Modelling Menstrual Cycle Length in Athletes Using State-space Models

Modelling Menstrual Cycle Length in Athletes Using State-space Models | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Modelling Menstrual Cycle Length in Athletes Using State-space Models Thiago Oliveira, Georgie Bruinvels, Charles Pedlar, John Newell This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-122553/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 20 Aug, 2021 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract The ability to predict menstrual cycle length to a high degree of precision enables female athletes to track their period and tailor their training and nutrition correspondingly knowing when to push harder when to prioritise recovery and how to minimise the impact of menstrual symptoms on performance. Such individualisation is possible if cycle length can be predicted to a high degree of accuracy. To achieve this, a hybrid predictive model was built using data on 16,990 cycles collected from a sample of 2,178women (mean age 33.89 years, range 14.98 - 47.10, number of menstrual cycles ranging from 4 - 53). To capture the within-subject temporal correlation, a mixed-effect state-space model was fitted incorporating a Bayesian approach for process forecasting to predict the duration (in days) of the next menstrual cycle. The modelling procedure was split into three steps(i) a time trend component using a random walk with an overdispersion parameter, (ii) an autocorrelation component using an autoregressive moving-average (ARMA) model, and (iii) a linear predictor to account for covariates (e.g. injury, stomach cramps, training intensity). The inclusion of an overdispersion parameter suggested that 26.81% [24.14%,29.58%] of cycles in the sample were overdispersed where the random walk standard deviation under a non-overdispersed cycle is 1.0530 [1.0060,1.0526] days while under an overdispersed cycle it increased to 4.7386 [4.5379,4.9492] days. To assess the performance and prediction accuracy of the model, each woman’s last observation was used as test data. The Root Mean Square Error (RMSE), Concordance Correlation Coefficient (CCC) and Pearson correlation coefficient (r) between the observed and predicted values were calculated. The model had an RMSE of 1.6126 days, a precision of 0.7501 and overall accuracy of 0.9855. In the absence of hormonal measurements, knowing how aspects of physiology and psychology are changing across the menstrual cycle has the potential to help female athletes personalise their training, nutrition and recovery tailored to their cycle to sustain peak performance at the highest level and gain a competitive edge. In conclusion, the hybrid model presented here is a useful approach for predicting menstrual cycle length which in turn can be used to support female athlete wellness to optimise performance Computational Physics Mathematical Physics menstrual cycle length athletes space models basal body temperature (BBT) Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Full Text Cite Share Download PDF Status: Published Journal Publication published 20 Aug, 2021 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Major revision 11 Jun, 2021 Reviews received at journal 22 Apr, 2021 Reviews received at journal 11 Apr, 2021 Reviewers agreed at journal 05 Apr, 2021 Reviewers agreed at journal 02 Apr, 2021 Reviewers invited by journal 28 Mar, 2021 Editor assigned by journal 09 Mar, 2021 Editor invited by journal 08 Dec, 2020 Submission checks completed at journal 08 Dec, 2020 First submitted to journal 05 Dec, 2020 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About In Review Editorial Policies Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-122553","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":6043604,"identity":"e692a819-e9aa-4dd5-a57e-61ae7871bcc7","order_by":0,"name":"Thiago Oliveira","email":"","orcid":"","institution":"The Insight Centre for Data Analytics, NUI Galway, Ireland","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Thiago","middleName":"","lastName":"Oliveira","suffix":""},{"id":6043605,"identity":"cad8046f-6e78-4d4a-b33a-91368c031620","order_by":1,"name":"Georgie Bruinvels","email":"","orcid":"","institution":"Orreco, Galway, Ireland","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Georgie","middleName":"","lastName":"Bruinvels","suffix":""},{"id":6043606,"identity":"5ea8189d-8a63-4d1f-851b-1a392daa023d","order_by":2,"name":"Charles Pedlar","email":"","orcid":"","institution":"Orreco, Galway, Ireland","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Charles","middleName":"","lastName":"Pedlar","suffix":""},{"id":6043607,"identity":"aeae5267-a953-434d-b304-c99b102f0217","order_by":3,"name":"John Newell","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABCklEQVRIiWNgGAWjYBACxgYeKIudufEBA4MEkAHmShChhZmx2QCskpmAFgYGhJY2iDJmAg5jbu899oBxh01iP1BLdWGbhV1/M4/hZx4GCzmcDus5l27AeCYtcWYzY9vtmW0SyTMO8xhL8zBIGOPUMiPHTIKx7XDuhsNALbxALQyHeTeAtCQ24NfyP3c/UEsxSIv8Yd7Nv4Fa6gloOZC7AegXZqAWO4PDvNtAtiTg9ssZM4nEtuT6GYcZm6V5zkkkGB7m/2Y5x0DCEJcthu09ZhIf2+yM+dubD37mKauzlzvelnzjTUWdPC5bwGYhuwHsayYeA1waGBgwzLIHO/cHbh2jYBSMglEw8gAA27FNkPXJW2QAAAAASUVORK5CYII=","orcid":"","institution":"School of Mathematics, Statistics \u0026 Applied Mathematics, National University of Ireland Galway, Ireland","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"John","middleName":"","lastName":"Newell","suffix":""}],"badges":[],"createdAt":"2020-12-05 14:44:05","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-122553/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-122553/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-021-95960-1","type":"published","date":"2021-08-20T15:02:17+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":4163919,"identity":"0030dca0-f32f-4ccb-8975-df4c73557825","added_by":"auto","created_at":"2020-12-10 16:43:31","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":204021,"visible":true,"origin":"","legend":"Histogram with BMI absolute frequency; and classification based on body mass index (BMI)","description":"","filename":"Figure1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-122553/v1/9a9bb7e4daee1b8c0e4efbc0.jpg"},{"id":4163920,"identity":"a1daeb02-d154-4b3a-a1fb-ef540a2d1253","added_by":"auto","created_at":"2020-12-10 16:43:31","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":272353,"visible":true,"origin":"","legend":"Example of six women profiles showing the probability that the proposed model considers an observation as\noverdispersed, where λ represents the probability of λij being equal 1 for a given observation","description":"","filename":"Figure2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-122553/v1/4531e51c1d7b05fa38f5057c.jpg"},{"id":4163921,"identity":"47f64cee-2eb7-4bdf-9f34-8520b3d4147e","added_by":"auto","created_at":"2020-12-10 16:43:31","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":262330,"visible":true,"origin":"","legend":"(a) Trace plots of Markov chains and (b) Markov chain Monte Carlo (MCMC) draws from the posterior\ndistribution of the parameters β0, θ0, π, σn, σw, and σε, based on a sample of length 3000","description":"","filename":"Figure3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-122553/v1/f53e810e9762da3aef71481e.jpg"},{"id":4163922,"identity":"4b9701e4-c286-4a0c-b515-17688d523ba5","added_by":"auto","created_at":"2020-12-10 16:43:31","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":100467,"visible":true,"origin":"","legend":"(a) Residual autocorrelation plot, and (b) residual versus age","description":"","filename":"Figure4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-122553/v1/dd0c59fbf187fdea130c07d9.jpg"},{"id":4163923,"identity":"97151362-6429-4b18-b970-6f951d2df86e","added_by":"auto","created_at":"2020-12-10 16:43:31","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":167984,"visible":true,"origin":"","legend":"Age versus fitted menstrual cycle length for six women with more than 40 repeated measurements with addition\nof 95% credible interval (dashed line), 80%, 95%, and 99% forecast intervals for the next cycle, and observed menstrual cycle\nlength as points. The estimated concordance correlation coefficient (CCC), and Pearson correlation coefficient (r) between\nfitted and observed values are described for each woman","description":"","filename":"Figure5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-122553/v1/c1eede7d9751ebc6f2c86815.jpg"},{"id":4163924,"identity":"29d280ad-b9d2-434d-a9da-702c9b0a7b66","added_by":"auto","created_at":"2020-12-10 16:43:32","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":220994,"visible":true,"origin":"","legend":"Age versus fitted menstrual cycle length for six women with more than 40 repeated measurements with addition\nof 95% credible interval (dashed line), 80%, 95%, and 99% forecast intervals for the next cycle, and observed menstrual cycle\nlength as points using the model yij = mij +\nγij +cij , where we just drop the term rij out. The estimated concordance\ncorrelation coefficient (CCC), and Pearson correlation coefficient (r) between fitted and observed values are described for each\nwoman","description":"","filename":"Figure6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-122553/v1/f41794a0a2a34489c1a10565.jpg"},{"id":4163925,"identity":"bebcfbd6-bd03-4aa3-96b5-61b08a347851","added_by":"auto","created_at":"2020-12-10 16:43:32","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":281947,"visible":true,"origin":"","legend":"(a) Individual profile of 2178 women over time; (b) ; (c) Individual profile for six women from the data with\naddition of linear trend; (d) Bivariate density plot between weight and height given age; (e) Marginal proportion of symptoms\nreported, where the label \"Yes\" is related with \"the event was reported at least once time\" and \"No\" otherwise","description":"","filename":"Figure7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-122553/v1/4d49be24e5802abfcfbb26df.jpg"},{"id":4163926,"identity":"ae72ac43-7c54-4c76-8ab3-632baf5ae1ba","added_by":"auto","created_at":"2020-12-10 16:43:32","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":64585,"visible":true,"origin":"","legend":"Representation of residuals (Residualij = yij − ˆmij ) over time considering there are probability 1−π of Y be a\nstandard cycle (non overdispersed) or π of Y to be a non-standard one (overdispersed), with\nV ar (Y |standard cycle) \u003c V ar (Y |non-standard cycle)","description":"","filename":"Figure8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-122553/v1/5b8045c5ec1bcf7a782aa062.jpg"},{"id":4163927,"identity":"08ee755f-0dc1-4c80-b34f-d1b70b91a78a","added_by":"auto","created_at":"2020-12-10 16:43:32","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":41778,"visible":true,"origin":"","legend":"Stages 1 and 2 of the model selection procedure\nLMM: linear mixed effect model; rij : overdispersion parameter at observational level; ARMA(p,q): Autoregressive moving average\nmodel of order p and q.","description":"","filename":"Figure9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-122553/v1/728f79daa8846e7cd5e28498.jpg"},{"id":4163928,"identity":"9b317163-849f-4fd3-b08b-60dec1481197","added_by":"auto","created_at":"2020-12-10 16:43:32","extension":"jpg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":84043,"visible":true,"origin":"","legend":"(a) One-step-ahead forecast to access the forecasting accuracy of training data; (b)time series cross validation for\nthe new group (group 2) of women. Training data are represented by blue circles while test data by red ones.","description":"","filename":"Figure10.jpg","url":"https://assets-eu.researchsquare.com/files/rs-122553/v1/aa66b0b6a6f3ce52d4c161e4.jpg"},{"id":13564022,"identity":"6bc20d67-01d1-4664-8cae-ab4c9c2116ee","added_by":"auto","created_at":"2021-09-17 03:19:02","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3398788,"visible":true,"origin":"","legend":"","description":"","filename":"FitRWomanPaper.pdf","url":"https://assets-eu.researchsquare.com/files/rs-122553/v1_covered.pdf"},{"id":4163930,"identity":"0bd80891-9031-4716-99e3-842f645c8972","added_by":"auto","created_at":"2020-12-10 16:43:36","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3884218,"visible":true,"origin":"","legend":"","description":"","filename":"FitRWomanPaper.pdf","url":"https://assets-eu.researchsquare.com/files/rs-122553/v1_stamped.pdf"}],"financialInterests":"","formattedTitle":"\u003cp\u003eModelling Menstrual Cycle Length in Athletes Using State-space Models\u003c/p\u003e","fulltext":[{"header":"Full Text","content":"\u003cp\u003eThis preprint is available for \u003ca href='/article/rs-122553/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"menstrual cycle length, athletes, space models, basal body temperature (BBT)","lastPublishedDoi":"10.21203/rs.3.rs-122553/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-122553/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe ability to predict menstrual cycle length to a high degree of precision enables female athletes to track their period and tailor their training and nutrition correspondingly knowing when to push harder when to prioritise recovery and how to minimise the impact of menstrual symptoms on performance. Such individualisation is possible if cycle length can be predicted to a high degree of accuracy. To achieve this, a hybrid predictive model was built using data on 16,990 cycles collected from a sample of 2,178women (mean age 33.89 years, range 14.98 - 47.10, number of menstrual cycles ranging from 4 - 53). To capture the within-subject temporal correlation, a mixed-effect state-space model was fitted incorporating a Bayesian approach for process forecasting to predict the duration (in days) of the next menstrual cycle. The modelling procedure was split into three steps(i) a time trend component using a random walk with an overdispersion parameter, (ii) an autocorrelation component using an autoregressive moving-average (ARMA) model, and (iii) a linear predictor to account for covariates (e.g. injury, stomach cramps, training intensity). The inclusion of an overdispersion parameter suggested that 26.81% [24.14%,29.58%] of cycles in the sample were overdispersed where the random walk standard deviation under a non-overdispersed cycle is 1.0530 [1.0060,1.0526] days while under an overdispersed cycle it increased to 4.7386 [4.5379,4.9492] days. To assess the performance and prediction accuracy of the model, each woman’s last observation was used as test data. The Root Mean Square Error (RMSE), Concordance Correlation Coefficient (CCC) and Pearson correlation coefficient (r) between the observed and predicted values were calculated. The model had an RMSE of 1.6126 days, a precision of 0.7501 and overall accuracy of 0.9855. In the absence of hormonal measurements, knowing how aspects of physiology and psychology are changing across the menstrual cycle has the potential to help female athletes personalise their training, nutrition and recovery tailored to their cycle to sustain peak performance at the highest level and gain a competitive edge. In conclusion, the hybrid model presented here is a useful approach for predicting menstrual cycle length which in turn can be used to support female athlete wellness to optimise performance\u003c/p\u003e","manuscriptTitle":"Modelling Menstrual Cycle Length in Athletes Using State-space Models","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2020-12-10 16:43:29","doi":"10.21203/rs.3.rs-122553/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major revision","date":"2021-06-11T05:54:46+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2021-04-22T11:28:17+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2021-04-11T17:06:26+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"47246de1-deb4-460d-9f7a-216f79927524","date":"2021-04-05T18:35:52+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"23ac7508-9ed0-49e6-aa5a-a8a14baae9ce","date":"2021-04-02T10:52:02+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2021-03-28T11:43:41+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2021-03-09T22:46:33+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2020-12-08T08:53:51+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2020-12-08T08:19:51+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2020-12-05T14:41:45+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"a2b12458-8255-4ac8-90cd-739156c89d2a","owner":[],"postedDate":"December 10th, 2020","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":1410854,"name":"Computational Physics"},{"id":1410855,"name":"Mathematical Physics"}],"tags":[],"updatedAt":"2021-08-29T15:08:18+00:00","versionOfRecord":{"articleIdentity":"rs-122553","link":"https://doi.org/10.1038/s41598-021-95960-1","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2021-08-20 15:02:17","publishedOnDateReadable":"August 20th, 2021"},"versionCreatedAt":"2020-12-10 16:43:29","video":"","vorDoi":"10.1038/s41598-021-95960-1","vorDoiUrl":"https://doi.org/10.1038/s41598-021-95960-1","workflowStages":[]},"version":"v1","identity":"rs-122553","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-122553","identity":"rs-122553","version":["v1"]},"buildId":"i_I_jhV-QviBjPLXJga9V","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}