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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.
In the context of data science, data projection and clustering are common procedures. The chosen analysis method is crucial to avoid faulty pattern recognition. It is therefore necessary to know the properties and especially the limitations of projection and clustering algorithms. This report describes a collection of datasets that are grouped together in the Fundamental Clustering and Projection Suite (FCPS). The FCPS contains 10 datasets with the names "Atom", "Chainlink", "EngyTime", "Golfball", "Hepta", "Lsun", "Target", "Tetra", "TwoDiamonds", and "WingNut". Common clustering methods occasionally identified non-existent clusters or assigned data points to the wrong clusters in the FCPS suite. Likewise, common data projection methods could only partially reproduce the data structure correctly on a two-dimensional plane. In conclusion, the FCPS dataset collection addresses general challenges for clustering and projection algorithms such as lack of linear separability, different or small inner class spacing, classes defined by data density rather than data spacing, no cluster structure at all, outliers, or classes that are in contact. This report describes a collection of datasets that are grouped together in the Fundamental Clustering and Projection Suite (FCPS). It is designed to address specific problems of structure discovery in high-dimensional spaces.
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.
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. ...
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.
BACKGROUND: Micro-RNAs (miRNA) are attributed to the systems biological role of a regulatory mechanism of the expression of protein coding genes. Research has identified miRNAs dysregulations in several but distinct pathophysiological processes, which hints at distinct systems-biology functions of miRNAs. The present analysis approached the role of miRNAs from a genomics perspective and assessed the biological roles of 2954 genes and 788 human miRNAs, which can be considered to interact, based on empirical evidence and computational predictions of miRNA versus gene interactions.
RESULTS: From a genomics perspective, the biological processes in which the genes that are influenced by miRNAs are involved comprise of six major topics comprising biological regulation, cellular metabolism, information processing, development, gene expression and tissue homeostasis. The usage of this knowledge as a guidance for further research is sketched for two genetically defined functional areas: cell death and gene expression. Results suggest that the latter points to a fundamental role of miRNAs consisting of hyper-regulation of gene expression, i.e., the control of the expression of such genes which control specifically the expression of genes.
CONCLUSIONS: Laboratory research identified contributions of miRNA regulation to several distinct biological processes. The present analysis transferred this knowledge to a systems-biology level. A comprehensible and precise description of the biological processes in which the genes that are influenced by miRNAs are notably involved could be made. This knowledge can be employed to guide future research concerning the biological role of miRNA (dys-) regulations. The analysis also suggests that miRNAs especially control the expression of genes that control the expression of genes.
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.
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.
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.
Process pharmacology : a pharmacological data science approach to drug development and therapy
(2016)
A novel functional-genomics based concept of pharmacology that uses artificial intelligence techniques for mining and knowledge discovery in "big data" providing comprehensive information about the drugs’ targets and their functional genomics is proposed. In “process pharmacology”, drugs are associated with biological processes. This puts the disease, regarded as alterations in the activity in one or several cellular processes, in the focus of drug therapy. In this setting, the molecular drug targets are merely intermediates. The identification of drugs for therapeutic or repurposing is based on similarities in the high-dimensional space of the biological processes that a drug influences. Applying this principle to data associated with lymphoblastic leukemia identified a short list of candidate drugs, including one that was recently proposed as novel rescue medication for lymphocytic leukemia. The pharmacological data science approach provides successful selections of drug candidates within development and repurposing tasks.
