Small sample sizes in biomedical research often led to poor reproducibility and challenges in translating findings into clinical applications. This problem stems from limited study resources, rare diseases, ethical considerations in animal studies, costly expert diagnosis, and others. As a contribution to the problem, we propose a novel generative algorithm based on self-organizing maps (SOMs) to computationally increase sample sizes. The proposed unsupervised generative algorithm uses neural networks to detect inherent structure even in small multivariate datasets, distinguishing between sparse "void" and dense "cloud" regions. Using emergent SOMs (ESOMs), the algorithm adapts to high-dimensional data structures and generates for each original data point k new points by randomly selecting positions within an adapted hypersphere with distances based on valid neighborhood probabilities. Experiments on artificial and biomedical (omics) datasets show that the generated data preserve the original structure without introducing artifacts. Random forests and support vector machines cannot distinguish between generated and original data, and the variables of original and generated data sets are not statistically different. The method successfully augments small group sizes, such as transcriptomics data from a rare form of leukemia and lipidomics data from arthritis research. The novel ESOM-based generative algorithm presents a promising solution for enhancing sample sizes in small or rare case datasets, even when limited training data are available. This approach can address challenges associated with small sample sizes in biomedical research, offering a tool for improving the reliability and robustness of scientific findings in this field. Availability: R library "Umatrix" (https://cran.r-project.org/package=Umatrix).

Loss of olfactory function is a typical acute coronavirus disease 2019 (COVID-19) symptom, at least in early variants of SARS-CoV2. The time that has elapsed since the emergence of COVID-19 now allows for assessing the long-term prognosis of its olfactory impact.Participants (n = 722) of whom n = 464 reported having had COVID-19 dating back with a mode of 174 days were approached in a museum as a relatively unbiased environment. Olfactory function was diagnosed by assessing odor threshold and odor identification performance. Subjects also rated their actual olfactory function on an 11-point numerical scale [0, horizontal ellipsis 10]. Neither the frequency of olfactory diagnostic categories nor olfactory test scores showed any COVID-19-related effects. Olfactory diagnostic categories (anosmia, hyposmia, or normosmia) were similarly distributed among former patients and controls (0.86%, 18.97%, and 80.17% for former patients and 1.17%, 17.51%, and 81.32% for controls). Former COVID-19 patients, however, showed differences in their subjective perception of their own olfactory function. The impact of this effect was substantial enough that supervised machine learning algorithms detected past COVID-19 infections in new subjects, based on reduced self-awareness of olfactory performance and parosmia, while the diagnosed olfactory function did not contribute any relevant information in this context.Based on diagnosed olfactory function, results suggest a positive prognosis for COVID-19-related olfactory loss in the long term. Traces of former infection are found in self-perceptions of olfaction, highlighting the importance of investigating the long-term effects of COVID-19 using reliable and validated diagnostic measures in olfactory testing.

BACKGROUND:Clinical pharmacology research has always involved computational analysis. With the abundance of drug-related data available, the integration of artificial intelligence (AI) and machine learning (ML) methods has emerged as a promising way to enhance clinical pharmacology research.METHODS:Based on an accepted definition of clinical pharmacology as a field of research dealing with all aspects of drug-human interactions, the analysis included publications from institutes specializing in clinical pharmacology. Research topics and the most used machine learning methods in clinical pharmacology were retrieved from the PubMed database and summarized.RESULTS:ML was identified in 674 publications attributed to clinical pharmacology research, with a significant increase in publication activity over the last decade. Notable research topics addressed by ML/AI included Covid-19-related clinical pharmacology research, clinical neuropharmacology, drug safety and risk assessment, clinical pharmacology related to cancer research, and antimicrobial and antiviral research unrelated to Covid-19. In terms of ML methods, neural networks, random forests, and support vector machines were frequently mentioned in the abstracts of the retrieved papers.CONCLUSIONS:ML, and AI in general, is increasingly being used in various research areas within clinical pharmacology. This report presents specific examples of applications and highlights the most used ML methods.

Fibromyalgia patients vary in clinical phenotype and treatment can be challenging. The pathophysiology of fibromyalgia is incompletely understood but appears to involve metabolic changes at rest or in response to stress. We enrolled 54 fibromyalgia patients and 31 healthy controls to this prospective study. Symptoms were assessed using the Fibromyalgia Impact Questionnaire (FIQ) and blood samples were collected for metabolomics analysis at baseline and after an oral glucose tolerance test and a cardiopulmonary exercise test. We identified key symptoms of fibromyalgia and related them to changes in metabolic pathways with supervised and unsupervised machine learning methods. Algorithms trained with the FIQ information assigned the fibromyalgia diagnosis in new data with balanced accuracy of 88% while fatigue alone already provided the diagnosis with 86% accuracy. Supervised analyses reduced the metabolomic information from 77 to 13 key markers. With these metabolites, fibromyalgia could be identified in new cases with 79% accuracy. In addition, 5-hydroxyindole-3-acetic acid and glutamine levels correlated with the severity of fatigue. Patients differed from controls at baseline in tyrosine and purine pathways, and in the pyrimidine pathway after the stress challenges. Several key markers are involved in glutaminergic neurotransmission. This data-driven analysis highlights fatigue as a key symptom of fibromyalgia. Fibromyalgia is associated with metabolic changes which also reflect the degree of fatigue. Responses to metabolic and physical stresses result in a metabolic pattern that allows discrimination of fibromyalgia patients from controls and narrows the focus on key pathophysiological processes in fibromyalgia as treatment targets.

Background: Fold change is a common metric in biomedical research for quantifying group differences in omics variables. However, inconsistent calculation methods and inadequate reporting lead to discrepancies in results. This study evaluated various fold-change calculation methods aiming at a recommendation of a preferred approach. Methods: The primary distinction in fold-change calculations lies in defining group expected values for log ratio computation. To challenge method interchangeability in a “stress test” scenario, we generated diverse artificial data sets with varying distributions (identity, uniform, normal, log-normal, and a mixture of these) and compared calculated fold-changes to known values. Additionally, we analyzed a multi-omics biomedical data set to estimate to what extent the findings apply to real-world data. Results: Using arithmetic means as expected values for treatment and reference groups yielded inaccurate fold-change values more frequently than other methods, particularly when subgroup distributions and/or standard deviations differed significantly. Conclusions: The arithmetic mean method, often perceived as standard or picked without considering alternatives, is inferior to other definitions of the group expected value. Methods using median, geometric mean, or paired fold-change combinations are more robust against violations of equal variances or dissimilar group distributions. Adhering to methods less sensitive to data distribution without trade-offs and accurately reporting calculation methods in scientific reports is a reasonable practice to ensure correct interpretation and reproducibility.

Background: Persistent postsurgical neuropathic pain (PPSNP) can occur after intraoperative damage to somatosensory nerves, with a prevalence of 29–57% in breast cancer surgery. Proteomics is an active research field in neuropathic pain and the first results support its utility for establishing diagnoses or finding therapy strategies. Methods: 57 women (30 non-PPSNP/27 PPSNP) who had experienced a surgeon-verified intercostobrachial nerve injury during breast cancer surgery, were examined for patterns in 74 serum proteomic markers that allowed discrimination between subgroups with or without PPSNP. Serum samples were obtained both before and after surgery. Results: Unsupervised data analyses, including principal component analysis and self-organizing maps of artificial neurons, revealed patterns that supported a data structure consistent with pain-related subgroup (non-PPSPN vs. PPSNP) separation. Subsequent supervised machine learning-based analyses revealed 19 proteins (CD244, SIRT2, CCL28, CXCL9, CCL20, CCL3, IL.10RA, MCP.1, TRAIL, CCL25, IL10, uPA, CCL4, DNER, STAMPB, CCL23, CST5, CCL11, FGF.23) that were informative for subgroup separation. In cross-validated training and testing of six different machine-learned algorithms, subgroup assignment was significantly better than chance, whereas this was not possible when training the algorithms with randomly permuted data or with the protein markers not selected. In particular, sirtuin 2 emerged as a key protein, presenting both before and after breast cancer treatments in the PPSNP compared with the non-PPSNP subgroup. Conclusions: The identified proteins play important roles in immune processes such as cell migration, chemotaxis, and cytokine-signaling. They also have considerable overlap with currently known targets of approved or investigational drugs. Taken together, several lines of unsupervised and supervised analyses pointed to structures in serum proteomics data, obtained before and after breast cancer surgery, that relate to neuroinflammatory processes associated with the development of neuropathic pain after an intraoperative nerve lesion.

Background: The categorization of individuals as normosmic, hyposmic, or anosmic from test results of odor threshold, discrimination, and identification may provide a limited view of the sense of smell. The purpose of this study was to expand the clinical diagnostic repertoire by including additional tests. Methods: A random cohort of n = 135 individuals (83 women and 52 men, aged 21 to 94 years) was tested for odor threshold, discrimination, and identification, plus a distance test, in which the odor of peanut butter is perceived, a sorting task of odor dilutions for phenylethyl alcohol and eugenol, a discrimination test for odorant enantiomers, a lateralization test with eucalyptol, a threshold assessment after 10 min of exposure to phenylethyl alcohol, and a questionnaire on the importance of olfaction. Unsupervised methods were used to detect structure in the olfaction-related data, followed by supervised feature selection methods from statistics and machine learning to identify relevant variables. Results: The structure in the olfaction-related data divided the cohort into two distinct clusters with n = 80 and 55 subjects. Odor threshold, discrimination, and identification did not play a relevant role for cluster assignment, which, on the other hand, depended on performance in the two odor dilution sorting tasks, from which cluster assignment was possible with a median 100-fold cross-validated balanced accuracy of 77–88%. Conclusions: The addition of an odor sorting task with the two proposed odor dilutions to the odor test battery expands the phenotype of olfaction and fits seamlessly into the sensory focus of standard test batteries.

Bayesian inference is ubiquitous in science and widely used in biomedical research such as cell sorting or “omics” approaches, as well as in machine learning (ML), artificial neural networks, and “big data” applications. However, the calculation is not robust in regions of low evidence. In cases where one group has a lower mean but a higher variance than another group, new cases with larger values are implausibly assigned to the group with typically smaller values. An approach for a robust extension of Bayesian inference is proposed that proceeds in two main steps starting from the Bayesian posterior probabilities. First, cases with low evidence are labeled as “uncertain” class membership. The boundary for low probabilities of class assignment (threshold ε) is calculated using a computed ABC analysis as a data-based technique for item categorization. This leaves a number of cases with uncertain classification (p < ε). Second, cases with uncertain class membership are relabeled based on the distance to neighboring classified cases based on Voronoi cells. The approach is demonstrated on biomedical data typically analyzed with Bayesian statistics, such as flow cytometric data sets or biomarkers used in medical diagnostics, where it increased the class assignment accuracy by 1–10% depending on the data set. The proposed extension of the Bayesian inference of class membership can be used to obtain robust and plausible class assignments even for data at the extremes of the distribution and/or for which evidence is weak.

Interactions of drugs with the classical epigenetic mechanism of DNA methylation or histone modification are increasingly being elucidated mechanistically and used to develop novel classes of epigenetic therapeutics. A data science approach is used to synthesize current knowledge on the pharmacological implications of epigenetic regulation of gene expression. Computer-aided knowledge discovery for epigenetic implications of current approved or investigational drugs was performed by querying information from multiple publicly available gold-standard sources to (i) identify enzymes involved in classical epigenetic processes, (ii) screen original biomedical scientific publications including bibliometric analyses, (iii) identify drugs that interact with epigenetic enzymes, including their additional non-epigenetic targets, and (iv) analyze computational functional genomics of drugs with epigenetic interactions. PubMed database search yielded 3051 hits on epigenetics and drugs, starting in 1992 and peaking in 2016. Annual citations increased to a plateau in 2000 and show a downward trend since 2008. Approved and investigational drugs in the DrugBank database included 122 compounds that interacted with 68 unique epigenetic enzymes. Additional molecular functions modulated by these drugs included other enzyme interactions, whereas modulation of ion channels or G-protein-coupled receptors were underrepresented. Epigenetic interactions included (i) drug-induced modulation of DNA methylation, (ii) drug-induced modulation of histone conformations, and (iii) epigenetic modulation of drug effects by interference with pharmacokinetics or pharmacodynamics. Interactions of epigenetic molecular functions and drugs are mutual. Recent research activities on the discovery and development of novel epigenetic therapeutics have passed successfully, whereas epigenetic effects of non-epigenetic drugs or epigenetically induced changes in the targets of common drugs have not yet received the necessary systematic attention in the context of pharmacological plasticity.

Chronic rhinosinusitis (CRS) is often treated by functional endoscopic paranasal sinus surgery, which improves endoscopic parameters and quality of life, while olfactory function was suggested as a further criterion of treatment success. In a prospective cohort study, 37 parameters from four categories were recorded from 60 men and 98 women before and four months after endoscopic sinus surgery, including endoscopic measures of nasal anatomy/pathology, assessments of olfactory function, quality of life, and socio-demographic or concomitant conditions. Parameters containing relevant information about changes associated with surgery were examined using unsupervised and supervised methods, including machine-learning techniques for feature selection. The analyzed cohort included 52 men and 38 women. Changes in the endoscopic Lildholdt score allowed separation of baseline from postoperative data with a cross-validated accuracy of 85%. Further relevant information included primary nasal symptoms from SNOT-20 assessments, and self-assessments of olfactory function. Overall improvement in these relevant parameters was observed in 95% of patients. A ranked list of criteria was developed as a proposal to assess the outcome of functional endoscopic sinus surgery in CRS patients with nasal polyposis. Three different facets were captured, including the Lildholdt score as an endoscopic measure and, in addition, disease-specific quality of life and subjectively perceived olfactory function.

Olfactory self-assessments have been analyzed with often negative but also positive conclusions about their usefulness as a surrogate for sensory olfactory testing. Patients with nasal polyposis have been highlighted as a well-predisposed group for reliable self-assessment. In a prospective cohort of n = 156 nasal polyposis patients, olfactory threshold, odor discrimination, and odor identification were tested using the "Sniffin' Sticks" test battery, along with self-assessments of olfactory acuity on a numerical rating scale with seven named items or on a 10-point scale with only the extremes named. Apparent highly significant correlations in the complete cohort proved to reflect the group differences in olfactory diagnoses of anosmia (n = 65), hyposmia (n = 74), and normosmia (n = 17), more than the true correlations of self-ratings with olfactory test results, which were mostly very weak. The olfactory self-ratings correlated with a quality of life score, however, only weakly. By contrast, olfactory self-ratings proved as informative in assigning the categorical olfactory diagnosis. Using an olfactory diagnostic instrument, which consists of a mapping rule of two numerical rating scales of one's olfactory function to the olfactory functional diagnosis based on the "Sniffin' Sticks" clinical test battery, the diagnoses of anosmia, hyposmia, or normosmia could be derived from the self-ratings at a satisfactorily balanced accuracy of about 80%. It remains to be seen whether this approach of translating self-assessments into olfactory diagnoses of anosmia, hyposmia, and normosmia can be generalized to other clinical cohorts in which olfaction plays a role.

Because it is associated with central nervous changes, and olfactory dysfunction has been reported with increased prevalence among persons with diabetes, this study addressed the question of whether the risk of developing diabetes in the next 10 years is reflected in olfactory symptoms. In a cross-sectional study, in 164 individuals seeking medical consulting for possible diabetes, olfactory function was evaluated using a standardized clinical test assessing olfactory threshold, odor discrimination, and odor identification. Metabolomics parameters were assessed via blood concentrations. The individual diabetes risk was quantified according to the validated German version of the “FINDRISK” diabetes risk score. Machine learning algorithms trained with metabolomics patterns predicted low or high diabetes risk with a balanced accuracy of 63–75%. Similarly, olfactory subtest results predicted the olfactory dysfunction category with a balanced accuracy of 85–94%, occasionally reaching 100%. However, olfactory subtest results failed to improve the prediction of diabetes risk based on metabolomics data, and metabolomics data did not improve the prediction of the olfactory dysfunction category based on olfactory subtest results. Results of the present study suggest that olfactory function is not a useful predictor of diabetes.

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 subgroup structure. In other data sets, t-SNE occasionally suggested the wrong number of subgroups 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.

Genetic association studies have shown their usefulness in assessing the role of ion channels in human thermal pain perception. We used machine learning to construct a complex phenotype from pain thresholds to thermal stimuli and associate it with the genetic information derived from the next-generation sequencing (NGS) of 15 ion channel genes which are involved in thermal perception, including ASIC1, ASIC2, ASIC3, ASIC4, TRPA1, TRPC1, TRPM2, TRPM3, TRPM4, TRPM5, TRPM8, TRPV1, TRPV2, TRPV3, and TRPV4. Phenotypic information was complete in 82 subjects and NGS genotypes were available in 67 subjects. A network of artificial neurons, implemented as emergent self-organizing maps, discovered two clusters characterized by high or low pain thresholds for heat and cold pain. A total of 1071 variants were discovered in the 15 ion channel genes. After feature selection, 80 genetic variants were retained for an association analysis based on machine learning. The measured performance of machine learning-mediated phenotype assignment based on this genetic information resulted in an area under the receiver operating characteristic curve of 77.2%, justifying a phenotype classification based on the genetic information. A further item categorization finally resulted in 38 genetic variants that contributed most to the phenotype assignment. Most of them (10) belonged to the TRPV3 gene, followed by TRPM3 (6). Therefore, the analysis successfully identified the particular importance of TRPV3 and TRPM3 for an average pain phenotype defined by the sensitivity to moderate thermal stimuli.

Early detection of patients with chronic diseases at risk of developing persistent pain is clinically desirable for timely initiation of multimodal therapies. Quality follow-up registries may provide the necessary clinical data; however, their design is not focused on a specific research aim, which poses challenges on the data analysis strategy. Here, machine-learning was used to identify early parameters that provide information about a future development of persistent pain in rheumatoid arthritis (RA). Data of 288 patients were queried from a registry based on the Swedish Epidemiological Investigation of RA. Unsupervised data analyses identified the following 3 distinct patient subgroups: low-, median-, and high-persistent pain intensity. Next, supervised machine-learning, implemented as random forests followed by computed ABC analysis-based item categorization, was used to select predictive parameters among 21 different demographic, patient-rated, and objective clinical factors. The selected parameters were used to train machine-learned algorithms to assign patients pain-related subgroups (1000 random resamplings, 2/3 training, and 1/3 test data). Algorithms trained with 3-month data of the patient global assessment and health assessment questionnaire provided pain group assignment at a balanced accuracy of 70%. When restricting the predictors to objective clinical parameters of disease severity, swollen joint count and tender joint count acquired at 3 months provided a balanced accuracy of RA of 59%. Results indicate that machine-learning is suited to extract knowledge from data queried from pain- and disease-related registries. Early functional parameters of RA are informative for the development and degree of persistent pain.

Background Parkinson's disease (PD) causes chronic pain in two-thirds of patients, in part originating from sensory neuropathies. The aim of the present study was to describe the phenotype of PD-associated sensory neuropathy and to evaluate its associations with lipid allostasis, the latter motivated by recent genetic studies associating mutations of glucocerebrosidase with PD onset and severity. Glucocerebrosidase catalyzes the metabolism of glucosylceramides. Methods We used quantitative sensory tests, pain ratings, and questionnaires and analyzed plasma levels of multiple bioactive lipid species using targeted lipidomic analyses. The study comprised 2 sets of patients and healthy controls: the first 128 Israeli PD patients and 224 young German healthy controls for exploration, the second 50/50 German PD patients and matched healthy controls for deeper analyses. Results The data showed a 70% prevalence of PD pain and sensory neuropathies with a predominant phenotype of thermal sensory loss plus mechanical hypersensitivity. Multivariate analyses of lipids revealed major differences between PD patients and healthy controls, mainly originating from glucosylceramides and endocannabinoids. Glucosylceramides were increased, whereas anandamide and lysophosphatidic acid 20:4 were reduced, stronger in patients with ongoing pain and with a linear relationship with pain intensity and sensory losses, particularly for glucosylceramide 18:1 and glucosylceramide 24:1. Conclusions Our data suggest that PD-associated sensory neuropathies and PD pain are in part caused by accumulations of glucosylceramides, raising the intriguing possibility of reducing PD pain and sensory loss by glucocerebrosidase substituting or refolding approaches. (c) 2020 The Authors.Movement Disorderspublished by Wiley Periodicals LLC. on behalf of International Parkinson and Movement Disorder Society.

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.

Background: Persistent pain in breast cancer survivors is common. Psychological and sleep-related factors modulate perception, interpretation and coping with pain and may contribute to the clinical phenotype. The present analysis pursued the hypothesis that breast cancer survivors form subgroups, based on psychological and sleep-related parameters that are relevant to the impact of pain on the patients’ life. Methods: We analysed 337 women treated for breast cancer, in whom psychological and sleep-related parameters as well as parameters related to pain intensity and interference had been acquired. Data were analysed by using supervised and unsupervised machine-learning techniques (i) to detect patient subgroups based on the pattern of psychological or sleep-related parameters, (ii) to interpret the detected cluster structure and (iii) to relate this data structure to pain interference and impact on life. Results: Artificial intelligence-based detection of data structure, implemented as self-organizing neuronal maps, identified two different clusters of patients. A smaller cluster (11.5% of the patients) had comparatively lower resilience, more depressive symptoms and lower extraversion than the other patients. In these patients, life-satisfaction, mood, and life in general were comparatively more impeded by persistent pain. Conclusions: The results support the initial hypothesis that psychological and sleep-related parameter patterns are meaningful for subgrouping patients with respect to how persistent pain after breast cancer treatments interferes with their life. This indicates that management of pain should address more complex features than just pain intensity. Artificial intelligence is a useful tool in the identification of subgroups of patients based on psychological factors.

BACKGROUND Persistent pain extending beyond 6 months after breast cancer surgery when adjuvant therapies have ended is a recognised phenomenon. The evolution of postsurgery pain is therefore of interest for future patient management in terms of possible prognoses for distinct groups of patients to enable better patient information. OBJECTIVE(S) An analysis aimed to identify subgroups of patients who share similar time courses of postoperative persistent pain. DESIGN Prospective cohort study. SETTING Helsinki University Hospital, Finland, between 2006 and 2010. PATIENTS A total of 763 women treated for breast cancer at the Helsinki University Hospital. INTERVENTIONS Employing a data science approach in a nonredundant reanalysis of data published previously, pain ratings acquired at 6, 12, 24 and 36 months after breast cancer surgery, were analysed for a group structure of the temporal courses of pain. Unsupervised automated evolutionary (genetic) algorithms were used for patient cluster detection in the pain ratings and for Gaussian mixture modelling of the slopes of the linear relationship between pain ratings and acquisition times. MAIN OUTCOME MEASURES Clusters or groups of patients sharing patterns in the time courses of pain between 6 and 36 months after breast cancer surgery. RESULTS Three groups of patients with distinct time courses of pain were identified as the best solutions for both clustering of the pain ratings and multimodal modelling of the slopes of their temporal trends. In two clusters/groups, pain decreased or remained stable and the two approaches suggested/identified similar subgroups representing 80/763 and 86/763 of the patients, respectively, in whom rather high pain levels tended to further increase over time. CONCLUSION In the majority of patients, pain after breast cancer surgery decreased rapidly and disappeared or the intensity decreased over 3 years. However, in about a tenth of patients, moderate-to-severe pain tended to increase during the 3-year follow-up.

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.