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Motivation: Calculating the magnitude of treatment effects or of differences between two groups is a common task in quantitative science. Standard effect size measures based on differences, such as the commonly used Cohen's, fail to capture the treatment-related effects on the data if the effects were not reflected by the central tendency. The present work aims at (i) developing a non-parametric alternative to Cohen’s d, which (ii) circumvents some of its numerical limitations and (iii) involves obvious changes in the data that do not affect the group means and are therefore not captured by Cohen’s d.
Results: We propose "Impact” as a novel non-parametric measure of effect size obtained as the sum of two separate components and includes (i) a difference-based effect size measure implemented as the change in the central tendency of the group-specific data normalized to pooled variability and (ii) a data distribution shape-based effect size measure implemented as the difference in probability density of the group-specific data. Results obtained on artificial and empirical data showed that “Impact”is superior to Cohen's d by its additional second component in detecting clearly visible effects not reflected in central tendencies. The proposed effect size measure is invariant to the scaling of the data, reflects changes in the central tendency in cases where differences in the shape of probability distributions between subgroups are negligible, but captures changes in probability distributions as effects and is numerically stable even if the variances of the data set or its subgroups disappear.
Conclusions: The proposed effect size measure shares the ability to observe such an effect with machine learning algorithms. Therefore, the proposed effect size measure is particularly well suited for data science and artificial intelligence-based knowledge discovery from big and heterogeneous data.
Finding subgroups in biomedical data is a key task in biomedical research and precision medicine. Already one-dimensional data, such as many different readouts from cell experiments, preclinical or human laboratory experiments or clinical signs, often reveal a more complex distribution than a single mode. Gaussian mixtures play an important role in the multimodal distribution of one-dimensional data. However, although fitting of Gaussian mixture models (GMM) is often aimed at obtaining the separate modes composing the mixture, current technical implementations, often using the Expectation Maximization (EM) algorithm, are not optimized for this task. This occasionally results in poorly separated modes that are unsuitable for determining a distinguishable group structure in the data. Here, we introduce “Distribution Optimization” an evolutionary algorithm to GMM fitting that uses an adjustable error function that is based on chi-square statistics and the probability density. The algorithm can be directly targeted at the separation of the modes of the mixture by employing additional criterion for the degree by which single modes overlap. The obtained GMM fits were comparable with those obtained with classical EM based fits, except for data sets where the EM algorithm produced unsatisfactory results with overlapping Gaussian modes. There, the proposed algorithm successfully separated the modes, providing a basis for meaningful group separation while fitting the data satisfactorily. Through its optimization toward mode separation, the evolutionary algorithm proofed particularly suitable basis for group separation in multimodally distributed data, outperforming alternative EM based methods.
Advances in flow cytometry enable the acquisition of large and high-dimensional data sets per patient. Novel computational techniques allow the visualization of structures in these data and, finally, the identification of relevant subgroups. Correct data visualizations and projections from the high-dimensional space to the visualization plane require the correct representation of the structures in the data. This work shows that frequently used techniques are unreliable in this respect. One of the most important methods for data projection in this area is the t-distributed stochastic neighbor embedding (t-SNE). We analyzed its performance on artificial and real biomedical data sets. t-SNE introduced a cluster structure for homogeneously distributed data that did not contain any subgroupstructure. Inotherdatasets,t-SNEoccasionallysuggestedthewrongnumberofsubgroups or projected data points belonging to different subgroups, as if belonging to the same subgroup. As an alternative approach, emergent self-organizing maps (ESOM) were used in combination with U-matrix methods. This approach allowed the correct identification of homogeneous data while in sets containing distance or density-based subgroups structures; the number of subgroups and data point assignments were correctly displayed. The results highlight possible pitfalls in the use of a currently widely applied algorithmic technique for the detection of subgroups in high dimensional cytometric data and suggest a robust alternative.
Pain and pain chronification are incompletely understood and unresolved medical problems that continue to have a high prevalence. It has been accepted that pain is a complex phenomenon. Contemporary methods of computational science can use complex clinical and experimental data to better understand the complexity of pain. Among data science techniques, machine learning is referred to as a set of methods that can automatically detect patterns in data and then use the uncovered patterns to predict or classify future data, to observe structures such as subgroups in the data, or to extract information from the data suitable to derive new knowledge. Together with (bio)statistics, artificial intelligence and machine learning aim at learning from data. ...
Background: Human genetic research has implicated functional variants of more than one hundred genes in the modulation of persisting pain. Artificial intelligence and machine‐learning techniques may combine this knowledge with results of genetic research gathered in any context, which permits the identification of the key biological processes involved in chronic sensitization to pain.
Methods: Based on published evidence, a set of 110 genes carrying variants reported to be associated with modulation of the clinical phenotype of persisting pain in eight different clinical settings was submitted to unsupervised machine‐learning aimed at functional clustering. Subsequently, a mathematically supported subset of genes, comprising those most consistently involved in persisting pain, was analysed by means of computational functional genomics in the Gene Ontology knowledgebase.
Results: Clustering of genes with evidence for a modulation of persisting pain elucidated a functionally heterogeneous set. The situation cleared when the focus was narrowed to a genetic modulation consistently observed throughout several clinical settings. On this basis, two groups of biological processes, the immune system and nitric oxide signalling, emerged as major players in sensitization to persisting pain, which is biologically highly plausible and in agreement with other lines of pain research.
Conclusions: The present computational functional genomics‐based approach provided a computational systems‐biology perspective on chronic sensitization to pain. Human genetic control of persisting pain points to the immune system as a source of potential future targets for drugs directed against persisting pain. Contemporary machine‐learned methods provide innovative approaches to knowledge discovery from previous evidence.
Significance: We show that knowledge discovery in genetic databases and contemporary machine‐learned techniques can identify relevant biological processes involved in Persitent pain.
Background: Prevention of persistent pain following breast cancer surgery, via early identification of patients at high risk, is a clinical need. Supervised machine-learning was used to identify parameters that predict persistence of significant pain.
Methods: Over 500 demographic, clinical and psychological parameters were acquired up to 6 months after surgery from 1,000 women (aged 28–75 years) who were treated for breast cancer. Pain was assessed using an 11-point numerical rating scale before surgery and at months 1, 6, 12, 24, and 36. The ratings at months 12, 24, and 36 were used to allocate patents to either "persisting pain" or "non-persisting pain" groups. Unsupervised machine learning was applied to map the parameters to these diagnoses.
Results: A symbolic rule-based classifier tool was created that comprised 21 single or aggregated parameters, including demographic features, psychological and pain-related parameters, forming a questionnaire with "yes/no" items (decision rules). If at least 10 of the 21 rules applied, persisting pain was predicted at a cross-validated accuracy of 86% and a negative predictive value of approximately 95%.
Conclusions: The present machine-learned analysis showed that, even with a large set of parameters acquired from a large cohort, early identification of these patients is only partly successful. This indicates that more parameters are needed for accurate prediction of persisting pain. However, with the current parameters it is possible, with a certainty of almost 95%, to exclude the possibility of persistent pain developing in a woman being treated for breast cancer.
Based on increasing evidence suggesting that MS pathology involves alterations in bioactive lipid metabolism, the present analysis was aimed at generating a complex serum lipid-biomarker. Using unsupervised machine-learning, implemented as emergent self-organizing maps of neuronal networks, swarm intelligence and Minimum Curvilinear Embedding, a cluster structure was found in the input data space comprising serum concentrations of d = 43 different lipid-markers of various classes. The structure coincided largely with the clinical diagnosis, indicating that the data provide a basis for the creation of a biomarker (classifier). This was subsequently assessed using supervised machine-learning, implemented as random forests and computed ABC analysis-based feature selection. Bayesian statistics-based biomarker creation was used to map the diagnostic classes of either MS patients (n = 102) or healthy subjects (n = 301). Eight lipid-markers passed the feature selection and comprised GluCerC16, LPA20:4, HETE15S, LacCerC24:1, C16Sphinganine, biopterin and the endocannabinoids PEA and OEA. A complex classifier or biomarker was developed that predicted MS at a sensitivity, specificity and accuracy of approximately 95% in training and test data sets, respectively. The present successful application of serum lipid marker concentrations to MS data is encouraging for further efforts to establish an MS biomarker based on serum lipidomics.
The Gini index is a measure of the inequality of a distribution that can be derived from Lorenz curves. While commonly used in, e.g., economic research, it suffers from ambiguity via lack of Lorenz dominance preservation. Here, investigation of large sets of empirical distributions of incomes of the World’s countries over several years indicated firstly, that the Gini indices are centered on a value of 33.33% corresponding to the Gini index of the uniform distribution and secondly, that the Lorenz curves of these distributions are consistent with Lorenz curves of log-normal distributions. This can be employed to provide a Lorenz dominance preserving equivalent of the Gini index. Therefore, a modified measure based on log-normal approximation and standardization of Lorenz curves is proposed. The so-called UGini index provides a meaningful and intuitive standardization on the uniform distribution as this characterizes societies that provide equal chances. The novel UGini index preserves Lorenz dominance. Analysis of the probability density distributions of the UGini index of the World’s counties income data indicated multimodality in two independent data sets. Applying Bayesian statistics provided a data-based classification of the World’s countries’ income distributions. The UGini index can be re-transferred into the classical index to preserve comparability with previous research.
Background: To prevent persistent post-surgery pain, early identification of patients at high risk is a clinical need. Supervised machine-learning techniques were used to test how accurately the patients’ performance in a preoperatively performed tonic cold pain test could predict persistent post-surgery pain.
Methods: We analysed 763 patients from a cohort of 900 women who were treated for breast cancer, of whom 61 patients had developed signs of persistent pain during three yr of follow-up. Preoperatively, all patients underwent a cold pain test (immersion of the hand into a water bath at 2–4 °C). The patients rated the pain intensity using a numerical ratings scale (NRS) from 0 to 10. Supervised machine-learning techniques were used to construct a classifier that could predict patients at risk of persistent pain.
Results: Whether or not a patient rated the pain intensity at NRS=10 within less than 45 s during the cold water immersion test provided a negative predictive value of 94.4% to assign a patient to the "persistent pain" group. If NRS=10 was never reached during the cold test, the predictive value for not developing persistent pain was almost 97%. However, a low negative predictive value of 10% implied a high false positive rate.
Conclusions: Results provide a robust exclusion of persistent pain in women with an accuracy of 94.4%. Moreover, results provide further support for the hypothesis that the endogenous pain inhibitory system may play an important role in the process of pain becoming persistent.
The comprehensive assessment of pain-related human phenotypes requires combinations of nociceptive measures that produce complex high-dimensional data, posing challenges to bioinformatic analysis. In this study, we assessed established experimental models of heat hyperalgesia of the skin, consisting of local ultraviolet-B (UV-B) irradiation or capsaicin application, in 82 healthy subjects using a variety of noxious stimuli. We extended the original heat stimulation by applying cold and mechanical stimuli and assessing the hypersensitization effects with a clinically established quantitative sensory testing (QST) battery (German Research Network on Neuropathic Pain). This study provided a 246 × 10-sized data matrix (82 subjects assessed at baseline, following UV-B application, and following capsaicin application) with respect to 10 QST parameters, which we analyzed using machine-learning techniques. We observed statistically significant effects of the hypersensitization treatments in 9 different QST parameters. Supervised machine-learned analysis implemented as random forests followed by ABC analysis pointed to heat pain thresholds as the most relevantly affected QST parameter. However, decision tree analysis indicated that UV-B additionally modulated sensitivity to cold. Unsupervised machine-learning techniques, implemented as emergent self-organizing maps, hinted at subgroups responding to topical application of capsaicin. The distinction among subgroups was based on sensitivity to pressure pain, which could be attributed to sex differences, with women being more sensitive than men. Thus, while UV-B and capsaicin share a major component of heat pain sensitization, they differ in their effects on QST parameter patterns in healthy subjects, suggesting a lack of redundancy between these models.
Background: The quantification of global DNA methylation has been established in epigenetic screening. As more practicable alternatives to the HPLC-based gold standard, the methylation analysis of CpG islands in repeatable elements (LINE-1) and the luminometric methylation assay (LUMA) of overall 5-methylcytosine content in “CCGG” recognition sites are most widely used. Both methods are applied as virtually equivalent, despite the hints that their results only partly agree. This triggered the present agreement assessments.
Results: Three different human cell types (cultured MCF7 and SHSY5Y cell lines treated with different chemical modulators of DNA methylation and whole blood drawn from pain patients and healthy volunteers) were submitted to the global DNA methylation assays employing LINE-1 or LUMA-based pyrosequencing measurements. The agreement between the two bioassays was assessed using generally accepted approaches to the statistics for laboratory method comparison studies. Although global DNA methylation levels measured by the two methods correlated, five different lines of statistical evidence consistently rejected the assumption of complete agreement. Specifically, a bias was observed between the two methods. In addition, both the magnitude and direction of bias were tissue-dependent. Interassay differences could be grouped based on Bayesian statistics, and these groups allowed in turn to re-identify the originating tissue.
Conclusions: Although providing partly correlated measurements of DNA methylation, interchangeability of the quantitative results obtained with LINE-1 and LUMA was jeopardized by a consistent bias between the results. Moreover, the present analyses strongly indicate a tissue specificity of the differences between the two methods.
The presence of cerebral lesions in patients with neurosensory alterations provides a unique window into brain function. Using a fuzzy logic based combination of morphological information about 27 olfactory-eloquent brain regions acquired with four different brain imaging techniques, patterns of brain damage were analyzed in 127 patients who displayed anosmia, i.e., complete loss of the sense of smell (n = 81), or other and mechanistically still incompletely understood olfactory dysfunctions including parosmia, i.e., distorted perceptions of olfactory stimuli (n = 50), or phantosmia, i.e., olfactory hallucinations (n = 22). A higher prevalence of parosmia, and as a tendency also phantosmia, was observed in subjects with medium overall brain damage. Further analysis showed a lower frequency of lesions in the right temporal lobe in patients with parosmia than in patients without parosmia. This negative direction of the differences was unique for parosmia. In anosmia, and also in phantosmia, lesions were more frequent in patients displaying the respective symptoms than in those without these dysfunctions. In anosmic patients, lesions in the right olfactory bulb region were much more frequent than in patients with preserved sense of smell, whereas a higher frequency of carriers of lesions in the left frontal lobe was observed for phantosmia. We conclude that anosmia, and phantosmia, are the result of lost function in relevant brain areas whereas parosmia is more complex, requiring damaged and intact brain regions at the same time.
Background: High-dimensional biomedical data are frequently clustered to identify subgroup structures pointing at distinct disease subtypes. It is crucial that the used cluster algorithm works correctly. However, by imposing a predefined shape on the clusters, classical algorithms occasionally suggest a cluster structure in homogenously distributed data or assign data points to incorrect clusters. We analyzed whether this can be avoided by using emergent self-organizing feature maps (ESOM).
Methods: Data sets with different degrees of complexity were submitted to ESOM analysis with large numbers of neurons, using an interactive R-based bioinformatics tool. On top of the trained ESOM the distance structure in the high dimensional feature space was visualized in the form of a so-called U-matrix. Clustering results were compared with those provided by classical common cluster algorithms including single linkage, Ward and k-means.
Results: Ward clustering imposed cluster structures on cluster-less "golf ball", "cuboid" and "S-shaped" data sets that contained no structure at all (random data). Ward clustering also imposed structures on permuted real world data sets. By contrast, the ESOM/U-matrix approach correctly found that these data contain no cluster structure. However, ESOM/U-matrix was correct in identifying clusters in biomedical data truly containing subgroups. It was always correct in cluster structure identification in further canonical artificial data. Using intentionally simple data sets, it is shown that popular clustering algorithms typically used for biomedical data sets may fail to cluster data correctly, suggesting that they are also likely to perform erroneously on high dimensional biomedical data.
Conclusions: The present analyses emphasized that generally established classical hierarchical clustering algorithms carry a considerable tendency to produce erroneous results. By contrast, unsupervised machine-learned analysis of cluster structures, applied using the ESOM/U-matrix method, is a viable, unbiased method to identify true clusters in the high-dimensional space of complex data.
Graphical abstract: 3-D representation of high dimensional data following ESOM projection and visualization of group (cluster) structures using the U-matrix, which employs a geographical map analogy of valleys where members of the same cluster are located, separated by mountain ranges marking cluster borders.
Next-generation sequencing (NGS) provides unrestricted access to the genome, but it produces ‘big data’ exceeding in amount and complexity the classical analytical approaches. We introduce a bioinformatics-based classifying biomarker that uses emergent properties in genetics to separate pain patients requiring extremely high opioid doses from controls. Following precisely calculated selection of the 34 most informative markers in the OPRM1, OPRK1, OPRD1 and SIGMAR1 genes, pattern of genotypes belonging to either patient group could be derived using a k-nearest neighbor (kNN) classifier that provided a diagnostic accuracy of 80.6±4%. This outperformed alternative classifiers such as reportedly functional opioid receptor gene variants or complex biomarkers obtained via multiple regression or decision tree analysis. The accumulation of several genetic variants with only minor functional influences may result in a qualitative consequence affecting complex phenotypes, pointing at emergent properties in genetics.
The human sense of smell is often analyzed as being composed of three main components comprising olfactory threshold, odor discrimination and the ability to identify odors. A relevant distinction of the three components and their differential changes in distinct disorders remains a research focus. The present data-driven analysis aimed at establishing a cluster structure in the pattern of olfactory subtest results. Therefore, unsupervised machine-learning was applied onto olfactory subtest results acquired in 10,714 subjects with nine different olfactory pathologies. Using the U-matrix, Emergent Self-organizing feature maps (ESOM) identified three different clusters characterized by (i) low threshold and good discrimination and identification, (ii) very high threshold associated with absent to poor discrimination and identification ability, or (iii) medium threshold, i.e., in the mid-range of possible thresholds, associated with reduced discrimination and identification ability. Specific etiologies of olfactory (dys)function were unequally represented in the clusters (p < 2.2 · 10−16). Patients with congenital anosmia were overrepresented in the second cluster while subjects with postinfectious olfactory dysfunction belonged frequently to the third cluster. However, the clusters provided no clear separation between etiologies. Hence, the present verification of a distinct cluster structure encourages continued scientific efforts at olfactory test pattern recognition.
Aim: Exposure to opioids has been associated with epigenetic effects. Studies in rodents suggested a role of varying degrees of DNA methylation in the differential regulation of μ-opioid receptor expression across the brain.
Methods: In a translational investigation, using tissue acquired postmortem from 21 brain regions of former opiate addicts, representing a human cohort with chronic opioid exposure, μ-opioid receptor expression was analyzed at the level of DNA methylation, mRNA and protein.
Results & conclusion: While high or low μ-opioid receptor expression significantly correlated with local OPRM1 mRNA levels, there was no corresponding association with OPRM1 methylation status. Additional experiments in human cell lines showed that changes in DNA methylation associated with changes in μ-opioid expression were an order of magnitude greater than differences in brain. Hence, different degrees of DNA methylation associated with chronic opioid exposure are unlikely to exert a major role in the region-specificity of μ-opioid receptor expression in the human brain.
Computed ABC analysis for rational selection of most informative variables in multivariate data
(2015)
Objective: Multivariate data sets often differ in several factors or derived statistical parameters, which have to be selected for a valid interpretation. Basing this selection on traditional statistical limits leads occasionally to the perception of losing information from a data set. This paper proposes a novel method for calculating precise limits for the selection of parameter sets.
Methods: The algorithm is based on an ABC analysis and calculates these limits on the basis of the mathematical properties of the distribution of the analyzed items. The limits implement the aim of any ABC analysis, i.e., comparing the increase in yield to the required additional effort. In particular, the limit for set A, the "important few", is optimized in a way that both, the effort and the yield for the other sets (B and C), are minimized and the additional gain is optimized.
Results: As a typical example from biomedical research, the feasibility of the ABC analysis as an objective replacement for classical subjective limits to select highly relevant variance components of pain thresholds is presented. The proposed method improved the biological interpretation of the results and increased the fraction of valid information that was obtained from the experimental data.
Conclusions: The method is applicable to many further biomedical problems including the creation of diagnostic complex biomarkers or short screening tests from comprehensive test batteries. Thus, the ABC analysis can be proposed as a mathematically valid replacement for traditional limits to maximize the information obtained from multivariate research data.
Biomedical data obtained during cell experiments, laboratory animal research, or human studies often display a complex distribution. Statistical identification of subgroups in research data poses an analytical challenge. Here were introduce an interactive R-based bioinformatics tool, called “AdaptGauss”. It enables a valid identification of a biologically-meaningful multimodal structure in the data by fitting a Gaussian mixture model (GMM) to the data. The interface allows a supervised selection of the number of subgroups. This enables the expectation maximization (EM) algorithm to adapt more complex GMM than usually observed with a noninteractive approach. Interactively fitting a GMM to heat pain threshold data acquired from human volunteers revealed a distribution pattern with four Gaussian modes located at temperatures of 32.3, 37.2, 41.4, and 45.4 °C. Noninteractive fitting was unable to identify a meaningful data structure. Obtained results are compatible with known activity temperatures of different TRP ion channels suggesting the mechanistic contribution of different heat sensors to the perception of thermal pain. Thus, sophisticated analysis of the modal structure of biomedical data provides a basis for the mechanistic interpretation of the observations. As it may reflect the involvement of different TRP thermosensory ion channels, the analysis provides a starting point for hypothesis-driven laboratory experiments.
Background: It is assumed that different pain phenotypes are based on varying molecular pathomechanisms. Distinct ion channels seem to be associated with the perception of cold pain, in particular TRPM8 and TRPA1 have been highlighted previously. The present study analyzed the distribution of cold pain thresholds with focus at describing the multimodality based on the hypothesis that it reflects a contribution of distinct ion channels.
Methods: Cold pain thresholds (CPT) were available from 329 healthy volunteers (aged 18 - 37 years; 159 men) enrolled in previous studies. The distribution of the pooled and log-transformed threshold data was described using a kernel density estimation (Pareto Density Estimation (PDE)) and subsequently, the log data was modeled as a mixture of Gaussian distributions using the expectation maximization (EM) algorithm to optimize the fit.
Results: CPTs were clearly multi-modally distributed. Fitting a Gaussian Mixture Model (GMM) to the log-transformed threshold data revealed that the best fit is obtained when applying a three-model distribution pattern. The modes of the identified three Gaussian distributions, retransformed from the log domain to the mean stimulation temperatures at which the subjects had indicated pain thresholds, were obtained at 23.7 °C, 13.2 °C and 1.5 °C for Gaussian #1, #2 and #3, respectively.
Conclusions: The localization of the first and second Gaussians was interpreted as reflecting the contribution of two different cold sensors. From the calculated localization of the modes of the first two Gaussians, the hypothesis of an involvement of TRPM8, sensing temperatures from 25 - 24 °C, and TRPA1, sensing cold from 17 °C can be derived. In that case, subjects belonging to either Gaussian would possess a dominance of the one or the other receptor at the skin area where the cold stimuli had been applied. The findings therefore support a suitability of complex analytical approaches to detect mechanistically determined patterns from pain phenotype data.
Computational analyses of functions of gene sets obtained in microarray analyses or by topical database searches are increasingly important in biology. To understand their functions, the sets are usually mapped to Gene Ontology knowledge bases by means of over-representation analysis (ORA). Its result represents the specific knowledge of the functionality of the gene set. However, the specific ontology typically consists of many terms and relationships, hindering the understanding of the ‘main story’. We developed a methodology to identify a comprehensibly small number of GO terms as “headlines” of the specific ontology allowing to understand all central aspects of the roles of the involved genes. The Functional Abstraction method finds a set of headlines that is specific enough to cover all details of a specific ontology and is abstract enough for human comprehension. This method exceeds the classical approaches at ORA abstraction and by focusing on information rather than decorrelation of GO terms, it directly targets human comprehension. Functional abstraction provides, with a maximum of certainty, information value, coverage and conciseness, a representation of the biological functions in a gene set plays a role. This is the necessary means to interpret complex Gene Ontology results thus strengthening the role of functional genomics in biomarker and drug discovery.