the energy-efficiency gap within the household sector. The computation of an indicator for such a literacy measure has followed a somewhat less refined approach though. This paper demonstrates the use of a model-based clustering strategy in order to differentiate the population based on the level of energy-related financial literacy. Using a Swiss data with 6, 722 respondents, we are able to identify three latent groups that represent low, mid and high levels of literacy. We use this new measure within an ordered logit setting with the goal of explaining the determinants of the level of energy-related financial literacy and compare empirical results using classical indicators and approaches. The empirical findings suggest a significant gender-gap among the Swiss population, i.e. females, even those with university education, are less likely to possess a high level of energy-related financial literacy. Individuals who display strong concern for free-riding on their own energy reduction behavior, are also found to have higher odds of belonging to the low literacy group. The results show that it is possible to identify latent classes that have a general and intuitive meaning and provides support to the model-based clustering approach as a sophisticated alternative. This could be a useful approach when empirical researchers are interested in (attribute-based) latent groups of consumers. The identification of latent classes also provides a possibility to target consumers belonging to these classes with specific policy measures in order to increase their level of literacy.

Subject level clustering using a negative binomial model for small transcriptomic studies

BackgroundUnsupervised clustering represents one of the most widely applied methods in analysis of high-throughput ‘omics data. A variety of unsupervised model-based or parametric clustering methods and non-parametric clustering methods have been proposed for RNA-seq count data, most of which perform well for large samples, e.g. N ≥ 500. A common issue when analyzing limited samples of RNA-seq count data is that the data follows an over-dispersed distribution, and thus a Negative Binomial likelihood model is often used. Thus, we have developed a Negative Binomial model-based (NBMB) clustering approach for application to RNA-seq studies.ResultsWe have developed a Negative Binomial Model-Based (NBMB) method to cluster samples using a stochastic version of the expectation-maximization algorithm. A simulation study involving various scenarios was completed to compare the performance of NBMB to Gaussian model-based or Gaussian mixture modeling (GMM). NBMB was also applied for the clustering of two RNA-seq studies; type 2 diabetes study (N = 96) and TCGA study of ovarian cancer (N = 295). Simulation results showed that NBMB outperforms GMM applied with different transformations in majority of scenarios with limited sample size. Additionally, we found that NBMB outperformed GMM for small clusters distance regardless of sample size. Increasing total number of genes with fixed proportion of differentially expressed genes does not change the outperformance of NBMB, but improves the overall performance of GMM. Analysis of type 2 diabetes and ovarian cancer tumor data with NBMB found good agreement with the reported disease subtypes and the gene expression patterns. This method is available in an R package on CRAN named NB.MClust.ConclusionUse of Negative Binomial model based clustering is advisable when clustering over dispersed RNA-seq count data.

Structural stability, quantitative change: A latent class analysis approach towards gender role attitudes in Germany

Since the 1960s, social science surveys have aimed to assess respondents' attitudes towards gender roles. In this paper, a model-based clustering approach towards gender role attitudes is proposed in contrast to commonly used dimensional methods. Working from a role theory perspective, we expect different profiles in the population when it comes to role expectations. Using data from the German General Social Survey in 1991 and 2012, we identify attitude patterns via multi-group latent class analysis, taking differences between Eastern and Western Germany into account. Five latent classes representing different combinations of role expectations towards couples and parents and varying levels of intensity are distinguished. Attitude change is assessed by comparing latent class prevalence over time, while statistically testing for measurement equivalence. The analysis reveals a regionally variable decrease in traditional role models: Eastern Germany exhibits a faster pace of ‘de-traditionalization’ and less potential for role conflicts regarding working mothers.

Variable selection methods for model-based clustering

Model-based clustering is a popular approach for clustering multivariate data which has seen applications in numerous fields. Nowadays, high-dimensional data are more and more common and the model-based clustering approach has adapted to deal with the increasing dimensionality. In particular, the development of variable selection techniques has received a lot of attention and research effort in recent years. Even for small size problems, variable selection has been advocated to facilitate the interpretation of the clustering results. This review provides a summary of the methods developed for variable selection in model-based clustering. Existing R packages implementing the different methods are indicated and illustrated in application to two data analysis examples.

Developmental trajectories of children’s symbolic numerical magnitude processing skills and associated cognitive competencies

Although symbolic numerical magnitude processing skills are key for learning arithmetic, their developmental trajectories remain unknown. Therefore, we delineated during the first 3years of primary education (5–8years of age) groups with distinguishable developmental trajectories of symbolic numerical magnitude processing skills using a model-based clustering approach. Three clusters were identified and were labeled as inaccurate, accurate but slow, and accurate and fast. The clusters did not differ in age, sex, socioeconomic status, or IQ. We also tested whether these clusters differed in domain-specific (nonsymbolic magnitude processing and digit identification) and domain-general (visuospatial short-term memory, verbal working memory, and processing speed) cognitive competencies that might contribute to children’s ability to (efficiently) process the numerical meaning of Arabic numerical symbols. We observed minor differences between clusters in these cognitive competencies except for verbal working memory for which no differences were observed. Follow-up analyses further revealed that the above-mentioned cognitive competencies did not merely account for the cluster differences in children’s development of symbolic numerical magnitude processing skills, suggesting that other factors account for these individual differences. On the other hand, the three trajectories of symbolic numerical magnitude processing revealed remarkable and stable differences in children’s arithmetic fact retrieval, which stresses the importance of symbolic numerical magnitude processing for learning arithmetic.

Identifying hybridization and admixture using SNPs: application of the DArTseq platform in phylogeographic research on vertebrates

Next-generation sequencing (NGS) approaches are increasingly being used to generate multi-locus data for phylogeographic and evolutionary genetics research. We detail the applicability of a restriction enzyme-mediated genome complexity reduction approach with subsequent NGS (DArTseq) in vertebrate study systems at different evolutionary and geographical scales. We present two case studies using SNP data from the DArTseq molecular marker platform. First, we used DArTseq in a large phylogeographic study of the agamid lizard Ctenophorus caudicinctus, including 91 individuals and spanning the geographical range of this species across arid Australia. A low-density DArTseq assay resulted in 28 960 SNPs, with low density referring to a comparably reduced set of identified and sequenced markers as a cost-effective approach. Second, we applied this approach to an evolutionary genetics study of a classic frog hybrid zone (Litoria ewingii–Litoria paraewingi) across 93 individuals, which resulted in 48 117 and 67 060 SNPs for a low- and high-density assay, respectively. We provide a docker-based workflow to facilitate data preparation and analysis, then analyse SNP data using multiple methods including Bayesian model-based clustering and conditional likelihood approaches. Based on comparison of results from the DArTseq platform and traditional molecular approaches, we conclude that DArTseq can be used successfully in vertebrates and will be of particular interest to researchers working at the interface between population genetics and phylogenetics, exploring species boundaries, gene exchange and hybridization.

Energy paths in the European Union: A model-based clustering approach

This paper examines typical “energy paths”, i.e. the intertemporal development of the energy mixes of the member states of the European Union over 1971–2010. We apply model-based clustering to detect major energy profiles and their compositional dynamics. The seven identified clusters show typical combinations of energy carriers dominating the primary energy consumption of a country. We find that countries tend to take a path towards higher quality energy mixes over time, however path inertia and dependencies arise from both infrastructure and resource endowments. Higher energy quality profiles are usually associated with higher national income and energy use per capita, providing some evidence of the existence of a national-level energy ladder. We also find convergence in energy intensity over time, and a relationship between a country's own resources and import dependency.

Comparative transcriptome analyses of flower development in four species of Achimenes (Gesneriaceae)

BackgroundFlowers have an amazingly diverse display of colors and shapes, and these characteristics often vary significantly among closely related species. The evolution of diverse floral form can be thought of as an adaptive response to pollination and reproduction, but it can also be seen through the lens of morphological and developmental constraints. To explore these interactions, we use RNA-seq across species and development to investigate gene expression and sequence evolution as they relate to the evolution of the diverse flowers in a group of Neotropical plants native to Mexico—magic flowers (Achimenes, Gesneriaceae).ResultsThe assembled transcriptomes contain between 29,000 and 42,000 genes expressed during development. We combine sequence orthology and coexpression clustering with analyses of protein evolution to identify candidate genes for roles in floral form evolution. Over 25% of transcripts captured were distinctive to Achimenes and overrepresented by genes involved in transcription factor activity. Using a model-based clustering approach we find dynamic, temporal patterns of gene expression among species. Selection tests provide evidence of positive selection in several genes with roles in pigment production, flowering time, and morphology. Combining these approaches to explore genes related to flower color and flower shape, we find distinct patterns that correspond to transitions of floral form among Achimenes species.ConclusionsThe floral transcriptomes developed from four species of Achimenes provide insight into the mechanisms involved in the evolution of diverse floral form among closely related species with different pollinators. We identified several candidate genes that will serve as an important and useful resource for future research. High conservation of sequence structure, patterns of gene coexpression, and detection of positive selection acting on few genes suggests that large phenotypic differences in floral form may be caused by genetic differences in a small set of genes. Our characterized floral transcriptomes provided here should facilitate further analyses into the genomics of flower development and the mechanisms underlying the evolution of diverse flowers in Achimenes and other Neotropical Gesneriaceae.

Energy Paths in the European Union: A Model-Based Clustering Approach

This paper examines typical “energy paths”, i.e. the intertemporal development of the energy mixes of the member states of the European Union over 1971-2010. We apply model based clustering to detect major energy profiles and their compositional dynamics. The seven identified clusters show typical combinations of energy carriers dominating the primary energy consumption of a country. We find that countries tend to take a path towards higher quality energy mixes over time, however path inertia and dependencies arise from both infrastructure and resource endowments. Higher energy quality profiles are usually associated with higher national income and energy use per capita, supporting some evidence on the existence of a national-level energy ladder. We also find convergence in energy intensity over time, and a relationship between own resources and import dependency.

A Longitudinal Study of Polish Attitudes to Emigration: A Latent Markov Model Approach

Latent class analysis can be viewed as a special case of model-based clustering for multivariate discrete data. When longitudinal data are to be analysed, the research questions concern some form of change over time. The latent Markov model is a variation of the latent class model that is applied to estimate not only the prevalence of latent class membership, but the incidence of transitions over time in latent class membership. In 2004, Poland joined the European Union, prompting a number of Poles to leave the country. To examine this event, a model-based clustering approach for grouping and detecting inhomogeneities of public attitudes to emigration from Poland was used. It focuses especially on latent Markov models with covariates, which additionally made it possible to investigate the dynamic pattern of Poles’ attitudes to emigration for different demographic features. depmixS4, Rsolnp and LMest packages of R were used.

Assessment of the genetic variation in alfalfa genotypes using SRAP markers for breeding purposes

The molecular diversity studies of alfalfa (Medicago sativa L.) germplasm could contribute to a more precise selection of parental populations in many breeding programs. Sequence-related amplified polymorphism (SRAP) markers were used to assess the genetic diversity of 110 individual plants from 13 selected alfalfa cultivars, landraces, and natural populations from Tunisia, Australia, Serbia, and Kazakhstan. Ten polymorphic SRAP primer combinations generated 137 alleles with 0.90 polymorphism information content. The percentage of polymorphic bands per genotype ranged from 57.66% to 70.07% with a mean of 64.29% and overall value of 100%. The genotype Sardi 10 had the highest value for the effective number of alleles; Nei’s gene diversity and Shannon information index, exhibited the highest variability level (Ne = 1.453, He = 0.259, I = 0.381, respectively), whereas the genotype Nera exhibited the lowest variability level (Ne = 1.359, He = 0.211, I = 0.317, respectively). The AMOVA analysis showed that 68% of the variance was within the genotypes; this was in line with the coefficient of genetic differentiation (Gst = 0.370). The genetic relatedness of alfalfa individuals analyzed by the neighbor-joining dendrogram was consistent with the Bayesian model-based clustering approach. The exceptions were individuals from genotypes Slavija and Nera, which were grouped separately by STRUCTURE analyses. These results provide useful information for the management of alfalfa genetic resources and the rational use of local and foreign alfalfa populations in breeding programs focused on the development of new, high-yielding cultivars more adapted to drought conditions in North Africa.

A timecourse analysis of systemic and gonadal effects of temperature on sexual development of the red-eared slider turtle Trachemys scripta elegans

Temperature dependent sex determination (TSD) is the process by which the environmental temperature experienced during embryogenesis influences the sex of an organism, as in the red-eared slider turtle Trachemys scripta elegans. In accord with current paradigms of vertebrate sex determination, temperature is believed to exert its effects on sexual development in T. scripta entirely within the middle third of development, when the gonad is forming. However, whether temperature regulates the transcriptome in T. scripta early embryos in a manner that could influence secondary sex characteristics or establish a pro-male or pro-female environment has not been investigated. In addition, apart from a handful of candidate genes, very little is known about potential similarities between the expression cascade during TSD and the genetic cascade that drives mammalian sex determination. Here, we conducted an unbiased transcriptome-wide analysis of the effects of male- and female-promoting temperatures on the turtle embryo prior to gonad formation, and on the gonad during the temperature sensitive period. We found sexually dimorphic expression reflecting differences in steroidogenic enzymes and brain development prior to gonad formation. Within the gonad, we mapped a cascade of differential expression similar to the genetic cascade established in mammals. Using a Hidden Markov Model based clustering approach, we identified groups of genes that show heterochronic shifts between M. musculus and T. scripta. We propose a model in which multiple factors influenced by temperature accumulate during early gonadogenesis, and converge on the antagonistic regulation of aromatase to canalize sex determination near the end of the temperature sensitive window of development.

Analysis of the genetic diversity and structure across a wide range of germplasm reveals prominent gene flow in apple at the European level.

BackgroundThe amount and structure of genetic diversity in dessert apple germplasm conserved at a European level is mostly unknown, since all diversity studies conducted in Europe until now have been performed on regional or national collections. Here, we applied a common set of 16 SSR markers to genotype more than 2,400 accessions across 14 collections representing three broad European geographic regions (North + East, West and South) with the aim to analyze the extent, distribution and structure of variation in the apple genetic resources in Europe.ResultsA Bayesian model-based clustering approach showed that diversity was organized in three groups, although these were only moderately differentiated (FST = 0.031). A nested Bayesian clustering approach allowed identification of subgroups which revealed internal patterns of substructure within the groups, allowing a finer delineation of the variation into eight subgroups (FST = 0.044). The first level of stratification revealed an asymmetric division of the germplasm among the three groups, and a clear association was found with the geographical regions of origin of the cultivars. The substructure revealed clear partitioning of genetic groups among countries, but also interesting associations between subgroups and breeding purposes of recent cultivars or particular usage such as cider production. Additional parentage analyses allowed us to identify both putative parents of more than 40 old and/or local cultivars giving interesting insights in the pedigree of some emblematic cultivars.ConclusionsThe variation found at group and subgroup levels may reflect a combination of historical processes of migration/selection and adaptive factors to diverse agricultural environments that, together with genetic drift, have resulted in extensive genetic variation but limited population structure. The European dessert apple germplasm represents an important source of genetic diversity with a strong historical and patrimonial value. The present work thus constitutes a decisive step in the field of conservation genetics. Moreover, the obtained data can be used for defining a European apple core collection useful for further identification of genomic regions associated with commercially important horticultural traits in apple through genome-wide association studies.Electronic supplementary materialThe online version of this article (doi:10.1186/s12870-016-0818-0) contains supplementary material, which is available to authorized users.

Development of microsatellite markers and their use in genetic diversity and population structure analysis in Casuarina

Casuarina is a widely cultivated plantation tree species in coastal India, primarily due to its fast growth, high productivity and suitable for pulp and paper production. However, genetic studies of Casuarina have been hindered by lack of genomic resources and genetic markers. Knowledge of the genetic diversity and population structure of Casuarina germplasms will provide the basis for utilizing and improving resource in the breeding program. Keeping this in view, in the present study, we have identified a total of 11,503 simple sequence repeat (SSR) makers from 86,415 expressed sequence tags (ESTs) of Casuarina equisetifolia and C. junghuhniana after redundancy elimination. Dinucleotide repeats were the most abundant accounting for 72.5 % of all microsatellites, followed by trimer (23.4 %), hexamer (1.7 %), tetramer (1.5 %), and very few pentamer (0.6 %) repeats. Of these, 50 markers were used to estimate genetic diversity and population structure among 96 accessions of C. cunninghamiana and C. junghuhniana. EST-SSR markers revealed high level of polymorphism, detecting a total of 829 alleles with an average of 17 alleles per locus. Polymorphic information content (PIC) values ranged from 0.32 to 0.93, with an average of 0.78 per locus. The average observed (Ho) and expected heterozygosity (He) obtained was high and fairly similar in C. cunninghamiana and C. junghuhniana, thereby suggesting highly heterogeneous nature of Casuarina. Population structure using a Bayesian model-based clustering approach identified clear delineation between C. cunninghamiana and C junghuhniana. Further, these markers were also evaluated in four species of Casuarina confirming high rate of cross-species transferability. The results of this study can provide valuable insights for genetic and genomic research in Casuarina.

An analysis of temporal and spatial patterns in Italian hospitalization rates for multiple diagnosis

In this paper, the Italian hospitalization database provided by the Ministry of Health is analyzed in terms of the temporal and spatial patterns of the hospitalization rates. The database covers the period 2010–2012 and the rates are evaluated for 110 Italian provinces and 18 diagnosis groups as defined by the ICD-9 classification.The analysis is based on a novel model-based clustering approach which enables clustering of spatially registered time series with respect to latent temporal patterns. The clustering result is analyzed to study the spatial distribution of the latent temporal patterns and their trend in order to identify possible critical areas in terms of increasing rates. Additionally, emerging spatial patterns may help common causes driving the hospitalization rates to be identified.

Using joint multivariate analyses of leaf morphology and molecular-genetic markers for taxon identification in three hybridizing European white oak species (Quercus spp.)

We show that joint multivariate analyses of leaf morphological characters and molecular-genetic markers improve the taxonomic assignment in hybridizing European white oaks. However, model-based approaches using genetic data alone represent straightforward alternatives to laborious, detailed morphological assessments. In European white oaks, species delimitation is debated because of large overlap of morphological characteristics likely due to hybridization. We tested whether joint multivariate analyses of leaf morphology and molecular markers improve the identification of three oak species (Quercus petraea, Quercus pubescens, Quercus robur) compared to approaches using morphological or genetic variables only. We assessed 13 leaf morphological characters and applied eight nuclear microsatellite markers in almost 1400 trees of 71 oak populations across Switzerland. We performed two multivariate approaches with three variable sets (morphology, genetics, combined) and assessed their performance in separating the taxa. We also compared the taxon assignment to a model-based clustering approach (Structure) based on genetic data alone. A joint use of morphological and genetic variables led to an improved taxon assignment. Whereas Q. robur could clearly be separated from the two other taxa, there was a certain overlap between Q. petraea and Q. pubescens. The Structure clustering led to the same taxon assignment in 85 % of the individuals. It is important to consider both morphological and genetic properties in morphologically similar and hybridizing species. However, it might be more efficient to concentrate only on genetic markers than on time-consuming morphological assessments.

Statistical approaches and software for clustering islet cell functional heterogeneity

ABSTRACTWorldwide efforts are underway to replace or repair lost or dysfunctional pancreatic β-cells to cure diabetes. However, it is unclear what the final product of these efforts should be, as β-cells are thought to be heterogeneous. To enable the analysis of β-cell heterogeneity in an unbiased and quantitative way, we developed model-free and model-based statistical clustering approaches, and created new software called TraceCluster. Using an example data set, we illustrate the utility of these approaches by clustering dynamic intracellular Ca2+ responses to high glucose in ∼300 simultaneously imaged single islet cells. Using feature extraction from the Ca2+ traces on this reference data set, we identified 2 distinct populations of cells with β-like responses to glucose. To the best of our knowledge, this report represents the first unbiased cluster-based analysis of human β-cell functional heterogeneity of simultaneous recordings. We hope that the approaches and tools described here will be helpful for those studying heterogeneity in primary islet cells, as well as excitable cells derived from embryonic stem cells or induced pluripotent cells.

Genetic Diversity, Population Structure, Parentage Analysis, and Construction of Core Collections in the French Apple Germplasm Based on SSR Markers

In-depth characterization of apple genetic resources is a prerequisite for genetic improvement and for germplasm management. In this study, we fingerprinted a very large French collection of 2163 accessions with 24 SSR markers in order to evaluate its genetic diversity, population structure, and genetic relationships, to link these features with cultivar selection date or usage (old or modern, dessert or cider cultivars), and to construct core collections. Most markers were highly discriminating and powerful for varietal identification, with a probability of identity P (ID) over the 21 retained SSR loci close to 10−28. Pairwise comparisons revealed 34 % redundancy and 18.5 % putative triploids. The results showed that the germplasm is highly diverse with an expected heterozygosity H e of 0.82 and observed heterozygosity H o of 0.83. A Bayesian model-based clustering approach revealed a weak but significant structure in three subgroups (FST = 0.014–0.048) corresponding, albeit approximately, to the three subpopulations defined beforehand (Old Dessert, Old Cider, and Modern Cultivars). Parentage analyses established already known and yet unknown relationships, notably between old cultivars, with the frequent occurrence of cultivars such as “King of Pippin” and “Calville Rouge d’Hiver” as founders. Finally, core collections based on allelic diversity were constructed. A large dessert core collection of 278 cultivars contained 90 % of the total dessert allelic diversity, whereas a dessert subcore collection of 48 cultivars contained 71 % of diversity. For cider apples, a 48-cultivar core collection contained 83 % of the total cider allelic diversity.

Finite mixture clustering of human tissues with different levels of IGF-1 splice variants mRNA transcripts.

BackgroundThis study addresses a recurrent biological problem, that is to define a formal clustering structure for a set of tissues on the basis of the relative abundance of multiple alternatively spliced isoforms mRNAs generated by the same gene. To this aim, we have used a model-based clustering approach, based on a finite mixture of multivariate Gaussian densities. However, given we had more technical replicates from the same tissue for each quantitative measurement, we also employed a finite mixture of linear mixed models, with tissue-specific random effects.ResultsA panel of human tissues was analysed through quantitative real-time PCR methods, to quantify the relative amount of mRNA encoding different IGF-1 alternative splicing variants. After an appropriate, preliminary, equalization of the quantitative data, we provided an estimate of the distribution of the observed concentrations for the different IGF-1 mRNA splice variants in the cohort of tissues by employing suitable kernel density estimators. We observed that the analysed IGF-1 mRNA splice variants were characterized by multimodal distributions, which could be interpreted as describing the presence of several sub-population, i.e. potential tissue clusters. In this context, a formal clustering approach based on a finite mixture model (FMM) with Gaussian components is proposed. Due to the presence of potential dependence between the technical replicates (originated by repeated quantitative measurements of the same mRNA splice isoform in the same tissue) we have also employed the finite mixture of linear mixed models (FMLMM), which allowed to take into account this kind of within-tissue dependence.ConclusionsThe FMM and the FMLMM provided a convenient yet formal setting for a model-based clustering of the human tissues in sub-populations, characterized by homogeneous values of concentrations of the mRNAs for one or multiple IGF-1 alternative splicing isoforms.The proposed approaches can be applied to any cohort of tissues expressing several alternatively spliced mRNAs generated by the same gene, and can overcome the limitations of clustering methods based on simple comparisons between splice isoform expression levels.