TITLE



TITLEConstipation predominant irritable bowel syndrome and functional constipation are not discrete disorders: a machine learning approachSHORT TITLEChronic constipation: a viscerosensory spectrumAuthors & AFFILIATIONSJames K. Ruffle MBBS BSc (1,2,5), Linda Tinkler MSc (3), Christopher Emmett MD FRCS (3), Alexander C. Ford MBChB FRCP (4), Parashkev Nachev FRCP PhD (5), Qasim Aziz FRCP PhD (1), Adam D. Farmer FRCP PhD (1,6)* & Yan Yiannakou MBChB MRCP MD (3)*.Centre for Neuroscience, Surgery and Trauma, Blizard Institute, Wingate Institute of Neurogastroenterology, Barts and the London School of Medicine & Dentistry, Queen Mary University of London, 26 Ashfield Street, London, E1 2AJ, UKDepartment of Radiology, University College London Hospital NHS Foundation Trust, London NW1 2BU, UK.Durham Bowel Dysfunction Service, University Hospital North Durham, County Durham and Darlington NHS Trust,?DH1 5TW, UKLeeds Institute of Medical Research at St. James’s, University of Leeds, Leeds, LS2 9JT, UK. Institute of Neurology, UCL, London WC1N 3BG, UKDepartment of Gastroenterology, University Hospitals Midlands NHS Trust, Stoke on Trent, Staffordshire, ST4 6QG, UK*Adam D. Farmer & Yan Yiannakou are joint senior authors.Article TypeSupplementary Material to Original ArticleWord Count1750Figures, Tables, Page COUNT4 Supplementary FiguresSUPPLEMENTARY METHODSStatistical analysisStatistical analysis was performed using MATLAB (R2018b, MathWorks, Massachusetts, USA), SPSS (version 25, IBM, New York, USA) and Prism (version 8, GraphPad, La Jolla, CA, USA). Additional post-hoc analyses and visualization of relationships with data were undertaken within Python (v3.6) (packages: NumPy, SciPy, Pandas, Matplotlib, Seaborn), and Graph-Tool ADDIN EN.CITE <EndNote><Cite><Author>Peixoto</Author><Year>2018</Year><RecNum>2264</RecNum><DisplayText>(1)</DisplayText><record><rec-number>2264</rec-number><foreign-keys><key app="EN" db-id="w0p0a29x7zepxpedez6vtpvi2xpxfsrw0zdr" timestamp="1570879639" guid="65aaece4-5bbd-4dd8-9086-ca8285cbc9fa">2264</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Peixoto, Tiago P.</author></authors></contributors><titles><title>Nonparametric weighted stochastic block models</title><secondary-title>Physical Review E</secondary-title></titles><periodical><full-title>Physical Review E</full-title></periodical><pages>012306</pages><volume>97</volume><number>1</number><dates><year>2018</year><pub-dates><date>01/16/</date></pub-dates></dates><publisher>American Physical Society</publisher><urls><related-urls><url>;(1).Comparison of the groups of continuous variables (e.g. age) were undertaken by two-tailed unpaired t-tests. Comparison of the groups with nominal scale data (e.g. gender) were statistically compared with Fisher’s exact test or Chi-squared where appropriate. Comparison of the groups with ordinal scale data (e.g. Likert scales of symptom reporting) was undertaken with Mann-Whitney U. Principal component analysisGiven the large amount of data collected from each patient, it was likely that there would be a number of redundant features. To exclude any such redundancy, we used principal component analysis (PCA) to generate unique features, which would combine redundant overlapping data. This approach minimizes multi-collinearity, balances feature domains, and is computationally resourceful in reducing the number of features fed to a machine model. All aforementioned demographics, questionnaire, examination, and investigatory parameters were submitted to this analysis to generate these unique disease features. All variables collected and input to PCA are provided in the file ‘Supplementary Data - Input Vectors’. Firstly, descriptive statistics of all measures and a correlation matrix for all variables was generated by Pearson correlation coefficient, with critical value threshold of p < 0.05. A visual heatmap of this data matrix and variable-variable inter-relationship provided as Supplementary Figure 3. Following this, the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy was performed, a statistical test that indicates the proportion of variance in variables that might be caused by underlying factors. Higher values (tending to 1.0) indicate that factor analysis is appropriate, and an absolute minimum value of 0.5 is typically taken as a cut-off for statistical suitability ADDIN EN.CITE <EndNote><Cite><Author>Kaiser</Author><Year>1974</Year><RecNum>2262</RecNum><DisplayText>(2)</DisplayText><record><rec-number>2262</rec-number><foreign-keys><key app="EN" db-id="w0p0a29x7zepxpedez6vtpvi2xpxfsrw0zdr" timestamp="1570879639" guid="40afa6a8-8172-4fd0-8709-61f0d9633506">2262</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Kaiser, Henry F.</author></authors></contributors><titles><title>An index of factorial simplicity</title><secondary-title>Psychometrika</secondary-title></titles><periodical><full-title>Psychometrika</full-title></periodical><pages>31-36</pages><volume>39</volume><number>1</number><dates><year>1974</year><pub-dates><date>March 01</date></pub-dates></dates><isbn>1860-0980</isbn><label>Kaiser1974</label><work-type>journal article</work-type><urls><related-urls><url>;(2). Subsequently, the Bartlett’s test of sphericity was performed, which tests the hypothesis that the correlation matrix is an identity matrix, which if non-correlative would suggest variables are unrelated and therefore unsuitable for factor-driven structure detection. Greater statistical significance indicates a factor analysis is suitable for the data matrix.PCA is a mathematical process which applies orthogonal transformation to a given number of correlated variables into a smaller number of uncorrelated variables, referred to as ‘principal components’ (PCs). The orthogonal transformation determines multiple orthogonal lines of best fit to the data matrix, and the greatest variance of the matrix lies on the first axis (the first PC). Sequential components account for as much of the remaining variance as possible under the constraint that it is orthogonal to the preceding components. The magnitude of variation in the total sample accounted for by each factor is expressed as an eigenvalue, and the correlation between the component and the original variable is referred to as ‘component loading’. After generation of PCs, rotation of factor axes is applied to determine a more interpretable pattern of data variance and relatability. Specifically, we used direct oblimin (oblique) rotation, as this technique relaxes the orthogonality constraint and allows components to be correlated. The rationale for this was because we suspected that certain components would be inter-related (for instance, a pain component might relate to one related to quality of life), an inter-relationship we would later probe as a function of an undirected graph. Given the number of input vectors and factors demonstrable on initial scree plot, we thresholded PCs to an eigenvalue of > 1 (Kaiser criterion), cross-checking by reviewing contributory variance in the process, and exported all components fulfilling these criteria. The individual variables of the PCs were all manually reviewed in post-hoc analysis to ascertain the nature of the component (e.g. a selection of univariate variables forming a pain component, compared with a stool transit one). Non-extracted components were also examined at this stage to ensure key aspects of constipation pathophysiology were not erroneously excluded by these criteria, which might otherwise not capture minutiae that engender differences between IBS-C and FC.Supervised machine learning to classify IBS-C or FCModels trained for supervised learning to classify IBS-C of FC were as follows: Linear Discriminant; Quadratic Discriminant; Logistic Regression; Gaussian Na?ve Bayes; Kernel Na?ve Bayes; Linear Support Vector Machine; Quadratic Support Vector Machine; Cubic Support Vector Machine; Fine Gaussian Support Vector Machine; Medium Gaussian Support Vector Machine; Coarse Gaussian Support Vector Machine; Fine K-Nearest Neighbors; Medium K-Nearest Neighbors; Coarse K-Nearest Neighbors; Cosine K-Nearest Neighbors; Cubic K-Nearest Neighbors; Weighted K-Nearest Neighbor; Ensemble of Bagged Trees; Ensemble of Subspace K-Nearest Neighbors; Ensemble of Random Under-Sampling Boosted Trees; Neural Network [Scaled conjugate gradient backpropagation]. Models were all trained on a single machine with processor-parallelized four core central processing unit (CPU).To avoid a model-specific phenomenon, we trained an array of different machine learning models, ranging from logistic regression, na?ve Bayes, support vector machines, and neural networks. All modelling encompassed 5-fold cross-validation. Models were all appropriately partitioned into training (70%), validation (15%), and testing (15%) subsets, by random data division. Model performance was only ever evaluated with testing data, a subsample of locked data to which the model was wholly na?ve. Input feature vectors were the aforementioned principal components (PCs), and the predictive target, or ‘ground truth’, was the Rome III diagnosis of IBS-C or FC. All data were standardized for model optimization. There was no large class imbalance, with a 45:55 sample ratio belonging to a diagnosis of either FC or IBS-C, respectively. We statistically compared the receiver operator characteristic (ROC) curves of each model group using the Hanley and McNeil method ADDIN EN.CITE <EndNote><Cite><Author>Hanley</Author><Year>1982</Year><RecNum>2263</RecNum><DisplayText>(26)</DisplayText><record><rec-number>2263</rec-number><foreign-keys><key app="EN" db-id="w0p0a29x7zepxpedez6vtpvi2xpxfsrw0zdr" timestamp="1570879639" guid="6b665a56-970e-4966-ba60-84ee8aaabd67">2263</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Hanley, J. A.</author><author>McNeil, B. J.</author></authors></contributors><titles><title>The meaning and use of the area under a receiver operating characteristic (ROC) curve</title><secondary-title>Radiology</secondary-title></titles><periodical><full-title>Radiology</full-title></periodical><pages>29-36</pages><volume>143</volume><number>1</number><edition>1982/04/01</edition><keywords><keyword>Evaluation Studies as Topic</keyword><keyword>Humans</keyword><keyword>Mathematics</keyword><keyword>*Models, Theoretical</keyword><keyword>Statistics as Topic</keyword><keyword>*Technology, Radiologic</keyword></keywords><dates><year>1982</year><pub-dates><date>Apr</date></pub-dates></dates><isbn>0033-8419 (Print)&#xD;0033-8419 (Linking)</isbn><accession-num>7063747</accession-num><urls><related-urls><url>;(26). Our primary modelling analysis was to train machine learning models based upon retrieved PCs. We considered that model results would be biased by the inclusion or exclusion of particular components. A priori, we hypothesized the greatest differences between IBS-C and FC patients would be abdominal pain. We also considered that additional viscerosensory measures, such as bloating or nausea, may in some way segregate the two. Therefore, to investigate this we trained the following models: i) a unisymptomatic model with the only feature being an abdominal pain component showing greatest statistical difference between IBS-C and FC (should PCA retrieve one); ii) a model using viscerosensory measures other than pain (should PCA retrieve one); iii) a syndromic model using all PCs occupying 95% of the total variance and iv) a syndromic model of all PCs, but excluding the abdominal pain component.Unsupervised machine learning to identify clustering patterns in chronic constipation patientsTo identify natural clustering of chronic constipation patients, we undertook two-step cluster analysis. Feature vectors were extracted PCs, all of which were standardized. Clustering distance measures were ascertained with log-likelihood, using the Schwarz’s Bayesian Information Criterion (BIC). We maintained a fully unsupervised approach to this analysis and specified no minimum or maximum number of clusters that could be identified. Rather, the most plausible number of clusters (including none) would be determined by Silhouette analysis. Independent of this unsupervised clustering technique using principal components, we used Uniform Manifold Approximation and Projection (UMAP) as a further dimension reduction technique for non-linear dimension reduction to validate findings ADDIN EN.CITE <EndNote><Cite><Author>McInees</Author><Year>2018</Year><RecNum>2294</RecNum><DisplayText>(26)</DisplayText><record><rec-number>2294</rec-number><foreign-keys><key app="EN" db-id="w0p0a29x7zepxpedez6vtpvi2xpxfsrw0zdr" timestamp="1570879639" guid="77f09d46-ff66-49d7-8671-635c981332ef">2294</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>McInees, L</author><author>Healy, J</author></authors></contributors><titles><title>UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction</title><secondary-title>ArXiv e-prints</secondary-title></titles><periodical><full-title>ArXiv e-prints</full-title></periodical><volume>1802.03426</volume><dates><year>2018</year></dates><urls></urls></record></Cite></EndNote>(26). This approach has been used increasingly in the machine learning field, and its mathematical approach is described in full elsewhere ADDIN EN.CITE <EndNote><Cite><Author>McInees</Author><Year>2018</Year><RecNum>2294</RecNum><DisplayText>(26)</DisplayText><record><rec-number>2294</rec-number><foreign-keys><key app="EN" db-id="w0p0a29x7zepxpedez6vtpvi2xpxfsrw0zdr" timestamp="1570879639" guid="77f09d46-ff66-49d7-8671-635c981332ef">2294</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>McInees, L</author><author>Healy, J</author></authors></contributors><titles><title>UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction</title><secondary-title>ArXiv e-prints</secondary-title></titles><periodical><full-title>ArXiv e-prints</full-title></periodical><volume>1802.03426</volume><dates><year>2018</year></dates><urls></urls></record></Cite></EndNote>(26). Inputs to UMAP were all raw data, z-scored before embeddings were calculated for standardization. Results of two-step cluster analysis were cross-compared with the findings of UMAP, and additionally aligned to the diagnostic label of IBS-C or FC. In post-processing, we further compared and visualized clustering outputs with a nonparametric Bayesian formulation of weighted stochastic block modelling ADDIN EN.CITE <EndNote><Cite><Author>Peixoto</Author><Year>2018</Year><RecNum>2264</RecNum><DisplayText>(27)</DisplayText><record><rec-number>2264</rec-number><foreign-keys><key app="EN" db-id="w0p0a29x7zepxpedez6vtpvi2xpxfsrw0zdr" timestamp="1570879639" guid="65aaece4-5bbd-4dd8-9086-ca8285cbc9fa">2264</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Peixoto, Tiago P.</author></authors></contributors><titles><title>Nonparametric weighted stochastic block models</title><secondary-title>Physical Review E</secondary-title></titles><periodical><full-title>Physical Review E</full-title></periodical><pages>012306</pages><volume>97</volume><number>1</number><dates><year>2018</year><pub-dates><date>01/16/</date></pub-dates></dates><publisher>American Physical Society</publisher><urls><related-urls><url>;(27). This approach allows for in depth understanding and visualization of how aspects of patient data cluster and interrelate as a function of a network. To evaluate the validity of clusters as syndromic segregations, we trained models with sequential feature additions and compared the performance, using the Hanley and McNeil method ADDIN EN.CITE <EndNote><Cite><Author>Hanley</Author><Year>1982</Year><RecNum>2263</RecNum><DisplayText>(28)</DisplayText><record><rec-number>2263</rec-number><foreign-keys><key app="EN" db-id="w0p0a29x7zepxpedez6vtpvi2xpxfsrw0zdr" timestamp="1570879639" guid="6b665a56-970e-4966-ba60-84ee8aaabd67">2263</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Hanley, J. A.</author><author>McNeil, B. J.</author></authors></contributors><titles><title>The meaning and use of the area under a receiver operating characteristic (ROC) curve</title><secondary-title>Radiology</secondary-title></titles><periodical><full-title>Radiology</full-title></periodical><pages>29-36</pages><volume>143</volume><number>1</number><edition>1982/04/01</edition><keywords><keyword>Evaluation Studies as Topic</keyword><keyword>Humans</keyword><keyword>Mathematics</keyword><keyword>*Models, Theoretical</keyword><keyword>Statistics as Topic</keyword><keyword>*Technology, Radiologic</keyword></keywords><dates><year>1982</year><pub-dates><date>Apr</date></pub-dates></dates><isbn>0033-8419 (Print)&#xD;0033-8419 (Linking)</isbn><accession-num>7063747</accession-num><urls><related-urls><url>;(28). Feature addition was in descending order of its feature importance, as predetermined by the unsupervised clustering analysis.SUPPLEMENTARY RESULTS A study flow chart is available as supplementary figure 1.Supplementary Figure 1: Study flow chart. *total clinic attendances for the period were 770, but two patients dissented from inclusion in the study. **list of secondary causes that were excluded are documented in the methods. Transit study resultsStool transit study were established for the cohort. We found no significant difference between groups for both total transit count and values partitioned by aspect of the colon. We provide visualization of this data below as Supplementary Figure 2.Supplementary Figure 2: Stool transit does not differ between IBS-C and FC. Strip-plot of all aspects of the stool-transit study, including the total count (total), and where partitioned into aspects of the colon (left colon, right colon, rectosigmoid), color-coded by diagnosis of IBS-C and FC. The two groups do not significantly differ by stool transit.Supplementary Figure 3: Principal component analysis correlation matrix. y-axis labels depict individual measure quantified in, whilst x-axis labels depict the feature domain of the measure (e.g. age and gender on the y-axis belonging to the demographical community on the x-axis. Feature domains are boxed out accordingly for ease of view. Color represents strength of positive or negative correlation (Pearson r), as per the color key. A more white/bright yellow square represents a stronger positive correlation (tending to r = 1), and more black/dark red represents a stronger negative correlation (tending to r = -1).Pain is only discriminative for IBS-C over FC if it directly features in diagnostic criteriaFirstly, we reviewed its frequency distribution, which showed that two clear peaks do exist (FC and IBS-C) (Supplementary Figure 4A), but there is a ‘trough’ between these two frequency distribution peaks (broadly IBS-C and FC), which still contains a large number of individuals who do not fit the label. We subsequently investigated the specific components of our dataset which belonged to this abdominal pain component: i) abdominal pain within the last 6 months; ii) abdominal pain on defecation; iii) abdominal pain related to the appearance of stool; and iv) abdominal pain related to stool frequency. Firstly, we investigated the proportions of patients with IBS-C and FC whom experienced these: i) 98% of IBS-C patients experienced abdominal pain within the last 6 months, but so too did 78% of FC patients; ii) 77% of IBS-C patients experienced pain on defecation, but so too did 34% of FC patients [despite the presence of this pain measure being inherently related to the diagnostic criteria for IBS-C] iii) 95% of IBS-C patients experienced pain related to the appearance of stool, whilst only 3% of FC patients did; iv) 82% of IBS-C patients experienced pain related to stool frequency, whilst only 7% of FC patients did. Crucially, these latter two variables [iii) and iv)], pain related to appearance of stool / stool frequency, are direct diagnostic criteria for IBS-C in both Rome III and IV (see Box 1 & 2), so a clear segregation here was expected. However, we identified clear overlap between the former two variables [i) and ii)], abdominal pain within the last 6 months and pain on defecation, which do not directly feature as discriminators in diagnostic criteria for IBS-C, which are therefore non-biased in comparing the two diagnoses, making them ideal pain features for further analysis. Indeed, we illustrated that, by using the metrics of abdominal pain related to appearance and frequency of stool, machine learning could accurately predict the diagnosis of IBS-C or FC with 96% accuracy. Again, this is expected as these are diagnostic criteria, deliberate circular logic (Supplementary Figure 4C). However, we subsequently subsampled our IBS-C and FC cohorts and extracted individuals who did experience abdominal pain of any kind to investigate pain measures that are not directly listed to diagnose these disorders (pain severity, abdominal pain within the last 6 months, abdominal pain during defecation) and statistically compared IBS-C and FC subgroups. We found that pain severity did not significantly differ between either IBS-C or FC patients, both in cohorts whom reported pain on defecation, and in those who reported pain within the last 6 months (Supplementary Figure 4D). We investigated further with supervised learning and ascertained that, by using these pain measures of PC6 which do not directly factor into the diagnostic criteria for IBS, the model becomes unable to accurately diagnose patient groups, with the best performing model accuracy at 53% (Supplementary Figure 4D). Therefore, in our sample, statistically significant differences between IBS-C and FC patients relating to pain were only those which form part of the diagnostic criteria: a circular, self-fulfilling, logic.Supplementary Figure 4: Self-fulfilling differences: IBS-C and FC differ only by pain measures which feature in diagnostic criteria. A) Kernel density plot of PC6: abdominal pain values throughout our whole cohort, identifying that two peaks do exist of groups of individuals (FC and IBS-C), but that a large number also lie between. Red lines indicate individual patients, which illustrate a continuous spectrum of increasing pain frequency and severity. B) Proportions of FC and IBS-C patients reporting i) abdominal pain within the last 6 months; ii) abdominal pain on defecation; iii) abdominal pain related to the appearance of stool; and iv) abdominal pain related to stool frequency – the four domains which formed PC6: Abdominal Pain. C) We extracted the pain measures which directly feature into IBS-C diagnostic criteria, abdominal pain relating to frequency and appearance of stool, and confirmed that these two measures, with machine learning, could accurately diagnose IBS-C / FC with high accuracy, deliberate circular logic by definition of how these disorders are separated. D) However, in extracting pain measures which do not directly factor into IBS-C diagnostic criteria, we show no significant differences in pain severity between FC and IBS-C patients who report pain on defecation, or pain within the last 6 months. Moreover, using these pain measures, machine learning is unable to accurately distinguish the two disorders better than chance accuracy. ADDIN EN.REFLIST References1.Peixoto TP. Nonparametric weighted stochastic block models. Physical Review E 2018;97:012306.2.Kaiser HF. An index of factorial simplicity. Psychometrika 1974;39:31-36. ................
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