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In a recent discussion on how to deal with data analysis issues initiated by reviewers of pain-related scientific manuscripts in the European Journal of Pain, a seemingly simple statistical issue was raised: two subsets of data in a paper had the same mean and standard deviation. A reviewer asked for a statistical test for or against the identity of the subset distributions. The authors insisted that if the mean and standard deviation were the same, this was sufficient evidence that the subsets of data were not significantly different.
This prompted a discussion among pain researchers, who are not necessarily primarily from the field of data science, a discussion of the importance of carefully examining the distribution of pain-related data in a journal whose primary audience is pain researchers seems warranted...
Recent advances in mathematical modelling and artificial intelligence have challenged the use of traditional regression analysis in biomedical research. This study examined artificial and cancer research data using binomial and multinomial logistic regression and compared its performance with other machine learning models such as random forests, support vector machines, Bayesian classifiers, k-nearest neighbours and repeated incremental clipping (RIPPER). The alternative models often outperformed regression in accurately classifying new cases. Logistic regression had a structural problem similar to early single-layer neural networks, which limited its ability to identify variables with high statistical significance for reliable class assignment. Therefore, regression is not always the best model for class prediction in biomedical datasets. The study emphasises the importance of validating selected models and suggests that a mixture of experts approach may be a more advanced and effective strategy for analysing biomedical datasets.
Sex differences in pain perception have been extensively studied, but precision medicine applications such as sex-specific pain pharmacology have barely progressed beyond proof-of-concept. A data set of pain thresholds to mechanical (blunt and punctate pressure) and thermal (heat and cold) stimuli applied to non-sensitized and sensitized (capsaicin, menthol) forearm skin of 69 male and 56 female healthy volunteers was analyzed for data structures contingent with the prior sex structure using unsupervised and supervised approaches. A working hypothesis that the relevance of sex differences could be approached via reversibility of the association, i.e., sex should be identifiable from pain thresholds, was verified with trained machine learning algorithms that could infer a person's sex in a 20% validation sample not seen to the algorithms during training, with balanced accuracy of up to 79%. This was only possible with thresholds for mechanical stimuli, but not for thermal stimuli or sensitization responses, which were not sufficient to train an algorithm that could assign sex better than by guessing or when trained with nonsense (permuted) information. This enabled the translation to the molecular level of nociceptive targets that convert mechanical but not thermal information into signals interpreted as pain, which could eventually be used for pharmacological precision medicine approaches to pain. By exploiting a key feature of machine learning, which allows for the recognition of data structures and the reduction of information to the minimum relevant, experimental human pain data could be characterized in a way that incorporates "non" logic that could be translated directly to the molecular pharmacological level, pointing toward sex-specific precision medicine for pain.
Selecting the k best features is a common task in machine learning. Typically, a few features have high importance, but many have low importance (right-skewed distribution). This report proposes a numerically precise method to address this skewed feature importance distribution in order to reduce a feature set to the informative minimum of items. Computed ABC analysis (cABC) is an item categorization method that aims to identify the most important items by partitioning a set of non-negative numerical items into subsets "A", "B", and "C" such that subset "A" contains the "few important" items based on specific properties of ABC curves defined by their relationship to Lorenz curves. In its recursive form, the cABC analysis can be applied again to subset "A". A generic image dataset and three biomedical datasets (lipidomics and two genomics datasets) with a large number of variables were used to perform the experiments. The experimental results show that the recursive cABC analysis limits the dimensions of the data projection to a minimum where the relevant information is still preserved and directs the feature selection in machine learning to the most important class-relevant information, including filtering feature sets for nonsense variables. Feature sets were reduced to 10% or less of the original variables and still provided accurate classification in data not used for feature selection. cABC analysis, in its recursive variant, provides a computationally precise means of reducing information to a minimum. The minimum is the result of a computation of the number of k most relevant items, rather than a decision to select the k best items from a list. In addition, there are precise criteria for stopping the reduction process. The reduction to the most important features can improve the human understanding of the properties of the data set. The cABC method is implemented in the Python package "cABCanalysis" available at https://pypi.org/project/cABCanalysis/.
Recent scientific evidence suggests that chronic pain phenotypes are reflected in metabolomic changes. However, problems associated with chronic pain, such as sleep disorders or obesity, may complicate the metabolome pattern. Such a complex phenotype was investigated to identify common metabolomics markers at the interface of persistent pain, sleep, and obesity in 71 men and 122 women undergoing tertiary pain care. They were examined for patterns in d = 97 metabolomic markers that segregated patients with a relatively benign pain phenotype (low and little bothersome pain) from those with more severe clinical symptoms (high pain intensity, more bothersome pain, and co-occurring problems such as sleep disturbance). Two independent lines of data analysis were pursued. First, a data-driven supervised machine learning-based approach was used to identify the most informative metabolic markers for complex phenotype assignment. This pointed primarily at adenosine monophosphate (AMP), asparagine, deoxycytidine, glucuronic acid, and propionylcarnitine, and secondarily at cysteine and nicotinamide adenine dinucleotide (NAD) as informative for assigning patients to clinical pain phenotypes. After this, a hypothesis-driven analysis of metabolic pathways was performed, including sleep and obesity. In both the first and second line of analysis, three metabolic markers (NAD, AMP, and cysteine) were found to be relevant, including metabolic pathway analysis in obesity, associated with changes in amino acid metabolism, and sleep problems, associated with downregulated methionine metabolism. Taken together, present findings provide evidence that metabolomic changes associated with co-occurring problems may play a role in the development of severe pain. Co-occurring problems may influence each other at the metabolomic level. Because the methionine and glutathione metabolic pathways are physiologically linked, sleep problems appear to be associated with the first metabolic pathway, whereas obesity may be associated with the second.
Feature selection is a common step in data preprocessing that precedes machine learning to reduce data space and the computational cost of processing or obtaining the data. Filtering out uninformative variables is also important for knowledge discovery. By reducing the data space to only those components that are informative to the class structure, feature selection can simplify models so that they can be more easily interpreted by researchers in the field, reminiscent of explainable artificial intelligence. Knowledge discovery in complex data thus benefits from feature selection that aims to understand feature sets in the thematic context from which the data set originates. However, a single variable selected from a very small number of variables that are technically sufficient for AI training may make little immediate thematic sense, whereas the additional consideration of a variable discarded during feature selection could make scientific discovery very explicit. In this report, we propose an approach to explainable feature selection (XFS) based on a systematic reconsideration of unselected features. The difference between the respective classifications when training the algorithms with the selected features or with the unselected features provides a valid estimate of whether the relevant features in a data set have been selected and uninformative or trivial information was filtered out. It is shown that revisiting originally unselected variables in multivariate data sets allows for the detection of pathologies and errors in the feature selection that occasionally resulted in the failure to identify the most appropriate variables.
Motivation: Gaussian mixture models (GMMs) are probabilistic models commonly used in biomedical research to detect subgroup structures in data sets with one-dimensional information. Reliable model parameterization requires that the number of modes, i.e., states of the generating process, is known. However, this is rarely the case for empirically measured biomedical data. Several implementations are available that estimate GMM parameters differently. This work aims to provide a comparative evaluation of automated GMM fitting methods.
Results and conclusions: The performance of commonly used algorithms for automatic parameterization and mode number determination was compared with respect to reproducing the ground truth of generated data derived from multiple normal distributions. Four main variants of Gaussian mode number detection algorithms and five variants of GMM parameter estimation methods were tested in a combinatory scenario. The combination of best performing mode number determination algorithms and GMM parameter estimation methods was then tested on artificial and real-live data sets known to display a GMM structure. None of the tested methods correctly determined the underlying data structure consistently. The likelihood ratio test had the best performance in identifying the mode number associated with the best GMM fit of the data distribution while the Markov chain Monte Carlo (MCMC) algorithm was best for GMM parameter estimation while. The combination of the two methods of number determination algorithms and GMM parameter estimation was consistently among the best and overall outperformed the available implementations.
Implementation: An automated tool for the detection of GMM based structures in (biomedical) datasets was created based on the present results and made freely available in the R library “opGMMassessment” at https://cran.r-project.org/package=opGMMassessment.
Knowledge discovery in biomedical data using supervised methods assumes that the data contain structure relevant to the class structure if a classifier can be trained to assign a case to the correct class better than by guessing. In this setting, acceptance or rejection of a scientific hypothesis may depend critically on the ability to classify cases better than randomly, without high classification performance being the primary goal. Random forests are often chosen for knowledge-discovery tasks because they are considered a powerful classifier that does not require sophisticated data transformation or hyperparameter tuning and can be regarded as a reference classifier for tabular numerical data. Here, we report a case where the failure of random forests using the default hyperparameter settings in the standard implementations of R and Python would have led to the rejection of the hypothesis that the data contained structure relevant to the class structure. After tuning the hyperparameters, classification performance increased from 56% to 65% balanced accuracy in R, and from 55% to 67% balanced accuracy in Python. More importantly, the 95% confidence intervals in the tuned versions were to the right of the value of 50% that characterizes guessing-level classification. Thus, tuning provided the desired evidence that the data structure supported the class structure of the data set. In this case, the tuning made more than a quantitative difference in the form of slightly better classification accuracy, but significantly changed the interpretation of the data set. This is especially true when classification performance is low and a small improvement increases the balanced accuracy to over 50% when guessing.
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.
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.