{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T17:21:38Z","timestamp":1787505698156,"version":"build-2736575974"},"reference-count":36,"publisher":"Wiley","issue":"18-19","license":[{"start":{"date-parts":[[2026,8,10]],"date-time":"2026-08-10T00:00:00Z","timestamp":1786320000000},"content-version":"vor","delay-in-days":9,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100000265","name":"Medical Research Council","doi-asserted-by":"publisher","award":["MR\/W016648\/1"],"award-info":[{"award-number":["MR\/W016648\/1"]}],"id":[{"id":"10.13039\/501100000265","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000272","name":"National Institute for Health and Care Research","doi-asserted-by":"publisher","award":["NIHR131974"],"award-info":[{"award-number":["NIHR131974"]}],"id":[{"id":"10.13039\/501100000272","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2026,8]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Network meta\u2010analysis (NMA) is widely used in healthcare decision\u2010making, where estimates of the effect of multiple treatments on outcomes are required. For time\u2010to\u2010event outcomes such as survival or disease progression the most common approach is to model log hazard ratios; however, this relies on the proportional hazards assumption. Novel treatments such as immunotherapies are expected to display complex hazard functions that cannot be captured by standard parametric models, which results in non\u2010proportional hazards when comparing treatments from different classes. As a result, alternative models such as fractional polynomials or restricted cubic splines are often used. These allow substantial flexibility on the shape of the baseline hazard, but require time\u2010consuming model selection or are intractable for Bayesian analysis. We propose a flexible NMA model using M\u2010splines on the baseline hazard, with a novel weighted random walk prior distribution that provides shrinkage to avoid overfitting and is invariant to the choice of knots and timescale. Non\u2010proportional hazards are modeled either by stratifying by treatment or by introducing treatment effects on the spline coefficients, and covariates may be included on the log hazard rate and spline coefficients. Treatment and covariate effects on the spline coefficients are given random walk prior distributions to smoothly model departures from proportionality over time. The methods are implemented in the user\u2010friendly R package multinma, which supports analyzes with aggregate data, individual participant data, or mixtures of both. We apply the methods to a NMA of progression\u2010free survival with treatments for non\u2010small cell lung cancer.<\/jats:p>","DOI":"10.1002\/sim.70695","type":"journal-article","created":{"date-parts":[[2026,8,11]],"date-time":"2026-08-11T03:42:27Z","timestamp":1786419747000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Network Meta\u2010Analysis of Survival Outcomes With Non\u2010Proportional Hazards Using Flexible M\u2010Splines"],"prefix":"10.1002","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2672-7841","authenticated-orcid":false,"given":"David M.","family":"Phillippo","sequence":"first","affiliation":[{"name":"Bristol Medical School University of Bristol  Bristol UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-6565-0790","authenticated-orcid":false,"given":"Ayman","family":"Sadek","sequence":"additional","affiliation":[{"name":"Bristol Medical School University of Bristol  Bristol UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7813-3749","authenticated-orcid":false,"given":"Hugo","family":"Pedder","sequence":"additional","affiliation":[{"name":"Bristol Medical School University of Bristol  Bristol UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2198-3205","authenticated-orcid":false,"given":"Nicky J.","family":"Welton","sequence":"additional","affiliation":[{"name":"Bristol Medical School University of Bristol  Bristol UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,8,10]]},"reference":[{"key":"e_1_2_9_2_1","unstructured":"M. J.Rutherford P. C.Lambert M. J.Sweeting et al. \u201cNICE DSU Technical Support Document 21: Flexible Methods for Survival Analysis \u201d 2020 Technical Report National Institute for Health and Care Excellence; London UK."},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jval.2022.07.009"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.1203"},{"key":"e_1_2_9_5_1","unstructured":"S. L.Brilleman E. M.Elci J. B.Novik andR.Wolfe \u201cBayesian Survival Analysis Using the Rstanarm R Package \u201d 2020arXiv https:\/\/doi.org\/10.48550\/ARXIV.2002.09633."},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.2307\/2986270"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2399"},{"key":"e_1_2_9_8_1","unstructured":"S.Dias N. J.Welton A. J.Sutton andA. E.Ades \u201cNICE DSU Technical Support Document 2: A Generalised Linear Modelling Framework for Pair\u2010Wise and Network Meta\u2010Analysis of Randomised Controlled Trials \u201d 2011 Technical Report National Institute for Health and Care Excellence; London UK."},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/(sici)1097\u20100258(19961230)15:24<2733::aid\u2010sim562>3.0.co;2\u20100"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.1875"},{"key":"e_1_2_9_11_1","volume-title":"Statistics in PracticeHoboken","author":"Dias S.","year":"2018"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1002\/jrsm.25"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1002\/jrsm.1405"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1017\/rsm.2025.21"},{"key":"e_1_2_9_15_1","doi-asserted-by":"publisher","DOI":"10.1186\/1471\u20102288\u201011\u201061"},{"key":"e_1_2_9_16_1","doi-asserted-by":"publisher","DOI":"10.1002\/jrsm.1253"},{"key":"e_1_2_9_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jval.2022.11.017"},{"key":"e_1_2_9_18_1","doi-asserted-by":"publisher","DOI":"10.1186\/1471\u20102288\u201012\u20109"},{"key":"e_1_2_9_19_1","doi-asserted-by":"publisher","DOI":"10.1186\/s12874\u2010023\u201002094\u20101"},{"key":"e_1_2_9_20_1","doi-asserted-by":"publisher","DOI":"10.1093\/jrsssa\/qnaf169"},{"key":"e_1_2_9_21_1","unstructured":"D. M.Phillippo \u201cmultinma: Network Meta\u2010Analysis of Individual and Aggregate Data in Stan. R Package \u201d 2024 R Package https:\/\/doi.org\/10.5281\/zenodo.3904454."},{"key":"e_1_2_9_22_1","doi-asserted-by":"publisher","DOI":"10.3310\/GJNW3422"},{"key":"e_1_2_9_23_1","unstructured":"S.Dias N. J.Welton A. J.Sutton D. M.Caldwell G.Lu andA. E.Ades \u201cNICE DSU Technical Support Document 4: Inconsistency in Networks of Evidence Based on Randomised Controlled Trials \u201d 2011 Technical Report National Institute for Health and Care Excellence; London UK."},{"key":"e_1_2_9_24_1","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1177012761"},{"key":"e_1_2_9_25_1","doi-asserted-by":"publisher","DOI":"10.6339\/21\u2010jds1020"},{"key":"e_1_2_9_26_1","unstructured":"Z.LiandJ.Cao \u201cGeneral P\u2010Splines for Non\u2010Uniform B\u2010Splines \u201d 2022arXiv https:\/\/doi.org\/10.48550\/ARXIV.2201.06808."},{"key":"e_1_2_9_27_1","volume-title":"R: A Language and Environment for Statistical Computing","author":"R Core Team","year":"2024"},{"key":"e_1_2_9_28_1","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v076.i01"},{"key":"e_1_2_9_29_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11222\u2010016\u20109696\u20104"},{"key":"e_1_2_9_30_1","unstructured":"D. M.Phillippo A. E.Ades S.Dias S.Palmer K. R.Abrams andN. 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