Pain

Pain. 159(1): 11-24

Quantitative sensory testing response patterns to capsaicin- and ultraviolet-B–induced local skin hypersensitization in healthy subjects: a machine-learned analysis

Jörn Lötschab*, Gerd Geisslingerab, Sarah Heinemanna, Florian Lerchbc, Bruno G. Oertelab, Alfred Ultschc

a. Institute of Clinical Pharmacology, Goethe-University, Frankfurt am Main, Germany

b. Fraunhofer Institute for Molecular Biology and Applied Ecology IME, Project Group Translational Medicine and Pharmacology TMP, Frankfurt am Main, Germany

c. DataBionics Research Group, University of Marburg, Marburg, Germany

*. Corresponding author. Address: Goethe-University, Theodor-Stern-Kai 7, 60590 Frankfurt am Main, Germany. Tel.: +49-69-6301-4589; fax: +49-69-6301-4354. E-mail address: j.loetsch@em.uni-frankfurt.de (J. Lötsch).

Copyright © 2017 The Author(s). Published by Wolters Kluwer Health, Inc. on behalf of the International Association for the Study of Pain.

DOI: 10.1097/j.pain.0000000000001008

Published in print: January 2018

Published online: 16 August 2017

Abstract

Machine learning identified differences in ultraviolet-B– and capsaicin-induced hypersensitization in the quantitative sensory testing parameter patterns acquired in 82 healthy subjects.

Abstract

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.

1. Introduction

Biomedical research using cell experiments, laboratory animals, or human volunteers often produces complex multidimensional data. The complex trait of pain, which is known to rely on a complex network of molecular nociceptive pathways,³⁴ results in a similarly complex phenotypic representation.⁵⁵ Therefore, the assessment of pain-related human phenotypes requires detailed diagnostic approaches.4,7,28 Consequently, combinations of several experimental nociceptive stimuli are used to address particular sensory attributes or different neuronal and molecular mechanisms of nociception or analgesia.⁷⁷ Standardized quantitative sensory testing (QST) protocols⁷¹ use combinations of thermal and various mechanical stimuli to explore the spectrum of sensory abnormalities that often accompany neuropathic pain.⁹⁵

Human pain research, based on the exploration of pain phenotypes with batteries of diagnostic tests, routinely produces complex biomedical data. The influence of different factors on the pain phenotype may result in a highly complex distribution of the data, and as a consequence, complex data analysis methods are required. Recent developments in computational and data science offer a multidisciplinary collaborative approach for extracting pertinent information from biomedical data and generating knowledge from that information.⁶⁷ These developments include machine-learning methods that structure the biomedical data into clusters.

In this study, we acquired complex data by experimentally inducing pain in healthy subjects²⁶ by using 2 different hypersensitization procedures established in human experimental pain research, consisting of application of ultraviolet-B (UV-B) or topical capsaicin to a small area of skin. We analyzed the effects of these treatments on the parameters of a QST battery using machine-learning⁵⁸ and feature selection²⁴ techniques, which provide a set of methods that can automatically detect patterns in data or perform other kinds of decision making under conditions of uncertainty.⁵⁸ The main classical types of machine learning, supervised and unsupervised learning (Box 1), were primarily used to explore data and to identify the QST parameters that are most affected by the hypersensitization procedures.

Text box 1. Overview on the main classical types of machine learning comprising supervised or unsupervised learning.

For supervised machine learning, the data space with a predefined division into an input space X and an output space Y. The input space comprises vectors >0 different parameters acquired during a study for n >0 cases. The output space Y comprises yi ∈ C = {1,…, c}, where c denotes the possible classes such as treatment groups or diagnoses. During learning, the data space is searched with the aim of identifying an intelligent algorithm that maps the input features to the output classes. By contrast, for unsupervised machine learning, the data space lacks class information, and the task is to find interesting structures in the d-dimensional feature space Du ⊂ Rd, which subsequently can be topically interpreted. In this study, both classes of machine-learned analysis were applied (1) to identify the most relevant effects of UV-B and topical capsaicin on quantitative sensory testing (QST) parameters and (2) to identify possible subgroups of subjects who share similar QST responses to the selected hypersensitization treatments.

The unsupervised machine-learning method used was the ESOM/U-matrix, which is a topology-preserving artificial neuronal network (Kohonen SOM38,39) used to project high-dimensional data points xi ϵ RD onto a 2-dimensional self-organizing network consisting of a large grid of neurons.⁸⁸ Training for this unsupervised model means adapting to the structures of the high-dimensional input data. On top of the trained ESOM, the distance structure in the high-dimensional feature space was visualized in the form of a U-matrix. This visualization displays the distances between the points in the high-dimensional space in a color-coded manner using a geographical map analogy where large “heights” represent large distances in the feature space while low “valleys” represent data subsets that are similar. “Mountain ranges” with “snow-covered” heights visually separate the clusters in the data.82,88

2. Methods

2.1. Subjects and study design

The study protocol complied with the Declaration of Helsinki on Biomedical Research Involving Human Subjects and was approved by the Ethics Committee of the Medical Faculty of the Goethe University, Frankfurt am Main, Germany (protocol number 28/11). Healthy volunteers who considered themselves to be of Anglo-American ethnicity (n = 100, 46 men), aged 19 to 42 years (mean ± standard deviation 25 ± 3.5 years), were enrolled after providing informed written consent. Exclusion criteria were drug intake during the previous week (except for oral contraceptives, vitamins, or hormone substitutes such as L-thyroxin), a current clinical condition involving pain, and current diseases, according to questioning and medical examination. Prior to the experimental tests, all subjects completed training sessions with pain tests applied to an area different from the planned test and control areas.

2.2. Application of experimental hypersensitization (treatments)

Experimental local hypersensitization of the skin was induced by either applying UV-B⁸⁰ or capsaicin cream⁶⁵ topically on the inner part of the subject's forearm. The application sides (left or right) of either model were randomized among subjects, with equal proportions of men and women in each treatment subgroup.

The UV-B pain model uses UV light to induce a small area of inflammation, allowing the assessment of mechanical and thermal thresholds.23,27,30 Irradiation of the skin was performed inside the forearm on an area without any superficial veins or birth marks, in a different area than was used in the experiments to assess hyperalgesia. First, to determine the minimal erythema dosage (MED), 6 areas of 1 cm² were irradiated at a cumulative UV-B dosage between 200 and 600 mW/cm² (UV-B lamp UV 109; Waldmann Medizintechnik, Villingen-Schwenningen, Germany). The lamp was placed at a distance of 2.5 cm from the skin. UV-B dosage was increased by extending the irradiation time. Minimal erythema dosage was determined as the smallest dosage that led to a visual reddening of the irradiated area of skin after 24 hours. Subsequently, for the actual experiments, a different area of skin on the inner forearm was chosen according to the same criteria as used for MED determination. This area was irradiated with double the MED, and the experiments were performed 24 hours after UV-B irradiation.

In the capsaicin experimental pain model, chemical methods of nociceptor stimulation were used to produce stable and long-lasting hyperalgesia with a low potential for skin injury, in the original publication supplemented by heat stimulation⁶⁵ and in this study with additional cold and mechanical stimuli. In this study, 150 mg of capsaicin cream (0.2%, manufactured by the local hospital pharmacy) was topically applied to a 3 × 3-cm² area of skin. Subsequently, the area was covered with a plaster for 30 minutes before the QST parameters were acquired.

2.3. Quantitative sensory testing and raw data processing

Quantitative sensory testing was performed twice in each subject, once at baseline and again following application of experimental hypersensitization. A clinically established QST test battery was used as proposed by the German Research Network on Neuropathic Pain.71,72 This battery includes thermal and mechanical stimuli grouped into 7 tests of sensory perception and pain (Table 1) administered in the following order: thermal testing, mechanical detection threshold, mechanical pain threshold, mechanical pain sensitivity, temporal pain summation, vibration detection threshold (VDT), and pressure pain threshold (PPT). The room temperature was kept at 20 to 25°C during testing. Measurements were taken by trained investigators fully adhering to previously published instructions,66,71,72 which are briefly recapitulated in Table 1.

See full tableTable 1. Components of the quantitative sensory testing battery of the German research network on neuropathic pain.71,72

The 7 tests provided a total of 13 different QST parameters, which were processed according to the published instructions,66,71,72 including log-transformation of some parameters as specified in Table 1, in the column headed “Basic data processing.” Subsequently, each QST parameter value was mapped onto the distribution of a reference group consisting of a total of 180 healthy subjects, in whom a data set of 1080 values was obtained. This map serves as the reference for all QST-based diagnoses.⁴⁸ Therefore, according to the standard QST procedure, the individual QST parameter values were z-transformed as

where the QST reference values and standard deviations were values published in a methodological article⁴⁸ with regard to the subject's sex, age, and body site tested. The signs of the z-scores were adjusted to denote that a score >0 indicates high sensitivity and a score <0 indicates low sensitivity, according to the standard instructions.

2.4. Data analysis

Complete data were obtained from 82 subjects. Following the exclusion of differences between left-hand and right-hand sides in the baseline measurements, which was supported by nonsignificant paired t tests⁷⁹ performed for each QST parameter, transformed baseline data (z-values) were averaged between the 2 test sides. As observed previously,18,45 the QST parameters dynamic mechanical allodynia and paradoxical heat sensations did not vary among the subjects, and the QST parameter vibration detection threshold displayed only 2 different values in the whole cohort (0 or 1) that did not change following application of the hypersensitization procedures. Therefore, these parameters were omitted from the analyses.

The analyzed data set consisted of 10 QST parameters acquired in 82 healthy subjects in the 3 study conditions (treatments): (1) baseline, (2) following application of UV-B, and (3) following topical application of capsaicin. The z-transformed QST parameter values obtained according to the standard procedure of the QST battery⁴⁸ provided the data space . The cases xi ∈ X were the QST parameters acquired from the volunteers in our study, and the output space Y comprising yi ∈ C = {1,2,3} was given by the 3 different study conditions. This data space was analyzed using machine-learning⁵⁸ and feature selection techniques²⁴ to (1) identify the QST parameters most affected by the hypersensitization treatments and (2) explore the data space for high-dimensional structures associated with the hypersensitization conditions or with subject subgroups sharing similar responses to the hypersensitization treatments. Finally, (3) the key results of the machine-learned analysis were verified by comparing them with the results of a standard variance analytical approach.

All analyses were performed using the R software package (version 3.3.3 for Linux; http://CRAN.R-project.org/, Ref. 68) on an Intel Xeon computer running on Ubuntu Linux 16.04.2 64-bit. The steps of the machine-learned analysis are described in detail as follows.

2.4.1. Machine-learned analysis to identify the quantitative sensory testing parameters most affected by hypersensitization

To identify the QST parameters that were most affected by UV-B or topical capsaicin application, we started with the hypothesis that these parameters can provide the basis for the correct association of a measurement with the hypersensitization treatments under which the data had been acquired. We approached this task using supervised machine learning. Our analysis included (1) a feature selection step, which aimed at identifying the most relevant QST parameters (features) for correct assignment to different classes or treatments, which was followed by (2) creation of a classifier that allowed us to explore differences in the effects of the hypersensitization treatments.

2.4.1.1. Feature selection

The QST parameters differing most relevantly among the 3 experimental conditions, and thus qualifying as basis by which to distinguish the study conditions, were identified using techniques of unsupervised machine learning⁵⁸ and feature selection.²⁴ Specifically, the input-output pairs were submitted to random forest machine learning. A random forest consists of a set of different, uncorrelated, and often very simple decision trees.⁹ Each decision tree uses a tree data structure with conditions on variables (parameters) as vertices and classes as leaves. Each tree in the random forest votes for a class. The final classification assigned to a data point follows the majority of these class votes.

In our analysis, in 1000 repeated experiments the original data set was split into 2/3 training and 1/3 test data subsets, by means of class-proportional bootstrap resampling from the training data set²⁰ using the R library “sampling” (https://cran.r-project.org/package=sampling, Ref. 83), to increase the robustness of the analysis. For each of the 1000 experiments, 500 random decision trees were created, each tree containing d ∈ {1,…,10} features randomly drawn from the d = 10 QST parameters. The number of trees was based on visual analysis of the relationship between the number of decision trees and the accuracy of the classification. This analysis indicated no improvement beyond approximately 300 trees; therefore, building 500 trees was considered to provide robust results. Within this analysis, bootstrap resampling was used again to split the training data subset into further training and test subsamples, and trees were created on these training subsamples and applied to test subsamples. Thus, the whole analysis accommodated the concept of a nested cross-validation analysis,⁹³ with the inner loop consisting of the decision tree analysis on data resampled from the training data subset and the outer loop consisting of the 1000 splits of the whole data set into training and test data. The trees were analyzed with respect to the features included and the accuracy of classification into the 3 treatment groups. For each feature, we computed the mean decrease in Gini impurity (https://en.wikipedia.org/wiki/Decision_tree_learning#Gini_impurity) while excluding the respective parameter from a random forest building. We thus provided a rating criterion for the importance of each QST parameter to serve as a basis to conclude the experimental condition, under which its value had been acquired, ie, the amount of this decrease indicated the importance of the particular feature. We performed these calculations using the “randomForest” library (https://cran.r-project.org/package=randomForest, Ref. 44).

Following each of the 1000 random forest analyses on resampled data, we submitted the values of the mean decreases in Gini impurity to computed ABC analysis while excluding the parameter from random forest analysis.⁸⁷ ABC analysis is a categorization technique for selection of the most important subset among a larger set of items, and we chose it because it fit the basic requirements of feature selection using filtering techniques,⁷⁵ ie, it easily scales to very high-dimensional data sets, is computationally simple and fast, and is independent of the classification algorithm. ABC analysis aims at dividing a set of data into 3 distinct subsets called “A,” “B,” and “C.” Set A should contain the “important few,” ie, those elements that allow us to obtain a maximal yield with a minimal effort.35,62 Set B comprises those elements where an increase in effort is proportional to the increase in yield. By contrast, set C contains the “trivial many,” ie, those elements with which the yield can only be achieved with a disproportionally great additional effort.35,62 The target QST parameters for further exploration of the hypersensitization effects were sought in ABC set “A.” The final size of the feature set was equal to the most frequent size of set “A” in the 1000 runs. The final members of the feature set were chosen in decreasing order of their appearances in ABC set “A” among the 1000 runs. These calculations were done using our software package (http://cran.r-project.org/package=ABCanalysis, Ref. 87).

2.4.1.2. Explorative analysis to identify the quantitative sensory testing parameters most affected by hypersensitization

The QST parameters most frequently assigned to set “A” in the 1000 random forests and ABC analysis of resampled data, at the number corresponding to the most frequent size of set “A,” were used to create a decision tree associating ranges of QST parameter values with the 3 study conditions. This tree was obtained by means of decision tree learning using the classification and regression tree algorithm.¹⁰ As in random forests, a tree data structure is created with conditions on variables (parameters) as vertices and classes as leaves. In random forests, tree structure is randomly created, making it impossible to interpret single trees, but in classical decision trees, local decisions follow statistical criteria and aim at providing a simple and easily understandable set of classification rules suitable for topical interpretation, which is why we chose to use them in the present exploratory analysis. We used the concept of Gini impurity to find optimal (local) mutually exclusive decisions. The calculations used the “ctree” function of the “party” software package (https://cran.r-project.org/package=party, Ref. 32). We assessed the significance of the splits at each decision node by applying permutation tests as implemented in the “ctree” function. Nodes were only split if the null hypothesis of independence between the response variable, ie, the treatment class, and the predictors, ie, the QST parameter values, could not be rejected at the given level of significance. Finally, we assessed the performance of the identified decision tree to correctly assign the treatment during which data had been acquired by calculating the overall classification accuracy of treatment assignment using standard equations.² We repeated these steps in 1000 runs of randomly resampled data subsets class—proportionally drawn from the complete data sets. The accuracy was the median of the values obtained in the 1000 runs, and the 95% confidence interval spanned between the 2.5th and 97.5th percentiles of the range of the 1000 associated accuracy values.

2.4.2. Machine-learned analysis of quantitative sensory testing parameter–based data structures

To identify response patterns of QST parameters to the hypersensitization treatments, we analyzed the baseline values together with parameters acquired after application of UV-B or capsaicin. We performed this analysis in 4 main steps, comprising (1) data preprocessing based on Bayesian statistics; (2) detection of distance- and density-based data structures based on emergent self-organizing maps followed by subgroup detection; (3) decision tree–based exploration of the QST parameter pattern of the data cluster structure we had obtained; and (4) topical characterization of the data structures, including sex differences.

2.4.2.1. Data preprocessing

The 10 × 246 matrix, we obtained (10 z-transformed QST parameters acquired in 82 subjects under 3 different treatments comprising baseline, UV-B, and capsaicin), provided the data space . We analyzed the parameters (features) with respect to their probability density function. We did so by applying the Pareto density estimation (PDE), which is a kernel density estimator particularly suitable for the discovery of groups.⁸⁶ For each of the 10 QST parameters, the magnitudes were described as either low, average, or high, reflecting the previous phenotypes of “low pain sensitivity,” “average pain sensitivity,” and “high pain sensitivity” proposed by Diatchenko et al.¹⁷ The association of each value to 1 of the 3 classes was obtained by means of Gaussian mixture modeling. That is, the PDE was described as , where N (x|mi, si) denotes Gaussian probability densities (component, mode) with means, mi, and standard deviations, si, while wi denotes the mixture weights controlling the relative contribution of each Gaussian component to the overall distribution, which add up to a value of 1, and M = 3 denotes the number of components in the mixture corresponding to the 3 proposed classes described above (low pain sensitivity, average pain sensitivity, and high pain sensitivity). We fitted this model to the PDE of the data using our “AdaptGauss” software package (https://cran.r-project.org/package=AdaptGauss, Refs. 43,90) and using the expectation maximization algorithm.¹⁵ Subsequently, we calculated the probabilities for each data value to belong to each of the 3 Gaussian components as the Bayesian posteriors.⁵⁰ Finally, we subtracted the probabilities of belonging to the small data value range from those of belonging to the high data value range, providing 10 vectors scaled in the interval [−1,…,1].

2.4.2.2. Detection of distance- and density-based data structures

The 10 × 246 matrix of Bayesian posteriors belonging to low, average, or high QST values within each parameter range across the whole study provided the unsupervised data space Du ⊂ [−1,1]¹⁰ that we explored for distance- and density-based structures. We performed this exploration by means of unsupervised machine learning.⁵⁸ The task was to identify data structures that reflected the treatments applied in the experiments and to suggest possible subgroups of responders to the treatments. Machine learning was implemented as emergent self-organizing feature maps (ESOMs)³⁸ that were combined with the U-matrix.⁸⁵ This method has been shown to provide an unbiased way to identify structures in biomedical data.⁸⁸ Specifically, ESOMs are based on a topology-preserving projection of high-dimensional data points xi ϵ RD onto a 2-dimensional self-organizing network consisting of a grid of neurons. This approach represents a topology-preserving mapping of high-dimensional data points onto a 2-dimensional grid of neurons that therefore favored more common clustering algorithms such as k-means, Ward, complete, and average linkage,⁴⁷ which in contrast to the ESOM/U-matrix method are prone to detect false structures in the data.⁸⁸ The neural network consisted of a 2-dimensional toroid grid⁸⁵ of so-called neurons with 50 rows and 80 columns (n = 4000 units; for SOM size determination, see Ref. 88). Each neuron holds, in addition to a position vector on the 2-dimensional grid, a further vector carrying “weights” of the same dimensions as the input dimensions. The weights were initially randomly drawn from the range of the data variables and were subsequently adapted to the data during the learning phase that used 30 training cycles.

After training of the neural network, we obtained an ESOM that represented the subjects on a 2-dimensional toroid map as the localizations of their respective “best matching units” (BMU), which are neurons on the grid that after ESOM learning carried the vector that was most similar to a subjects' data vector. On top of this grid, the distances between data points are calculated with the U-matrix.47,89 Every value (height) in the U-matrix depicts the average high-dimensional distance of a prototype to all immediate neighboring prototypes regarding a grid position. The U-matrix can be enhanced by calculating a P-matrix⁸⁵ displaying the point density for a neuron as , estimated as the number of data points belonging to the data space in a sphere with radius r belonging to the real numbers around the weight of each neuron on the ESOM's output grid. The U*-matrix combines distance structures (U-matrix) and density structures (P-matrix) into a single matrix.⁸⁵ The corresponding visualization technique is a topographical map with hypsometric colors,⁸¹ facilitating the recognition of distance- and density-based structures. Large “heights” in brown and white colors represent large distances between data points (subjects) separating “valleys” in green and blue colors that represent data points that are similar.

2.4.2.3. Assessment of cluster structures and hypersensitization response subgroups

The ESOM/U*-matrix analysis provided a distance- and density-based cluster structure of the data of the complete study. That is, each treatment had been regarded as a separate data subset leading to the representation of each subject 3 times on the ESOM with data points for each treatment. Therefore, cluster structures provided a basis to identify both (1) the effects of the hypersensitization treatments and (2) subgroups of subjects sharing response patterns to the treatments.

To explore the cluster structure, we submitted the z-values of the QST parameters to decision tree learning as described above, ie, using the classification and regression tree algorithm¹⁰ with the Gini impurity as basis of a dichotomous split criterion to find an optimum as implemented in the “ctree” function of the “party” package (https://cran.r-project.org/package=party, Ref. 32). An α-level of P = 0.001 was chosen for split significance and was corrected for multiple testing according to the procedure proposed by Bonferroni.⁸ The performance of the identified decision tree to correctly assign a data point to its U*-matrix–based cluster was assessed by calculating the overall classification accuracy of treatment assignment as accuracy [%] = number of correct treatment associations/total number of treatment associations.⁵¹

We approached the interpretation of the cluster-specific QST pattern by associating the original hypersensitization treatments to the U*-matrix–based clusters. Therefore, we analyzed the treatment vs cluster contingency table with respect to overrepresentation or underrepresentation of treatments in clusters. Specifically, we obtained the permutation distribution of this 2-way table and calculated the sum of squares of the Pearson residuals as the test statistic of independence.⁹⁷ We assessed test significance using Pearson χ² test.⁶⁴ This step allowed us to associate particular study conditions (baseline, UV-B, and capsaicin) with U*-matrix clusters. These calculations were done using the “vcd” library (https://cran.r-project.org/package=vcd, Ref. 54).

In addition to exploring the U*-matrix–derived clusters for treatments effects, we also looked at cluster membership with respect to sex differences. Therefore, we submitted cluster membership vs sex cross-tables, obtained for study treatments, decision-tree analysis, and ESOM/U*-matrix analysis, to Fisher exact tests.²¹

2.4.3. Reassessment of key results using analysis of variance

To reassess key results of machine-learned analyses using classical statistical methods, we analyzed the effects of UV-B or topical capsaicin on QST parameters by submitting the QST parameter z-values to conventional analysis of variance for repeated measures (rm-ANOVA) with “hypersensitization” (UV-B or capsaicin) as a within-subjects factor and “sex” as a between-subjects factor. The analyses were performed separately for each QST parameter. Each rm-ANOVA was followed by the analysis pairwise treatment differences by means of paired t tests.⁷⁹ The α-level was set at 0.05 and corrected for multiple testing,⁸ separately for each rm-ANOVA (ie, 3 t tests).

3. Results

The QST parameter values obtained during the baseline measurements did not significantly differ between the test sides (t tests: P always >0.05) and were therefore averaged to obtain the baseline condition data subset. For technical reasons, data from 18 subjects were incomplete. Moreover, the QST parameters dynamic mechanical allodynia and paradoxical heat sensations lacked intersubject variation, and VDT displayed only 2 different values (0 or 1), which suggested exclusion of these values from the analyses. With baseline QST parameters having been averaged between the 2 test sides, the data we analyzed were based on 3280 QST parameter values obtained in 82 subjects when counting the data in a similar manner as in the report of the reference values of the QST test battery that mentioned 1080 QST parameter values obtained in 180 subjects.⁴⁸ The distribution of the z-transformed data is shown in Figure 1.

Figure 1.View larger versionFigure 1. Distribution of the z-values of the quantitative sensory testing (QST) parameters at baseline (blue) and following hypersensitization induced by topical application of ultraviolet-B (violet), or capsaicin (orange-red). The density distribution is presented as probability density function (PDF), estimated by means of the Pareto density estimation (⁸⁶black line). Higher z-scores indicate higher sensitivity to the respective stimuli. The figure was created using the R software package (version 3.3.3 for Linux; http://CRAN.R-project.org/, Ref. 68). CDT, cold detection threshold; CPT, cold pain threshold; HPT, heat pain threshold; MDT, mechanical detection threshold; MPS, mechanical pain sensitivity to pinprick stimuli; MPT, mechanical pain threshold; PPT, pressure pain threshold; TSL, thermal sensory limen; VDT, vibration detection threshold; WDT, warmth detection threshold; WUR, wind-up ratio.

3.1. Quantitative sensory testing parameters most affected by ultraviolet-B– or topical capsaicin-induced hypersensitization

Supervised machine learning using 1000 random forest analyses (Fig. 2) of bootstrap resampled data indicated different contributions to correct treatment association for particular QST parameters. Specifically, only 4 different QST parameters (heat pain threshold, cold pain threshold, cold detection threshold, and thermal sensory limen) had been included in successful decision trees. In the ABC analyses (Fig. 2) that had followed each random forest analysis, set “A” comprising items that contribute most to the association with the study treatments took sizes of 0, 1, 2, or 3 QST parameters in 7, 517, 387, and 89 of the runs, respectively. Therefore, a set size of 1 QST parameter was chosen for further analysis, and the QST parameter most frequently assigned to set “A,” ie, in 993 runs, was HPT (Fig. 2).

Figure 2.View larger versionFigure 2. Machine-learned analysis to identify quantitative sensory testing (QST) parameters most affected by hypersensitization, implemented as random forest analysis followed by ABC analysis of the contribution of QST parameters to overall association of the measurements to the study treatments (baseline, ultraviolet-B, or capsaicin). (A) Dot chart³³ of the mean decrease in Gini impurity when the respective feature (QST parameter) is excluded from random forest decision tree building. The plot displays 1 typical example out of the analyses of 1000 bootstrap resampled data subsets. (B) Subsequent to random forest-based feature selection, the mean decrease in Gini impurity associated with each QST parameter was submitted to ABC analysis, which is an item selection procedure aiming at identification of the most profitable items from a larger list of items. The ABC plot (blue line) shows the cumulative distribution function of the mean decreases in accuracy, along with the uniform distribution (green line) in which each feature would have the same chance to contribute to the study condition assignment (for further details about computed ABC analysis, see Ref. 87). The red lines indicate the borders between ABC sets “A,” “B,” and “C.” Only set “A,” containing the most profitable item, was selected as the +relevant QST item subset. (C) Count of occurrences of QST parameters in ABC set “A” during the 1000 runs on bootstrap resampled data. The 4 parameters are those that ever appeared in set “A.” Most frequently, the set size was |{A}| = 1 parameter and most often the QST parameter “HPT.” Therefore, this parameter (blue) was selected as a sufficient basis for study treatment assignment during random forest–based feature selection for unsupervised machine-learned analysis. The figure was created using the R software package (version 3.3.3 for Linux; http://CRAN.R-project.org/, Ref. 68). In particular, the ABC analysis was performed and plotted using our “ABCanalysis” software package (http://cran.r-project.org/package=ABCanalysis, Ref. 87). CDT, cold detection threshold; CPT, cold pain threshold; HPT, heat pain threshold; MDT, mechanical detection threshold; MPS, mechanical pain sensitivity to pinprick stimuli; MPT, mechanical pain threshold; PPT, pressure pain threshold; TSL, thermal sensory limen; WDT, warmth detection threshold; WUR, wind-up ratio.

Decision tree analysis using the selected QST parameter (Fig. 3) provided an overall classification accuracy of 67.9% (cross-validated nonparametric 95% confidence interval obtained in 1000 resampling runs: 60.5%-75.3%), which was substantially above 33% chance of assigning a measurement to 1 of the 3 study conditions. However, it also provided 100 to 67.9 = 32.1% falsely classified data points. Exploration of the decision tree (Fig. 3) indicated that data acquired following topical application of capsaicin were almost always associated with high heat pain sensitivity, whereas data acquired during the baseline condition were almost always associated with low heat pain sensitivity. However, data acquired following UV-B treatment were partly found to be associated with medium heat pain, while a fraction of the data shared a decision node with baseline data indicating nonresponse to hypersensitization. The decision tree allowed only for statistically significant splits comprised 6 final nodes (Fig. 3). The distribution of study conditions was statistically highly significantly different across the terminal tree nodes (χ² statistics: P < 2·10⁻¹⁶).

Figure 3.View larger versionFigure 3. Decision tree associating ranges of the quantitative sensory testing (QST) parameter most affected by hypersensitization according to feature selection analysis (Fig. 2) with the 3 study conditions: baseline (1), ultraviolet-B (UV-B) (2), or capsaicin (3). The split criterion was the Gini impurity, and only statistically significant splits, based on permutation tests, were accepted. The tree ended in 6 terminal nodes (4, 5, 7, 8, 10, 11) at which the number of measurements assigned to the respective node is shown as bar plots, with separate bars for each study treatment (blue = baseline, violet = UV-B, red = capsaicin). Higher z-scores indicate higher sensitivity to the respective stimuli. At the upper left corner, an association plot is shown to visualize the residuals of an independence model for the contingency table.¹⁴ Each cell of the contingency table is represented by a rectangle that has a height proportional to the contribution to Pearson χ for the cell and width proportional to the square root of expected counts corresponding to the cell. Hence, the area of each box is proportional to the difference in observed and expected frequencies. The rectangles in each row are positioned relative to a baseline indicating independence, ie, if the observed frequency of a cell is greater than the expected frequency, the box rises above the baseline, but otherwise it falls below it. Each study treatment (lines) is plotted vs the decision tree terminal nodes (columns) as a result of a contingency table analysis, indicating the relative representations of each treatment across the tree nodes. The Pearson residuals are colored according to a perceptually uniform hue-chroma-luminance (HCL) given at the right margin of the association plot.⁵² The figure has been created using the R software package (version 3.3.3 for Linux; http://CRAN.R-project.org/, Ref. 68). Specifically, for drawing the tree and association plots, the “vcd” package (https://cran.r-project.org/package=vcd) was used⁵⁴ including the “strucplot” framework⁵³ and residual-based shadings.⁹⁷ HPT, heat pain threshold.

3.2. Quantitative sensory testing parameter–based data structures

Unsupervised machine learning identified structures in the data space comprising the variables d = 10 QST parameters, x, acquired from 82 subjects. Following projection of the vector space onto a toroid grid of 50 × 80 = 4000 neurons and training of a self-organizing map, a U*-matrix visualization was displayed on top of this SOM (Fig. 4) that visualized distance- and density-based data structures. The resulting ESOM visualized large gaps in the data space by large U-heights, whereas data located in close vicinity in the high-dimensional space were placed in regions with low U-heights on the U*-matrix. The valleys and ridges allowed the identification of 4 major clusters in the QST data space acquired during the present study (Fig. 4A, B). The study conditions (baseline, UV-B, and capsaicin) were unevenly represented in the clusters, as indicated by highly significant χ² statistics (P < 2·10⁻¹⁶).

Figure 4.View larger versionFigure 4. Machine-learned analysis aimed at detecting data structures of quantitative sensory testing (QST) parameter pattern acquired during the different study conditions (treatments). (A) U*-matrix visualization of distance- and density-based structures of the QST parameter pattern observed in 82 subjects under baseline conditions and following application of ultraviolet-B- or capsaicin-induced hypersensitization. The figure was created by projecting the data points onto a toroid grid of 4000 neurons where opposite edges are connected. The dots indicate the “best matching units” (BMUs) of the self-organizing map (SOM), which are those neurons whose weight vector is most similar to the input. A single neuron can be the BMU for more than 1 data point or subject; hence, the number of BMUs may not be equal to the number of acquired measurements. The U*-Matrix was colored as a geographical map with brown (up to snow-covered) heights and green valleys with blue lakes. Valleys indicate clusters and watersheds indicate borderlines between different clusters. The BMUs are colored according to the 4 clusters identified on the basis of this U*-matrix. (B) 3-D view of the same U*-star matrix, indicating cluster separation by “mountain ridges.” (C) Decision tree associating emergent self-organizing feature map (ESOM)/U*-matrix–derived clusters with ranges of QST parameters. Higher z-scores indicate higher sensitivity to the respective stimuli. The split criterion was the Gini impurity, and only statistically significant splits, based on permutation tests, were accepted. The tree ended in 6 terminal nodes (4, 5, 7, 8, 10, 11) at which the number of measurements assigned to the respective node is shown as bar plots, with separate bars for each U*-matrix–based cluster. (D) Association plot visualizing the residuals of an independence model for the treatment vs clusters contingency table.¹⁴ Each cell of the contingency table is represented by a rectangle that has height proportional to the contribution to Pearson χ for the cell and width proportional to the square root of expected counts corresponding to the cell. Hence, the area of each box is proportional to the difference in observed and expected frequencies. The rectangles in each row are positioned relative to a baseline indicating independence, ie, if the observed frequency of a cell is greater than the expected one, the box rises above the baseline, and falls below otherwise. Each study treatment (lines) is plotted vs the U*-matrix–derived clusters (columns) as a result of a contingency table analysis, indicating the relative representations of each cluster in across the tree nodes. The Pearson residuals are colored according to a perceptually uniform hue-chroma-luminance (HCL) given at the right margin of the association plot.⁵² The figure was created using the R software package (version 3.3.3 for Linux; http://CRAN.R-project.org/, Ref. 68). Specifically, for drawing the tree and association plots, the “vcd” software package (https://cran.r-project.org/package=vcd) was used,⁵⁴ including the “strucplot” framework⁵³ and residual-based shadings.⁹⁷ HPT, heat pain threshold; PPT, pressure pain; CPT, cold pain threshold; CDT, cold detection threshold.

Specifically, data acquired during the baseline condition were overrepresented in the first cluster and underrepresented in the 3 other clusters (Fig. 4D). Indeed, cluster 1 comprised 74 of the 82 measurements acquired during the baseline condition. The first cluster was, however, larger than a third of the data points as it also contained 45 measurements acquired following application of UV-B hypersensitization. Given that further subclusters did not emerge in this cluster, this fraction of data acquired during the UV-B condition points at nonresponders to this treatment. Consistently, the second cluster that contained measurements acquired following UV-B treatment was comparatively small (n = 28 data points) and contained 19 measurements acquired during the UV-B condition. Finally, data acquired following topical application of capsaicin were overrepresented in 2 different clusters in which all other study conditions were underrepresented (Fig. 4D). Indeed, 78 of the 82 measurements acquired following capsaicin application were located in clusters 3 or 4. The distribution on 2 different clusters indicated clear subgroups in the response to capsaicin hypersensitization.

Decision tree analysis of the U*-matrix–derived clusters (Fig. 4C), based on statistically significant data splits and providing an overall cluster association accuracy of 87.8% (95% CI: 83.05%-91.6%), indicated that again, heat pain sensitivity (QST parameter HPT) was the major distinctive criterion among the clusters as it had resulted in the supervised machine-learned analysis. However, additional QST parameters played a role in correct cluster assignment. Specifically, high sensitivity to cold stimulation was important for assignment to the cluster containing the most data acquired following application of UV-B induced hypersensitization. By contrast, the 2 clusters to which most of the data acquired following application of capsaicin-induced hypersensitization were assigned could be distinguished by sensitivity to pressure pain (QST parameter PPT; Fig. 4C).

Thus, the difference in the response to capsaicin among subjects was mainly due to a different sensitivity to pressure pain. An analysis of the cluster membership vs sex cross-table (Fig. 5) indicated a different distribution of sexes among the U*-matrix–based clusters (Fisher exact test: P = 0.009881), in contrast to the original treatment vs sex distribution (P = 1) and to the sex distribution across the HPT-dependent decision tree nodes obtained in the supervised machine-learning analysis (P = 0.2125). This sex distribution prevailed between the 2 clusters associated with capsaicin treatment (P = 0.03894). Cluster 4, characterized by a higher sensitivity to pressure pain, contained more women than men, while the opposite was observed for cluster 3, characterized by a comparatively lower sensitivity to pressure pain. Thus, unsupervised machine-learned analysis followed by knowledge discovery using decision tree analysis pointed at a higher sensitivity to pressure pain in women as compared to men, which was reflected in the projection of the high-dimensional data space onto a toroid SOM.

Figure 5.View larger versionFigure 5. Analysis of the distribution of the subjects' sex across study treatments or clusters. The mosaic plots represent contingency tables of the sexes vs the study treatments (left) or the machine-learned clusters (right). The size of the cells as proportional to the number of subjects included. While sexes did not differ across treatments, the sex distribution across the emergent self-organizing feature map/U*-matrix–derived clusters (Fig. 4) was uneven at a statistical significance level of P < 0.05 (Fisher exact test). The figure has been created using the R software package (version 3.3.3 for Linux; http://CRAN.R-project.org/, Ref. 68). In particular, in U*-matrix–based clusters 3 vs 4 there were significantly more men or women, respectively (P < 0.05).

3.3. Reassessment of key results using analysis of variance

Standard statistical analysis of the data indicated that the treatments exerted significant effects on all QST parameters except for warmth detection threshold, as indicated by the significance pattern of the results of the rm-ANOVA (Table 2). The significance pattern also indicated that the 2 treatments (UV-B or capsaicin) had influenced different QST parameters (Table 2). Moreover, the ANOVA supported a sex difference, particularly in pressure pain, as identified by means of unsupervised machine learning. Indeed, the highest statistical significance level among several significant sex differences in QST parameters (Table 2) was observed for PPT (F = 34.43, P = 9.57·10⁻⁸).

See full tableTable 2. Results of analyses of variance for repeated measures (rm-ANOVA) with post hoc t tests vs baseline of the values acquired after ultraviolet-B (UV-B) or capsaicin treatments, performed for 10 quantitative sensory testing (QST) parameters; dynamic mechanical allodynia and paradoxical heat sensations were omitted owing to the absence of intersubject variation, and vibration detection threshold was omitted as it displayed only values (0 or 1) that did not change after application of the sensitization procedures.

4. Discussion

This study assessed established models of heat hyperalgesia with a variety of noxious stimuli, extending the original heat stimulation by the application of cold and mechanical stimuli. Considering the potential use of human experimental pain models for analgesic drug research, we applied a clinically established QST battery that was originally developed to phenotype neuropathic pain in patients, which was also successfully used in a human experimental context on healthy subjects.18,45,46 To extract meaningful information from the resulting high-dimensional data, we applied machine-learning techniques with the aims of (1) identifying the most relevant effects of UV-B and topical capsaicin on QST parameters and (2) identifying possible subgroups of subjects who share similar QST responses to selected hypersensitization treatments. The results of these analyses indicated that (1) both UV-B– and capsaicin-induced experimental hypersensitization primarily increased subjects' sensitivity to heat; (2) UV-B additionally modulated sensitivity to cold; (3) subgroups of responders to topical application of capsaicin differed with respect to their sensitivity to pressure pain, and this could be attributed to sex differences; and (4) the response to the UV-B hypersensitization treatment was heterogeneous and included a group of nonresponders, which in the high-dimensional space of the QST pattern was indistinguishable from the absence of any hypersensitization treatment.

The present results are compatible with prior pathophysiological knowledge. Specifically, our results emphasize that both experimental pain models involve hypersensitization to heat stimuli as a major physiological mechanism. It has been recognized for decades that capsaicin excites TRPV1 ion channels,⁸⁴ and we have long known that TRPV1 is a heat sensor.¹² Similarly, UV irradiation has been shown to increase mRNAs level of TRPV1 by 2.4-fold in healthy subjects,⁴¹ and more recent studies have shown that TRPV4 is involved in thermal sensation.⁹⁶ For both models, reports indicate the reversal of these hypersensitization effects by TRPV1 antagonists as novel analgesics under drug development.3,11,73,76 However, UV-B radiation has been additionally shown to generate sunburn pain by activating epidermal TRPV4 ion channels, at least in mice,⁵⁷ which supports our observations that the 2 models share many similarities but are not identical in their effects on QST parameters.

In particular for UV-B, an effect on cold sensation was identified as a feature contributing to the correct association of a measurement with the treatment during which it had been acquired. This finding agrees with evidence from animal experiments that have shown an effect of cold stress on cultured keratinocytes from UV-B–injured skin.⁶¹ Cooler temperatures increase sensitivity to UV-B radiation in embryos and larvae of the frog Limnodynastes peronii.⁹² This finding is compatible with reported differences in UV-B– and capsaicin-induced hypersensitization that are claimed to affect the clinical translation of these models from experimental human studies on the effects of analgesics, in particular those targeting neuropathic pain.⁹¹ The involvement of cold sensitization might be an advantage with regard to understanding neuropathic pain, considering that cold sensitization–based models such as topical menthol application have been successfully used to show the effects of drugs established in the treatment of neuropathic pain, such as pregabalin.¹ From a human genetics perspective, a close relation between heat and cold sensitivity has been reported previously. First, the ion channels mentioned so far are temperature sensors,⁶³ but in another study, local capsaicin application was reported to affect cold sensation,⁶⁰ a finding that was interpreted as indicating interactions among TRP channels.¹³ For example, TRPA1 channels are often co-expressed with heat-gated TRPV1 channels49,78, and the transient receptor potential channels may act in concert,²² including heterodimerization or oligomerization of TRPV1 with TRPV3 and TRPA1.²⁹ Thus, the effects on cold pain observed following hypersensitization procedures that apparently address heat pain are biologically plausible.

The results of our study indicate that machine learning both in a supervised and unsupervised manner, and in particular the latter implemented as ESOM/U*-matrix–based clustering, are suitable methods to analyze human experimental pain data. This indication is supported by the compatibility of key results with a classical ANOVA. Moreover, by including techniques of feature selection involving hierarchical components, we designed this analysis to identify the most relevant effects of the hypersensitization procedures on QST parameters, rather than to establish merely statistical significances of differences from baseline or between the 2 treatments. Specifically, the results of supervised learning emphasize that both sensitization procedures primarily modulate sensitivity to heat pain, which corresponds to the major involvement of TRPV1 and TRPV4 ion channels known as heat or thermal sensors.12,96 This finding explains the degree of overlap observed in node 7 in Figure 3. Here, a possible dose effect might shift this overlap depending on the relative doses of capsaicin and UV-B. In this study, capsaicin was standardized among subjects with respect to the dose applied, whereas UV-B was standardized with respect to the erythema effect obtained. Application of the same UV-B irradiation dose to all subjects could shift the hypersensitizing effect toward less overlap if a low dose was selected or toward more overlap if a high dose was selected, which must be taken into account when interpreting Figure 3. However, more pronounced effects of capsaicin on HPT as compared to those of UV-B would indicate the greater importance of TRPV1 than TRPV4 for heat sensation12,96 at the molecular level.

Unsupervised machine learning followed a different approach, first identifying structures in the data of the whole study without reference to the study treatments. By contrast, the treatments emerged during data interpretation, aided by a further decision tree analysis. There, an additional importance of cold pain sensitivity came into play; however, this result is compatible with the findings of unsupervised learning. Indeed, in unsupervised learning the QST parameters cold detection threshold and cold pain threshold emerged in ABC set “B” (Fig. 2A) as important components of the decision tree exploring the clustering results of the ESOM (Fig. 4) and were only neglected because of the predefined focus of that analysis to pay attention to only the most important parameters. Hence, the results of the different implementations of machine learning were compatible with each other.

The main focus of this analysis was data exploration for relevant effects of treatments or demographic parameters modulating the individual perception of pain to make them accessible to expert interpretation of the study results. The analysis was not aimed at creating a general-purpose classifier for capsaicin or UV-B effects because its application would be limited to a particular human experimental setting. Therefore, methods of further sophistication of the classifier methods were not used, given the satisfactory results with respect to data interpretation. Such methods, however, may become important when classifiers of patients subgroups are addressed to provide a clinical diagnostic tool. In such projects, further cluster verification might become necessary. For example, it is known that different cluster algorithms may produce different results.⁴⁰ The present method seems to be comparatively robust in avoiding identification of false cluster structures in data.⁸⁸ A 20-fold repeated 80% resampling experiment delivered an average Rand Index⁶⁹ of 87.3% ± 3% for the coincidence of the subsampled clusters. More complex evaluations were not imperative, such as the addition of multiobjective clustering25,40 or ensemble methods.³¹

The present analysis identified data structures that pointed at subgroups of subjects. One of the structural findings consisted of the identification of 2 separate clusters populated with measurements taken after topical capsaicin application. This distribution of the measurements taken under capsaicin-induced hypersensitization could be explained by a different sex distribution. In the cluster containing more women, higher pressure pain sensitivity was an important criterion of distinction from the other cluster, as indicated by the PPT-dependent node in the decision tree (Fig. 4C). This finding agrees with repeated reports of women's higher sensitivity to pressure pain.19,36,37,42,59 It also agrees with most reports of the generally higher sensitivity to pain in women as compared to men (for reviews, see Refs. 5,6,16,70), which is also reflected in an overrepresentation of women among patients suffering from persistent pain.56,74,94 The second subgroup was indirectly extrapolated from the fraction of measurements acquired following UV-B hypersensitization that nevertheless were dissolved in a cluster together with measurements taken during the baseline condition. This finding points at nonresponders, for which the present data do not provide an explanation. Some obvious candidates are differences in the genes expressing TRPV1 or TRPV4, considering the involvement of these ion channels in the hypersensitization to UV-B discussed above; however, further TRP ion channels might be added.

5. Conclusions

In this study, we used machine-learning techniques for data exploration. Unsupervised machine learning, implemented as an ESOM/U*-matrix,⁸⁹ was able to depict the complete study on a single Kohonen map,³⁸ where the most relevant study results emerged. Combined with supervised machine learning implemented as random forest analysis,⁹ the present analysis produced results that are biologically plausible, agree with previous knowledge, and are compatible with classical ANOVA results. Specifically, the present study indicates that both UV-B and capsaicin induce experimental hyperalgesia mainly toward noxious heat stimuli. In addition, UV-B seems to also modulate experimental hyperalgesia toward cold stimuli. Moreover, experimental hyperalgesia, in particular when induced by topical application of capsaicin, toward noxious blunt pressure stimuli displays a clear sex dependency, with women being more sensitive than men. Hence, while UV-B and capsaicin share a major component of heat pain sensitization, they clearly differ in their effects on the QST parameter patterns in healthy subjects, suggesting nonredundancy between these models, which should be kept in mind when using them concomitantly, rather than alternatively, in experimental human studies such as studies of analgesic drug effects.

Conflict of interest statement

The authors have no conflicts of interest to declare.

This work was funded by the Landesoffensive zur Entwicklung wissenschaftlich—ökonomischer Exzellenz (LOEWE), LOEWE-Zentrum für Translationale Medizin und Pharmakologie (J.L., G.G.). The funders had no role in method design, data selection, and analysis, decision to publish, or preparation of the manuscript.

Acknowledgements

Conceived and designed the experiments: B. G. Oertel and J. Lötsch, G. Geisslinger. Performed the experiments: S. Heinemann and B. G. Oertel. Analyzed the data: J. Lötsch, A. Ultsch, and F. Lerch. Wrote the paper: J. Lötsch.

Footnotes

Sponsorships or competing interests that may be relevant to content are disclosed at the end of this article.

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Table 1.

Components of the quantitative sensory testing battery of the German research network on neuropathic pain.71,72

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Figure 1.

Distribution of the z-values of the quantitative sensory testing (QST) parameters at baseline (blue) and following hypersensitization induced by topical application of ultraviolet-B (violet), or capsaicin (orange-red). The density distribution is presented as probability density function (PDF), estimated by means of the Pareto density estimation (⁸⁶black line). Higher z-scores indicate higher sensitivity to the respective stimuli. The figure was created using the R software package (version 3.3.3 for Linux; http://CRAN.R-project.org/, Ref. 68). CDT, cold detection threshold; CPT, cold pain threshold; HPT, heat pain threshold; MDT, mechanical detection threshold; MPS, mechanical pain sensitivity to pinprick stimuli; MPT, mechanical pain threshold; PPT, pressure pain threshold; TSL, thermal sensory limen; VDT, vibration detection threshold; WDT, warmth detection threshold; WUR, wind-up ratio.

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Figure 2.

Machine-learned analysis to identify quantitative sensory testing (QST) parameters most affected by hypersensitization, implemented as random forest analysis followed by ABC analysis of the contribution of QST parameters to overall association of the measurements to the study treatments (baseline, ultraviolet-B, or capsaicin). (A) Dot chart³³ of the mean decrease in Gini impurity when the respective feature (QST parameter) is excluded from random forest decision tree building. The plot displays 1 typical example out of the analyses of 1000 bootstrap resampled data subsets. (B) Subsequent to random forest-based feature selection, the mean decrease in Gini impurity associated with each QST parameter was submitted to ABC analysis, which is an item selection procedure aiming at identification of the most profitable items from a larger list of items. The ABC plot (blue line) shows the cumulative distribution function of the mean decreases in accuracy, along with the uniform distribution (green line) in which each feature would have the same chance to contribute to the study condition assignment (for further details about computed ABC analysis, see Ref. 87). The red lines indicate the borders between ABC sets “A,” “B,” and “C.” Only set “A,” containing the most profitable item, was selected as the +relevant QST item subset. (C) Count of occurrences of QST parameters in ABC set “A” during the 1000 runs on bootstrap resampled data. The 4 parameters are those that ever appeared in set “A.” Most frequently, the set size was |{A}| = 1 parameter and most often the QST parameter “HPT.” Therefore, this parameter (blue) was selected as a sufficient basis for study treatment assignment during random forest–based feature selection for unsupervised machine-learned analysis. The figure was created using the R software package (version 3.3.3 for Linux; http://CRAN.R-project.org/, Ref. 68). In particular, the ABC analysis was performed and plotted using our “ABCanalysis” software package (http://cran.r-project.org/package=ABCanalysis, Ref. 87). CDT, cold detection threshold; CPT, cold pain threshold; HPT, heat pain threshold; MDT, mechanical detection threshold; MPS, mechanical pain sensitivity to pinprick stimuli; MPT, mechanical pain threshold; PPT, pressure pain threshold; TSL, thermal sensory limen; WDT, warmth detection threshold; WUR, wind-up ratio.

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Figure 3.

Decision tree associating ranges of the quantitative sensory testing (QST) parameter most affected by hypersensitization according to feature selection analysis (Fig. 2) with the 3 study conditions: baseline (1), ultraviolet-B (UV-B) (2), or capsaicin (3). The split criterion was the Gini impurity, and only statistically significant splits, based on permutation tests, were accepted. The tree ended in 6 terminal nodes (4, 5, 7, 8, 10, 11) at which the number of measurements assigned to the respective node is shown as bar plots, with separate bars for each study treatment (blue = baseline, violet = UV-B, red = capsaicin). Higher z-scores indicate higher sensitivity to the respective stimuli. At the upper left corner, an association plot is shown to visualize the residuals of an independence model for the contingency table.¹⁴ Each cell of the contingency table is represented by a rectangle that has a height proportional to the contribution to Pearson χ for the cell and width proportional to the square root of expected counts corresponding to the cell. Hence, the area of each box is proportional to the difference in observed and expected frequencies. The rectangles in each row are positioned relative to a baseline indicating independence, ie, if the observed frequency of a cell is greater than the expected frequency, the box rises above the baseline, but otherwise it falls below it. Each study treatment (lines) is plotted vs the decision tree terminal nodes (columns) as a result of a contingency table analysis, indicating the relative representations of each treatment across the tree nodes. The Pearson residuals are colored according to a perceptually uniform hue-chroma-luminance (HCL) given at the right margin of the association plot.⁵² The figure has been created using the R software package (version 3.3.3 for Linux; http://CRAN.R-project.org/, Ref. 68). Specifically, for drawing the tree and association plots, the “vcd” package (https://cran.r-project.org/package=vcd) was used⁵⁴ including the “strucplot” framework⁵³ and residual-based shadings.⁹⁷ HPT, heat pain threshold.

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Figure 4.

Machine-learned analysis aimed at detecting data structures of quantitative sensory testing (QST) parameter pattern acquired during the different study conditions (treatments). (A) U*-matrix visualization of distance- and density-based structures of the QST parameter pattern observed in 82 subjects under baseline conditions and following application of ultraviolet-B- or capsaicin-induced hypersensitization. The figure was created by projecting the data points onto a toroid grid of 4000 neurons where opposite edges are connected. The dots indicate the “best matching units” (BMUs) of the self-organizing map (SOM), which are those neurons whose weight vector is most similar to the input. A single neuron can be the BMU for more than 1 data point or subject; hence, the number of BMUs may not be equal to the number of acquired measurements. The U*-Matrix was colored as a geographical map with brown (up to snow-covered) heights and green valleys with blue lakes. Valleys indicate clusters and watersheds indicate borderlines between different clusters. The BMUs are colored according to the 4 clusters identified on the basis of this U*-matrix. (B) 3-D view of the same U*-star matrix, indicating cluster separation by “mountain ridges.” (C) Decision tree associating emergent self-organizing feature map (ESOM)/U*-matrix–derived clusters with ranges of QST parameters. Higher z-scores indicate higher sensitivity to the respective stimuli. The split criterion was the Gini impurity, and only statistically significant splits, based on permutation tests, were accepted. The tree ended in 6 terminal nodes (4, 5, 7, 8, 10, 11) at which the number of measurements assigned to the respective node is shown as bar plots, with separate bars for each U*-matrix–based cluster. (D) Association plot visualizing the residuals of an independence model for the treatment vs clusters contingency table.¹⁴ Each cell of the contingency table is represented by a rectangle that has height proportional to the contribution to Pearson χ for the cell and width proportional to the square root of expected counts corresponding to the cell. Hence, the area of each box is proportional to the difference in observed and expected frequencies. The rectangles in each row are positioned relative to a baseline indicating independence, ie, if the observed frequency of a cell is greater than the expected one, the box rises above the baseline, and falls below otherwise. Each study treatment (lines) is plotted vs the U*-matrix–derived clusters (columns) as a result of a contingency table analysis, indicating the relative representations of each cluster in across the tree nodes. The Pearson residuals are colored according to a perceptually uniform hue-chroma-luminance (HCL) given at the right margin of the association plot.⁵² The figure was created using the R software package (version 3.3.3 for Linux; http://CRAN.R-project.org/, Ref. 68). Specifically, for drawing the tree and association plots, the “vcd” software package (https://cran.r-project.org/package=vcd) was used,⁵⁴ including the “strucplot” framework⁵³ and residual-based shadings.⁹⁷ HPT, heat pain threshold; PPT, pressure pain; CPT, cold pain threshold; CDT, cold detection threshold.

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Figure 5.

Analysis of the distribution of the subjects' sex across study treatments or clusters. The mosaic plots represent contingency tables of the sexes vs the study treatments (left) or the machine-learned clusters (right). The size of the cells as proportional to the number of subjects included. While sexes did not differ across treatments, the sex distribution across the emergent self-organizing feature map/U*-matrix–derived clusters (Fig. 4) was uneven at a statistical significance level of P < 0.05 (Fisher exact test). The figure has been created using the R software package (version 3.3.3 for Linux; http://CRAN.R-project.org/, Ref. 68). In particular, in U*-matrix–based clusters 3 vs 4 there were significantly more men or women, respectively (P < 0.05).

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Table 2.

Results of analyses of variance for repeated measures (rm-ANOVA) with post hoc t tests vs baseline of the values acquired after ultraviolet-B (UV-B) or capsaicin treatments, performed for 10 quantitative sensory testing (QST) parameters; dynamic mechanical allodynia and paradoxical heat sensations were omitted owing to the absence of intersubject variation, and vibration detection threshold was omitted as it displayed only values (0 or 1) that did not change after application of the sensitization procedures.

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