{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T16:26:12Z","timestamp":1778257572021,"version":"3.51.4"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,7,25]],"date-time":"2022-07-25T00:00:00Z","timestamp":1658707200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,7,25]],"date-time":"2022-07-25T00:00:00Z","timestamp":1658707200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Med Inform Decis Mak"],"published-print":{"date-parts":[[2022,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Background<\/jats:title>\n                    <jats:p>Heart failure is a clinical syndrome characterised by a reduced ability of the heart to pump blood. Patients with heart failure have a high mortality rate, and physicians need reliable prognostic predictions to make informed decisions about the appropriate application of devices, transplantation, medications, and palliative care. In this study, we demonstrate that combining symbolic regression with the Cox proportional hazards model improves the ability to predict death due to heart failure compared to using the Cox proportional hazards model alone.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>We used a newly invented symbolic regression method called the QLattice to analyse a data set of medical records for 299 Pakistani patients diagnosed with heart failure. The QLattice identified non-linear mathematical transformations of the available covariates, which we then used in a Cox model to predict survival.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>An exponential function of age, the inverse of ejection fraction, and the inverse of serum creatinine were identified as the best risk factors for predicting heart failure deaths. A Cox model fitted on these transformed covariates had improved predictive performance compared with a Cox model on the same covariates without mathematical transformations.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusion<\/jats:title>\n                    <jats:p>Symbolic regression is a way to find transformations of covariates from patients\u2019 medical records which can improve the performance of survival regression models. At the same time, these simple functions are intuitive and easy to apply in clinical settings. The direct interpretability of the simple forms may help researchers gain new insights into the actual causal pathways leading to deaths.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1186\/s12911-022-01943-1","type":"journal-article","created":{"date-parts":[[2022,7,25]],"date-time":"2022-07-25T09:03:27Z","timestamp":1658739807000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Combining symbolic regression with the Cox proportional hazards model improves prediction of heart failure deaths"],"prefix":"10.1186","volume":"22","author":[{"given":"Casper","family":"Wilstrup","sequence":"first","affiliation":[]},{"given":"Chris","family":"Cave","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,7,25]]},"reference":[{"key":"1943_CR1","doi-asserted-by":"publisher","DOI":"10.1586\/erc.09.187","author":"LB Tan","year":"2010","unstructured":"Tan LB, Williams SG, Tan DKH, Cohen-Solal A. So many definitions of heart failure: are they all universally valid? A critical appraisal. Expert Rev Cardiovasc Ther. 2010. https:\/\/doi.org\/10.1586\/erc.09.187.","journal-title":"Expert Rev Cardiovasc Ther"},{"key":"1943_CR2","doi-asserted-by":"publisher","DOI":"10.1161\/CIR.0000000000000757","author":"SS Virani","year":"2020","unstructured":"Virani SS, Alonso A, Benjamin EJ, Bittencourt MS, Callaway CW, Carson AP, Chamberlain AM, Chang AR, Cheng S, Delling FN, Djousse L, Elkind MSV, Ferguson JF, Fornage M, Khan SS, Kissela BM, Knutson KL, Kwan TW, Lackland DT, Lewis TT, Lichtman JH, Longenecker CT, Loop MS, Lutsey PL, Martin SS, Matsushita K, Moran AE, Mussolino ME, Perak AM, Rosamond WD, Roth GA, Sampson UKA, Satou GM, Schroeder EB, Shah SH, Shay CM, Spartano NL, Stokes A, Tirschwell DL, VanWagner LB, Tsao CW, Wong SS, Heard DG. Heart disease and stroke statistics-2020 update: a report from the american heart association. Circulation. 2020. https:\/\/doi.org\/10.1161\/CIR.0000000000000757.","journal-title":"Circulation"},{"key":"1943_CR3","doi-asserted-by":"publisher","first-page":"7","DOI":"10.15420\/cfr.2016:25:2","volume":"3","author":"G Savarese","year":"2017","unstructured":"Savarese G, Lund LH. Global public health burden of heart failure. Card Fail Rev. 2017;3:7\u201311. https:\/\/doi.org\/10.15420\/cfr.2016:25:2.","journal-title":"Card Fail Rev"},{"key":"1943_CR4","doi-asserted-by":"publisher","DOI":"10.1001\/jama.293.5.572","author":"GC Fonarow","year":"2005","unstructured":"Fonarow GC, Adams KF, Abraham WT, Yancy CW, Boscardin WJ. Risk stratification for in-hospital mortality in acutely decompensated heart failure: classification and regression tree analysis. 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PLoS One. 2017. https:\/\/doi.org\/10.1371\/journal.pone.0181001.","journal-title":"PLoS One"},{"key":"1943_CR7","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0210602","author":"FM Zahid","year":"2019","unstructured":"Zahid FM, Ramzan S, Faisal S, Hussain I. Gender based survival prediction models for heart failure patients: a case study in pakistan. PLoS One. 2019. https:\/\/doi.org\/10.1371\/journal.pone.0210602.","journal-title":"PLoS One"},{"key":"1943_CR8","doi-asserted-by":"publisher","DOI":"10.1186\/s12911-020-1023-5","author":"D Chicco","year":"2020","unstructured":"Chicco D, Jurman G. Machine learning can predict survival of patients with heart failure from serum creatinine and ejection fraction alone. BMC Med Inform Decis Mak. 2020. https:\/\/doi.org\/10.1186\/s12911-020-1023-5.","journal-title":"BMC Med Inform Decis Mak"},{"key":"1943_CR9","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1972.tb00899.x","author":"DR Cox","year":"1972","unstructured":"Cox DR. Regression models and life-tables. J R Stat Soc Ser B. 1972. https:\/\/doi.org\/10.1111\/j.2517-6161.1972.tb00899.x.","journal-title":"J R Stat Soc Ser B"},{"issue":"19","key":"1943_CR10","doi-asserted-by":"publisher","first-page":"1404","DOI":"10.1093\/eurheartj\/ehs337","volume":"34","author":"SJ Pocock","year":"2012","unstructured":"Pocock SJ, Ariti CA, McMurray JJV, Maggioni A, K\u00f8ber L, Squire IB, Swedberg K, Dobson J, Poppe KK, Whalley GA, Doughty RN. On behalf of the meta-analysis global group in chronic heart failure (MAGGIC): predicting survival in heart failure: a risk score based on 39 372 patients from 30 studies. 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Zenodo"}],"container-title":["BMC Medical Informatics and Decision Making"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s12911-022-01943-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s12911-022-01943-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s12911-022-01943-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,25]],"date-time":"2022-07-25T09:04:18Z","timestamp":1658739858000},"score":1,"resource":{"primary":{"URL":"https:\/\/bmcmedinformdecismak.biomedcentral.com\/articles\/10.1186\/s12911-022-01943-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,25]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,12]]}},"alternative-id":["1943"],"URL":"https:\/\/doi.org\/10.1186\/s12911-022-01943-1","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2021.01.15.21249874","asserted-by":"object"}]},"ISSN":["1472-6947"],"issn-type":[{"value":"1472-6947","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,25]]},"assertion":[{"value":"18 January 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 July 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 July 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The original study containing the data used in this study was approved by the Institutional Review Board of Government College University (Faisalabad, Pakistan). It states that the Helsinki Declaration were followed [\n                      \n                      ]. The original study containing the data used in this study states that \u201cInformed consent was taken by the patients from whom the information on required characteristics were collected\/accessed.\u201d [\n                      \n                      ]","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"Not applicable","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"CW and CC are employees of Abzu, which is the company developing the QLattice technology. CW is also co-founder of the company and the inventor of the patent-pending QLattice technology.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"196"}}