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Statist Med 2:273–277\nCai T, Wei LJ, Wilcox M (2000) Semiparametric regression analysis for clustered failure time data. Biometrika 87:867–878\nChen K, Jin Z, Ying Z (2002) Semiparametric analysis of transformation models with censored data. Biometrika 89:659–668\nCheng SC, Wei LJ, Ying Z (1995) Analysis of transformation models with censored data. Biometrika 82:835–845\nCheng SC, Wei LJ, Ying Z (1997) Prediction of survival probabilities with semi-parametric transformation models. J Am Statist Assoc 92:227–235\nCox DR (1972) Regression models and life tables (with discussion). J Roy Statist Soc Ser B 34:187–220\nDabrowska DM (1997) Smoothed Cox regression. Ann Statist 25:1510–1540\nDabrowska DM (2005) Quantile regression in transformation models. arXiv:math.ST 05115082v1:1–34\nDabrowska DM (2006) Estimation in a class of semiparametric transformation models. arXiv:math.ST 0511506v2:1–48\nDabrowska DM, Doksum KA (1988) Partial likelihood in transformation models with censored data. Scand J Statist 15:1–24\nFine J, Ying Z, Wei LJ (1998) On the linear transformation model with censored data. Biometrika 85:980–986\nGill RD, Johansen S (1990) A survey of product-integration with a view towards application in survival analysis. Ann Statist 18:1501–1555\nJensen GV, Torp-Pedersen C, Hildebrandt P, Kober L, Nielsen FE, Melchior T, Joen T, Andersen PK (1997) Does in-hospital ventricular fibrillation affect prognosis after myocardial infarction?. Eur Heart J 18:919–924\nKosorok MR, Lee BL, Fine JP (2004) Robust inference for univariate proportional hazards frailty regression models. Ann Statist 32:1448–1491\nLin DY, Wei LJ, Ying Z (1993) Checking the Cox model with cumulative sums of martingale-based residuals. Biometrika 80:557–572\nMurphy S, Rossini A, Van Der Vaart A (1997) Maximum likelihood estimation in the proportional odds model. J Am Statist Assoc 92:968–976\nScheike TH, Zhang MJ (2002) An additive-multiplicative Cox–Aalen model. 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Biometrics 53: 1475–1484",{"doi":638},"10.2307\u002F2533513",{"id":18,"text":640,"url":18,"identifiers":641},"Andersen PK, Klein JP, Zhang MJ (1999) Testing for center effects in multi-centre survival studies: a Monto Carlo comparison of fixed and random effects tests. Stat Med 18: 1489–1500",{"doi":642},"10.1002\u002F(SICI)1097-0258(19990630)18:12\u003C1489::AID-SIM140>3.0.CO;2-#",{"id":18,"text":644,"url":18,"identifiers":645},"Breslow NE, Clayton DG (1993) Approximate inference in generalized linear mixed models. J Am Stat Assoc 88: 9–25",{},{"id":18,"text":647,"url":18,"identifiers":648},"Commenges D, Andersen PK (1995) Score test of homogeneity for survival data. Lifetime Data Anal 1: 145–160",{"doi":649},"10.1007\u002FBF00985764",{"id":18,"text":651,"url":18,"identifiers":652},"Feng SB, Wolfe RA, Port FK (2005) Frailty survival model analysis of the national deceased donor kidney transplant dataset using Poisson variance structures. J Am Stat Assoc 100: 728–735",{"doi":653},"10.1198\u002F016214505000000123",{"id":18,"text":655,"url":18,"identifiers":656},"Henderson R, Oman P (1999) Effect of frailty on marginal regression estimates in survival analysis. J Roy Stat Soc B 61: 367–379",{"doi":657},"10.1111\u002F1467-9868.00182",{"id":18,"text":659,"url":18,"identifiers":660},"Klein JP (1992) Semiparametric estimation of random effects using the Cox model based on the EM algorithm. Biometrics 48: 795–806",{"doi":661},"10.2307\u002F2532345",{"id":18,"text":663,"url":18,"identifiers":664},"Lawless JF, Zhan M (1998) Analysis of interval-grouped recurrent-event data using piecewise constant rate functions. Can J Stat 26: 549–565",{"doi":665},"10.2307\u002F3315717",{"id":18,"text":667,"url":18,"identifiers":668},"Nie L (2002) Laplace approximation in nonlinear mixed-effects models. PhD thesis, University of Illinois at Chicago",{},{"id":18,"text":670,"url":18,"identifiers":671},"Nie L (2007) Convergence rate of MLE in generalized linear and nonlinear mixed-effects models: theory and applications. J Stat Plan Infer 137: 1787–1804",{"doi":672},"10.1016\u002Fj.jspi.2005.06.010",{"id":18,"text":674,"url":18,"identifiers":675},"Nielsen GG, Gill RD, Andersen PK, Sorensen TIA (1992) A counting process approach to maximum likelihood estimation in frailty models. Scand J Stat 19: 25–43",{},{"id":18,"text":677,"url":18,"identifiers":678},"OPTN\u002FSRTR (2003) 2002 Annual report of the U.S. organ procurement and transplantation network and the scientific registry of transplant recipients: transplant Data 1992–2001. In: Department of Health and Human Services, Health Resources and Services Administration, Office of Special Programs, Division of Transplantation",{},{"id":18,"text":680,"url":18,"identifiers":681},"Ripatti S, Palmgren J (2000) Estimation of multivariate frailty models using penalized partial likelihood. Biometrics 56: 1016–1022",{"doi":682},"10.1111\u002Fj.0006-341X.2000.01016.x",{"id":18,"text":684,"url":18,"identifiers":685},"Sastry N (1997) A nested frailty model for survival data, with an application to the study of child survival in northeast Brazil. J Am Stat Assoc 92: 426–435",{"doi":686},"10.1080\u002F01621459.1997.10473994",{"id":18,"text":688,"url":18,"identifiers":689},"Stiratelli R, Laird N, Ware J (1984) Random effects models for serial observations with binary responses. Biometrics 40: 961–971",{"doi":690},"10.2307\u002F2531147",{"id":18,"text":692,"url":18,"identifiers":693},"Vaida F, Xu R (2000) Proportional hazards model with random effects. Stat Med 19: 3309–3324",{"doi":694},"10.1002\u002F1097-0258(20001230)19:24\u003C3309::AID-SIM825>3.0.CO;2-9",{"id":18,"text":696,"url":18,"identifiers":697},"Vonesh EF, Wang H, Nie L, Majumdar D (2002) Conditional second-order generalized estimating equations for generalized linear and nonlinear mixed-effects models. J Am Stat Assoc 97: 271–283",{"doi":698},"10.1198\u002F016214502753479400",{"id":18,"text":700,"url":18,"identifiers":701},"Wolfe RA, Ashby VB, Milford EL, Ojo AO, Ettenger RE, Agodoa LYC, Held PJ, Port FK (1999) Patient survival for waitlisted dialysis versus cadaveric renal transplant patients in the United States. New Engl J Med 341: 1725–1730",{"doi":702},"10.1056\u002FNEJM199912023412303",{"id":704,"createTime":705,"updateTime":706,"relativeEntities":707,"slug":708,"properties":709,"entityType":187,"verifyStatus":188,"verifyTime":720,"verifyNote":190,"languages":18,"translateLanguages":18,"viewCount":19,"primaryUrl":721,"fullTextUrl":18,"authors":722,"publicationType":211,"publisherRelationship":738,"citationCount":19,"citationInfo":788,"publishDate":791,"publishYear":789,"citationAnalyzeStatus":17,"lastCitationAnalyze":792,"indexDatabases":793,"openAccess":18,"references":18,"isForceReanalyzing":270},"f7535eb7-4d2d-42df-80ee-22ec06b0951e","2023-12-10T09:00:54.323+00:00","2026-07-22T19:12:31.318+00:00",[],"Mixture-regression-models-for-the-gap-time-distributions-and-illness-death-processes",{"abstract":710,"title":712,"gsPaper":714,"references":716,"doi":718},{"EN":711},"The aim of this study is to provide an analysis of gap event times under the illness–death model, where some subjects experience “illness” before “death” and others experience only “death.” Which event is more likely to occur first and how the duration of the “illness” influences the “death” event are of interest. Because the occurrence of the second event is subject to dependent censoring, it can lead to bias in the estimation of model parameters. In this work, we generalize the semiparametric mixture models for competing risks data to accommodate the subsequent event and use a copula function to model the dependent structure between the successive events. Under the proposed method, the survival function of the censoring time does not need to be estimated when developing the inference procedure. We incorporate the cause-specific hazard functions with the counting process approach and derive a consistent estimation using the nonparametric maximum likelihood method. Simulations are conducted to demonstrate the performance of the proposed analysis, and its application in a clinical study on chronic myeloid leukemia is reported to illustrate its utility.",{"EN":713},"Mixture regression models for the gap time distributions and illness–death processes",{"VOID":715},"[\"10519934419377649411\"]",{"VOID":717},"Andersen PK, Borgan Ø, Gill RD, Keiding N (1993) Statistical models based on counting processes. Springer, New York\nBennett S (1983) Analysis of survival data by the proportional odds model. Stat Med 2:273–277\nChang SH (2000) A two-sample comparison for multiple ordered event data. Biometrics 56:183–189\nChang IS, Hsiung CA, Wen CC, Wu YJ, Yang CC (2007) Non-parametric maximum-likelihood estimation in a semiparametric mixture model for competing-risks data. Scand J Stat 34:870–895\nChen L, Lin DY, Zeng D (2012) Checking semiparametric transformation models with censored data. Biostatistics 13:18–31\nChen YH (2009) Weighted Breslow-type and maximum likelihood estimation in semiparametric transformation models. Biometrika 96:591–600\nChen YH (2010) Semiparametric marginal regression analysis for dependent competing risks under an assumed copula. J R Stat Soc Ser B 72:235–251\nChen YH (2012) Maximum likelihood analysis of semicompeting risks data with semiparametric regression model. Lifetime Data Anal 18:36–57\nChoi S, Huang X (2014) Maximum likelihood estimation of semiparametric mixture component models for competing risks data. Biometrics 70:588–598\nClayton DG (1978) A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65:141–151\nCox DG (1972) Regression models and life-tables. J R Stat Soc Ser B 34:187–220\nFine JP (1999) Analysing competing risks data with transformation models. J R Stat Soc Ser B 61:817–830\nFrank MJ (1979) On the simultaneous association of \\(F(x, y)\\) and \\(x+y-F(x, y)\\). Aequat Math 19:194–226\nGumbel EJ (1960) Distributions des valeurs extremes en plusieurs dimensions. Publ Inst Stat Univ Paris 9:171–173\nHsieh JJ, Wang WJ, Ding AA (2008) Regression analysis based on semicompeting risks data. J R Stat Soc Ser B 70:3–20\nHuang Y (2000) Two-sample multistate accelerated sojourn times model. J Am Stat Assoc 95:619–627\nHuang Y (2002) Censored regression with the multistate accelerated sojourn times model. J R Stat Soc Ser B 64:17–29\nHuang X, Liu L (2007) A joint frailty model for survival and gap times between recurrent events. Biometrics 63:389–397\nHuang X, Zhang N (2008) Regression survival analysis with an assumed copula for dependent censoring: a sensitivity analysis approach. Biometrics 64:1090–1099\nHuang CH, Chen YH, Chuang YW (2017) Semiparametric regression analysis of recurrent gap times in the presence of competing risks. Stat Sin 27:1059–1077\nLin DY, Sun W, Ying Z (1999) Nonparametric estimation of the gap time distributions for serial events with censored data. Biometrika 86:59–70\nLu W, Peng L (2008) Semiparametric analysis of mixture regression models with competing risks data. Lifetime Data Anal 14:231–252\nPeng L, Fine JP (2007) Regression modeling of semicompeting risks data. Biometrics 63:96–108\nPrentice RL, Williams BJ, Peterson AV (1981) On the regression analysis of multivariate failure time data. Biometrika 68:373–379\nSchaubel DE, Cai J (2004) Regression methods for gap time hazard functions of sequentially ordered multivariate failure time data. Biometrika 91:291–303\nZeng D, Lin DY (2006) Efficient estimation of semiparametric transformation models for counting processes. Biometrika 93:627–640\nZeng D, Lin DY (2007) Maximum likelihood estimation in semiparametric regression models with censored data. J R Stat Soc Ser B 69:507–564",{"VOID":719},"10.1007\u002Fs10985-018-9418-7","2024-05-16T01:48:23.800+00:00","http:\u002F\u002Flink.springer.com\u002F10.1007\u002Fs10985-018-9418-7",[723],{"id":724,"sortIndex":19,"researcher":18,"roles":725,"affiliations":726,"properties":735,"displayName":737,"givenName":18,"familyName":18},"cd78d4f3-d13e-4716-9b4b-8b7c2e569b83",[196],[727],{"id":728,"sortIndex":19,"affiliation":729,"properties":18},"c3185779-2991-496c-8c82-a068401ae26a",{"id":728,"createTime":18,"updateTime":18,"relativeEntities":730,"slug":18,"properties":731,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":734,"statistic":18},[],{"title":732},{"VI":733},"Department of Statistics, National Taipei University, Taipei, Taiwan",[],{"title":736},{"VI":737},"Chia-Hui Huang",{"url":721,"publisher":739,"properties":784},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":740,"slug":10,"properties":741,"entityType":16,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":19,"subjectFields":744,"manageAffiliations":753,"indexDatabases":764,"url":18,"thumbnailPath":18,"statistic":779,"gsStatistic":18,"type":18,"analyzePriority":18},[],{"issn":742,"title":743},{"VOID":13},{"EN":15},[745,749],{"id":22,"createTime":18,"updateTime":18,"relativeEntities":746,"label":747,"description":748,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":25},{},{"id":28,"createTime":18,"updateTime":18,"relativeEntities":750,"label":751,"description":752,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":31},{},[754,759],{"id":35,"createTime":18,"updateTime":18,"relativeEntities":755,"slug":18,"properties":756,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":758,"statistic":18},[],{"title":757},{"EN":39},[],{"id":42,"createTime":18,"updateTime":18,"relativeEntities":760,"slug":18,"properties":761,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":763,"statistic":18},[],{"title":762},{"EN":46},[48],[765,772],{"id":51,"indexDatabase":766,"url":64,"indexYears":18,"academicFieldIds":771,"indexDatabaseRanking":18},{"id":53,"createTime":18,"updateTime":18,"relativeEntities":767,"label":768,"description":769,"key":60,"publicationTags":770,"standard":18},[],{"EN":56,"VI":56},{"EN":58,"VI":59},[62,63],[66,67],{"id":69,"indexDatabase":773,"url":80,"indexYears":81,"academicFieldIds":778,"indexDatabaseRanking":85},{"id":71,"createTime":18,"updateTime":18,"relativeEntities":774,"label":775,"description":776,"key":77,"publicationTags":777,"standard":18},[],{"EN":74,"VI":74},{"EN":74,"VI":76},[79],[83,84],{"impactFactor":19,"impactFactorByYear":780,"i10Index":100,"i10IndexLast5Year":101,"totalPublication":102,"totalPublicationByYear":781,"totalCitation":124,"totalCitationByYear":782,"totalCitationPerPublication":143,"totalCitationPerPublicationByYear":783,"hindexLast5Year":165,"hindex":165},{"2012":88,"2013":89,"2014":90,"2015":91,"2016":92,"2017":93,"2018":94,"2019":95,"2020":96,"2021":97,"2022":98,"2023":99},{"1995":104,"1996":105,"1997":106,"1998":106,"1999":107,"2000":108,"2001":109,"2002":110,"2003":105,"2004":108,"2005":107,"2006":111,"2007":112,"2008":113,"2009":114,"2010":104,"2011":115,"2012":107,"2013":116,"2014":117,"2015":114,"2016":118,"2017":119,"2018":120,"2019":121,"2020":114,"2021":117,"2022":113,"2023":122,"2024":123},{"1995":126,"1996":111,"2003":127,"2005":119,"2006":128,"2007":129,"2008":130,"2009":131,"2010":132,"2011":133,"2012":134,"2013":135,"2014":136,"2015":120,"2016":137,"2017":138,"2018":139,"2019":140,"2020":141,"2021":142},{"1995":145,"1996":146,"2003":147,"2005":148,"2006":149,"2007":150,"2008":151,"2009":152,"2010":153,"2011":154,"2012":155,"2013":156,"2014":157,"2015":158,"2016":159,"2017":160,"2018":161,"2019":162,"2020":163,"2021":164},{"pages":785,"volume":787},{"VOID":786},"168-188",{"VOID":491},{"total":19,"publishYear":789,"statisticByYear":790},2018,{},"2018-01-27","2026-07-22T19:12:31.317+00:00",[85,62],{"id":795,"createTime":796,"updateTime":797,"relativeEntities":798,"slug":799,"properties":800,"entityType":187,"verifyStatus":188,"verifyTime":811,"verifyNote":190,"languages":18,"translateLanguages":18,"viewCount":19,"primaryUrl":812,"fullTextUrl":18,"authors":813,"publicationType":211,"publisherRelationship":863,"citationCount":913,"citationInfo":914,"publishDate":917,"publishYear":915,"citationAnalyzeStatus":17,"lastCitationAnalyze":918,"indexDatabases":919,"openAccess":18,"references":18,"isForceReanalyzing":270},"6674f7fe-aa96-4f74-8122-95ca3a3f9a26","2024-01-24T08:51:33.173+00:00","2026-07-20T18:08:00.024+00:00",[],"The-Wally-plot-approach-to-assess-the-calibration-of-clinical-prediction-models",{"abstract":801,"title":803,"gsPaper":805,"references":807,"doi":809},{"EN":802},"A prediction model is calibrated if, roughly, for any percentage x we can expect that x subjects out of 100 experience the event among all subjects that have a predicted risk of x%. Typically, the calibration assumption is assessed graphically but in practice it is often challenging to judge whether a “disappointing” calibration plot is the consequence of a departure from the calibration assumption, or alternatively just “bad luck” due to sampling variability. We propose a graphical approach which enables the visualization of how much a calibration plot agrees with the calibration assumption to address this issue. The approach is mainly based on the idea of generating new plots which mimic the available data under the calibration assumption. The method handles the common non-trivial situations in which the data contain censored observations and occurrences of competing events. This is done by building on ideas from constrained non-parametric maximum likelihood estimation methods. Two examples from large cohort data illustrate our proposal. The ‘wally’ R package is provided to make the methodology easily usable.",{"EN":804},"The Wally plot approach to assess the calibration of clinical prediction models",{"VOID":806},"[\"4511289248729558525\"]",{"VOID":808},"Aalen OO, Johansen S (1978) An empirical transition matrix for non-homogeneous Markov chains based on censored observations. Scand J Stat 5:141–150\nAndersen PK, Borgan Ø, Gill RD, Keiding N (1993) Statistical models based on counting processes. Springer, New York\nAustin PC, Steyerberg EW (2014) Graphical assessment of internal and external calibration of logistic regression models by using loess smoothers. Stat Med 33(3):517–535\nBarber S, Jennison C (1999) Symmetric tests and confidence intervals for survival probabilities and quantiles of censored survival data. Biometrics 55(2):430–436\nBeyersmann J, Allignol A, Schumacher M (2011) Competing risks and multistate models with R. Springer Science & Business Media, Berlin\nBlanche P (2017) Confidence intervals for the cumulative incidence function via constrained NPMLE. https:\u002F\u002Fifsv.sund.ku.dk\u002Fbiostat\u002Fbiostat_annualreport\u002Findex.php5\u002FResearch_reports\nBlanche P, Proust-Lima C, Loubère L, Berr C, Dartigues J-F, Jacqmin-Gadda H (2015) Quantifying and comparing dynamic predictive accuracy of joint models for longitudinal marker and time-to-event in presence of censoring and competing risks. Biometrics 71(1):102–113\nBröcker J, Smith LA (2007) Increasing the reliability of reliability diagrams. Weather Forecast 22(3):651–661\nBuja A, Cook D, Hofmann H, Lawrence M, Lee E-K, Swayne DF, Wickham H (2009) Statistical inference for exploratory data analysis and model diagnostics. Philos Trans R Soc Lond A Math Phys Eng Sci 367(1906):4361–4383\nCamm A et al (2010) Guidelines for the management of atrial fibrillation: the task force for the management of atrial fibrillation of the european society of cardiology (esc). Eur Heart J 31:2369–2429\nCrowson CS, Atkinson EJ, Therneau TM (2016) Assessing calibration of prognostic risk scores. Stat Methods Med Res 25:1692–1706\nDemler OV, Paynter NP, Cook NR (2015) Tests of calibration and goodness-of-fit in the survival setting. Stat Med 34(10):1659–1680\nEfron B (1981) Censored data and the bootstrap. J Am Stat Assoc 76(374):312–319\nEkstrøm CT (2013) Teaching ’instant experience’ with graphical model validation techniques. Teach Stat 36(1):23–26\nFournier M-C, Foucher Y, Blanche P, Buron F, Giral M, Dantan E (2016) A joint model for longitudinal and time-to-event data to better assess the specific role of donor and recipient factors on long-term kidney transplantation outcomes. Eur J Epidemiol 31(5):469–479\nFreedman AN, Seminara D, Gail MH, Hartge P, Colditz GA, Ballard-Barbash R, Pfeiffer RM (2005) Cancer risk prediction models: a workshop on development, evaluation, and application. J Natl Cancer Inst 97(10):715–723\nGail MH, Pfeiffer RM (2005) On criteria for evaluating models of absolute risk. Biostatistics 6(2):227–239\nGerds TA, Cai T, Schumacher M (2008) The performance of risk prediction models. Biometr J 50(4):457–479\nGerds TA, Andersen PK, Kattan MW (2014) Calibration plots for risk prediction models in the presence of competing risks. Stat Med 33(18):3191–3203\nGeskus RB (2015) Data analysis with competing risks and intermediate states, vol 82. CRC Press, Boca Raton\nHandford M (2007) Where is Wally?. Walker Books Ltd, London\nKaplan E, Meier P (1958) Nonparametric estimation from incomplete observations. J Am Stat Assoc 53(282):457–481\nLemeshow S, Hosmer DW (1982) A review of goodness of fit statistics for use in the development of logistic regression models. Am J Epidemiol 115(1):92–106\nLi G, Sun Y (2000) A simulation-based goodness-of-fit test for survival data. Stat Probab Lett 47(4):403–410\nLin DY, Wei L-J, Ying Z (1993) Checking the Cox model with cumulative sums of martingale-based residuals. Biometrika 80(3):557–572\nLoy A, Follett L, Hofmann H (2016) Variations of Q–Q plots: the power of our eyes!. Am Stat 70(2):202–214\nMajumder M, Hofmann H, Cook D (2013) Validation of visual statistical inference, applied to linear models. J Am Stat Assoc 108(503):942–956\nMartinussen T, Scheike T (2006) Dynamic regression models for survival data. Springer, Berlin\nPepe M, Janes H (2013) Methods for evaluating prediction performance of biomarkers and tests. In: Lee M-L, Gail G, Cai T, Pfeiffer R, Gandy A (eds) Risk assessment and evaluation of predictions. Springer, Berlin\nPepe MS, Feng Z, Huang Y, Longton G, Prentice R, Thompson IM, Zheng Y (2008) Integrating the predictiveness of a marker with its performance as a classifier. Am J Epidemiol 167(3):362–368\nR Core Team (2017) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna\nRobins J, Ritov Y et al (1997) Toward a curse of dimentionality appropriate asymptotic theory for semi-parametric models. Stat Med 16(3):285–319\nSteyerberg E (2009) Clinical prediction models: a practical approach to development, validation, and updating. Springer, Berlin\nSteyerberg EW, Vickers AJ, Cook NR, Gerds T, Gonen M, Obuchowski N, Pencina MJ, Kattan MW (2010) Assessing the performance of prediction models: a framework for some traditional and novel measures. Epidemiology 21(1):128\nThomas DR, Grunkemeier GL (1975) Confidence interval estimation of survival probabilities for censored data. J Am Stat Assoc 70(352):865–871\nTukey J (1972) Some graphic and semigraphic displays. In: Bancroft T (ed) Statistical papers in honor of George W. Snedecor. Iowa State University, Ames, Iowa, p 293–316\nViallon V, Benichou J, Clavel-Chapelon F, Ragusa S (2009) How to evaluate the calibration of a disease risk prediction tool. Stat Med 28:901–916\nVickers A, Cronin A (2010) Everything you always wanted to know about evaluating prediction models (but were too afraid to ask). Urology 76(6):1298–1301",{"VOID":810},"10.1007\u002Fs10985-017-9414-3","2024-05-28T15:06:30.686+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs10985-017-9414-3",[814,831,848],{"id":815,"sortIndex":19,"researcher":18,"roles":816,"affiliations":817,"properties":826,"displayName":828,"givenName":18,"familyName":18},"d1f71c8f-78cd-4602-9cf4-992a44d841fe",[196],[818],{"id":819,"sortIndex":19,"affiliation":820,"properties":18},"48d9df0a-9a85-46f7-8579-5802224fe467",{"id":819,"createTime":18,"updateTime":18,"relativeEntities":821,"slug":18,"properties":822,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":825,"statistic":18},[],{"title":823},{"VI":824},"LMBA, University of South Brittany, Vannes, France",[],{"title":827,"gsAuthor":829},{"VI":828},"Paul Blanche",{"VOID":830},"[\"iriOv8oAAAAJ\"]",{"id":832,"sortIndex":308,"researcher":18,"roles":833,"affiliations":834,"properties":843,"displayName":845,"givenName":18,"familyName":18},"8fe82dca-a049-443d-bcbf-8e37dfd27c59",[196],[835],{"id":836,"sortIndex":19,"affiliation":837,"properties":18},"15b41fba-2409-4b67-8658-8440db2b5a97",{"id":836,"createTime":18,"updateTime":18,"relativeEntities":838,"slug":18,"properties":839,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":842,"statistic":18},[],{"title":840},{"VI":841},"Department of Biostatistics, University of Copenhagen, Copenhagen, Denmark",[],{"title":844,"gsAuthor":846},{"VI":845},"Thomas A. 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Notonly are there unlimited choices for the number of events requiredat each stage, but for each of these choices, there are unlimitedcombinations of accrual and follow-up at each stage that providethe required events. Methods are presented for determining optimalcombinations of accrual and follow-up for two-stage clinicaltrials with time to event end points. Optimization is based onminimizing the expected total study length as a function of theexpected accrual duration or sample size while providing an appropriateoverall size and power. Optimal values of expected accrual durationand minimum expected total study length are given assuming anexponential proportional hazards model comparing two treatmentgroups. The expected total study length can be substantiallydecreased by including a follow-up period during which accrualis suspended. Conditions that warrant an interim follow-up periodare considered, and the gain in efficiency achieved by includingan interim follow-up period is quantified. The gain in efficiencyshould be weighed against the practical difficulties in implementingsuch designs. An example is given to illustrate the use of thesetechniques in designing a clinical trial to compare two chemotherapyregimens for lung cancer. Practical considerations of includingan interim follow-up period are discussed.",{"EN":930},"Duration of Accrual and Follow-up for Two-Stage Clinical Trials",{"VOID":932},"[\"12684351488217473684\"]",{"VOID":934},"L. D. Case, T. M. Morgan and C. E. Davis, “Optimal restricted two-stage designs,” Controlled Clinical Trials vol. 8, pp. 146–155, 1987.\nT. Colton and K. McPherson, “Two-stage plans compared with fixed-sample-size and Wald SPRT-plans,” Journal of the American Statistical Association vol. 71, pp. 80–86, 1976.\nD. R. Cox, “Regression models and life-tables (with discussion),” Journal of the Royal Statistical Society, Series B vol. 34, pp. 187–220, 1972.\nC. De With, “Two-stage plans for the testing of binomial parameters,” Controlled Clinical Trials vol. 4, pp. 215–226, 1983.\nM. H. Gail, D. L. DeMets and E. V. Slud, “Simulation studies on increments of the two-sample logrank test for survival time data, with application to group sequential boundaries,” In Survival Analysis, Ed. J. Crowley and R. A. Johnson, pp. 287–301, Hayward, California: IMS Monograph Series, 1982.\nS. L. George and M. M. Desu, “Planning the size and duration of a clinical trial studying the time to some critical event,” Journal of Chronic Diseases, vol. 27, pp. 15–29, 1974.\nA. Hald, “Optimum double sampling tests of given strength. I. The normal distribution,” Journal of the American Statistical Association vol. 70, pp. 451–456, 1975.\nD. V. Jackson, P. J. Zekan, R. D. Caldwell, M. L. Slatkoff, R. W. Harding, L. D. Case, J. Hopkins, H. B. Muss, F. Richards, D. R. White, M. R. Cooper, J. J. Stuart, R. L. Capizzi and C. L. Spurr, “VP-16-214 in combination chemotherapy with chest irradiation for small-cell lung cancer: A randomized trial of the Piedmont Oncology Association.” Journal of Clinical Oncology vol. 2, pp. 1343–1351, 1984.\nK. Kim and A. A. Tsiatis, “Study duration for clinical trials with survival response and early stopping rule,” Biometrics vol. 46, pp. 81–92, 1990.\nK. K. G. Lan and D. L. DeMets, “Discrete sequential boundaries for clinical trials,” Biometrika vol. 70, pp. 659–663, 1983.\nT. M. Morgan, “Planning the duration of accrual and follow-up for clinical trials,” Journal of Chronic Diseases vol. 38, pp. 1009–1018, 1985.\nT. M. Morgan, “Nonparametric estimation of duration of accrual and total study length for clinical trials,” Biometrics vol. 43, pp. 903–912, 1987.\nD. B. Owen, “A double sample procedure,” Annals of Mathematical Statistics vol. 24, pp. 449–457, 1953.\nL. V. Rubinstein, M. H. Gail, and T. J. Santner, “Planning the duration of a comparative clinical trial with loss to follow-up and a period of continued observation,” Journal of Chronic Diseases vol. 34, pp. 469–479, 1981.\nD. A. Schoenfeld, “Sample-size formula for the proportional-hazards regression model,” Biometrics vol. 39, pp. 499–503, 1983.\nR. Simon, “Optimal two-stage designs for phase II clinical trials,” Controlled Clinical Trials vol. 10, pp. 1–10, 1989.\nA. A. Tsiatis, “The asymptotic joint distribution of the efficient scores test for the proportional hazards model calculated over time,” Biometrika vol. 68, pp. 311–315, 1981.\nA. A. Tsiatis, G. L. Rosner and D. L. Tritchler, “Group sequential tests with censored survival data adjusting for covariates,” Biometrika vol. 72, pp. 365–373, 1985.",{"VOID":936},"10.1023\u002FA:1009621009283","2024-06-24T01:39:36.730+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1023\u002FA:1009621009283",[940,955],{"id":941,"sortIndex":19,"researcher":18,"roles":942,"affiliations":943,"properties":952,"displayName":954,"givenName":18,"familyName":18},"f71cdd6f-cc7c-441d-9034-505673bb8760",[196],[944],{"id":945,"sortIndex":19,"affiliation":946,"properties":18},"0263aa84-0ae2-4f45-ab81-745b0ca5029a",{"id":945,"createTime":18,"updateTime":18,"relativeEntities":947,"slug":18,"properties":948,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":951,"statistic":18},[],{"title":949},{"VI":950},"Department of Public Health Sciences and the Comprehensive Cancer Center of Wake Forest University, Wake Forest University School of Medicine, USA",[],{"title":953},{"VI":954},"L. 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Nonparametric inference procedures for the location shift parameter with censored observations have recently been extensively studied. However, the validity of these procedures depends heavily on the model assumption. In this article, a class of graphical and numerical methods are proposed for checking the adequacy of the location shift model. Our graphical procedures are much less subjective than the eye-ball method based on the standard Q-Q plot. The proposed methods are illustrated with real-life examples.",{"EN":1032},"Checking adequacy of the semiparametric location shift model with censored data",{"VOID":1034},"[\"2768471348499122925\"]",{"VOID":1036},"10.1007\u002FBF00128572","2024-04-29T09:49:31.663+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002FBF00128572",[1040,1057,1072],{"id":1041,"sortIndex":19,"researcher":18,"roles":1042,"affiliations":1043,"properties":1052,"displayName":1054,"givenName":18,"familyName":18},"f859f321-db80-40b3-bd3d-dd93667a8628",[196],[1044],{"id":1045,"sortIndex":19,"affiliation":1046,"properties":18},"0fa43cd0-f132-4536-8a21-0a88e74612c0",{"id":1045,"createTime":18,"updateTime":18,"relativeEntities":1047,"slug":18,"properties":1048,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1051,"statistic":18},[],{"title":1049},{"VI":1050},"Department of Statistics, University of South Carolina, Columbia",[],{"title":1053,"gsAuthor":1055},{"VI":1054},"A. 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(1984), Analysis of Survival Data, London: Chapman Hall.",{},{"id":1148,"text":1166,"url":1150,"identifiers":1167},"Fischl M.A., Parker C.B., Pettinelli C., Wulfsohn M., Hirsch M.S., Collier A.C., Antoniskis D., Ho M., Richman D.D., Fuchs E., Merigan T.C., Reichman R.C., Gold J., Steigbigel N., Leoung G.S., Rasheed S., Tsiatis A. and The AIDS Clinical Trials Group (1990), “A Randomized Controlled Trial of a Reduced Daily Dose of Zidovudine in Patients with the Acquired Immunodeficiency Syndrome,” New England Journal of Medicine, 323, 1009–1114.",{"doi":1152},{"id":18,"text":1169,"url":18,"identifiers":1170},"Fleming T.F. and Harrington D.P. (1991), Counting Processes and Survival Analysis, New York: Wiley.",{},{"id":1148,"text":1172,"url":1150,"identifiers":1173},"Hsieh F. (1995), “The Empirical Process Approach for Semiparametric Two-Sample Models with Heterogeneous Treatment Effect”. 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(1993), “A Large Sample Study of Rank Estimation for Censored Regression Data,” The Annals of Statistics, 21, 76–99.",{"doi":1152},{"id":1199,"createTime":1200,"updateTime":1201,"relativeEntities":1202,"slug":1203,"properties":1204,"entityType":187,"verifyStatus":188,"verifyTime":1211,"verifyNote":190,"languages":18,"translateLanguages":18,"viewCount":557,"primaryUrl":1212,"fullTextUrl":18,"authors":1213,"publicationType":211,"publisherRelationship":1233,"citationCount":19,"citationInfo":1284,"publishDate":1287,"publishYear":1285,"citationAnalyzeStatus":17,"lastCitationAnalyze":1201,"indexDatabases":1288,"openAccess":18,"references":1289,"isForceReanalyzing":270},"c73cdc79-d0c9-4836-8055-f15fe48227f7","2023-12-08T23:26:48.712+00:00","2026-03-24T18:25:57.047+00:00",[],"Discussion-of-Commenges-and-Andersen",{"title":1205,"gsPaper":1207,"doi":1209},{"EN":1206},"Discussion of Commenges and 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G. Clayton. “A Monte Carlo Method for Bayesian Inference in Frailty Models,”Biometrics vol. 47 pp. 467–485, 1991.",{"doi":1152},{"id":1148,"text":1294,"url":1150,"identifiers":1295},"D. Clayton and J. Cuzick, “Multivariate Generalizations of the Proportional Hazards Model,”Journal of the Royal Statistical Society, Series A (with discussion), vol. 148 pp. 82–117, 1985.",{"doi":1152},{"id":1148,"text":1297,"url":1150,"identifiers":1298},"R. J. Gray, “A Bayesian Analysis of Institutional Effects in a Multicenter Cancer Clinical Trial,”Biometrics vol. 50 pp. 244–253, 1994.",{"doi":1152},{"id":1148,"text":1300,"url":1150,"identifiers":1301},"R. J. Gray, “Tests for Variation over Groups in Survival Data,”Journal of the American Statistical Association vol. 90 pp. 198–203, 1995.",{"doi":1152},{"id":1148,"text":1303,"url":1150,"identifiers":1304},"E. W. Lee, L. J. Wei and D. A. Amato, “Cox-type Regression Analysis for Large Numbers of Small Groups of Correlated Failure Time Observations,” inSurvival Analysis: State of the Art (J. P. Klein and P. K. Goel, eds.), Kluwer: Amsterdam, 1992, pp. 237–247.",{"doi":1152},{"id":1148,"text":1306,"url":1150,"identifiers":1307},"K. Y. Liang, “A Locally Most Powerful Test for Homogeneity with Many Strata,”Biometrika vol. 74 pp. 259–264, 1987.",{"doi":1152},{"id":1148,"text":1309,"url":1150,"identifiers":1310},"K. Y. Liang, S. G. Self and Y. C. Chang, “Modelling Marginal Hazards in Multivariate Failure Time Data,”Journal of the Royal Statistical Society, Series B vol. 55 pp. 441–453, 1993.",{"doi":1152},{"id":1148,"text":1312,"url":1150,"identifiers":1313},"G. G. Nielsen, R. D. Gill, P. K. Andersen, and T. I. A. Sørensen, “A Counting Process Approach to Maximum Likelihood Estimation in Frailty Models,”Scandinavian Journal of Statistics vol. 19 pp. 25–43, 1993.",{"doi":1152},{"id":1148,"text":1315,"url":1150,"identifiers":1316},"R. L. Prentice and J. Cai, “Covariance and Survivor Function Estimation Using Censored Multivariate Failure Time Data,”Biometrika vol. 79 pp. 495–512, 1992.",{"doi":1152},{"id":18,"text":1318,"url":18,"identifiers":1319},"D. K. Stangl and J. B. Greenhouse, Bayesian hierarchical survival models and model sensitivity analysis. Technical Report #560, Carnegie Mellon University, Department of Statistics, 1992.",{},{"id":1148,"text":1321,"url":1150,"identifiers":1322},"D. Stangl, “Prediction and Decision Making Using Bayesian Hierarchical Models,”Statistics in Medicine, in press.",{"doi":1152},{"id":1324,"createTime":1325,"updateTime":1326,"relativeEntities":1327,"slug":1328,"properties":1329,"entityType":187,"verifyStatus":188,"verifyTime":1340,"verifyNote":190,"languages":18,"translateLanguages":18,"viewCount":19,"primaryUrl":1341,"fullTextUrl":18,"authors":1342,"publicationType":211,"publisherRelationship":1395,"citationCount":18,"citationInfo":18,"publishDate":1444,"publishYear":1445,"citationAnalyzeStatus":1446,"lastCitationAnalyze":1447,"indexDatabases":1448,"openAccess":18,"references":18,"isForceReanalyzing":270},"bba2700c-da6d-448e-80e7-8059f39e0805","2024-02-18T23:37:26.810+00:00","2026-02-25T18:54:50.003+00:00",[],"The-built-in-selection-bias-of-hazard-ratios-formalized-using-structural-causal-models",{"abstract":1330,"title":1332,"gsPaper":1334,"references":1336,"doi":1338},{"EN":1331},"It is known that the hazard ratio lacks a useful causal interpretation. Even for data from a randomized controlled trial, the hazard ratio suffers from so-called built-in selection bias as, over time, the individuals at risk among the exposed and unexposed are no longer exchangeable. In this paper, we formalize how the expectation of the observed hazard ratio evolves and deviates from the causal effect of interest in the presence of heterogeneity of the hazard rate of unexposed individuals (frailty) and heterogeneity in effect (individual modification). For the case of effect heterogeneity, we define the causal hazard ratio. We show that the expected observed hazard ratio equals the ratio of expectations of the latent variables (frailty and modifier) conditionally on survival in the world with and without exposure, respectively. Examples with gamma, inverse Gaussian and compound Poisson distributed frailty and categorical (harming, beneficial or neutral) distributed effect modifiers are presented for illustration. This set of examples shows that an observed hazard ratio with a particular value can arise for all values of the causal hazard ratio. Therefore, the hazard ratio cannot be used as a measure of the causal effect without making untestable assumptions, stressing the importance of using more appropriate estimands, such as contrasts of the survival probabilities.",{"EN":1333},"The built-in selection bias of hazard ratios formalized using structural causal models",{"VOID":1335},"[]",{"VOID":1337},"Aalen OO, Borgan Ø, Gjessing HK (2008) Survival and Event History Analysis, 1st edn. Springer, New York\nAalen OO, Cook RJ, Røysland K (2015) Does Cox analysis of a randomized survival study yield a causal treatment effect? Lifetime Data Anal 21(4):579–593\nBalan TA, Putter H (2020) A tutorial on frailty models. Stat Methods Med Res 29(11):3424–3454\nBartlett JW, Morris TP, Stensrud MJ, Daniel RM, Vansteelandt SK, Burman CF (2020) The hazards of period specific and weighted hazard ratios. Stat Biopharm Res 12(4):518–519\nBennett S (1983) Analysis of survival data by the proportional odds model. Stat Med 2(2):273–277\nBongers S, Forré P, Peters J, Mooij JM (2021) Foundations of structural causal models with cycles and latent variables. Ann Stat 49(5):2885–2915\nBoyd AP, Kittelson JM, Gillen DL (2012) Estimation of treatment effect under non-proportional hazards and conditionally independent censoring. Stat Med 31(28):3504–3515\nCox DR (1972) Regression models and life-tables. J Roy Stat Soc B 34(2):187–220\nDaniel R, Zhang J, Farewell D (2021) Making apples from oranges: Comparing noncollapsible effect estimators and their standard errors after adjustment for different covariate sets. Biom J 63(3):528–557\nDe Neve J, Gerds TA (2020) On the interpretation of the hazard ratio in Cox regression. Biom J 62(3):742–750\nDidelez V, Stensrud MJ (2021) On the logic of collapsibility for causal effect measures. Biometrical Journal\nHernán MA (2010) The hazards of hazard ratios. Epidemiology 21(1):13–15\nHernán MA, Brumback B, Robins JM (2000) Marginal Structural Models to Estimate the Causal Effect of Zidovudine on the Survival of HIV-Positive Men. Epidemiology 11(5)\nHernán MA, Brumback B, Robins JM (2001) Marginal structural models to estimate the joint causal effect of nonrandomized treatments. J Am Stat Assoc 96(454):440–448\nHernán MA, Cole SR, Margolick J, Cohen M, Robins JM (2005) Structural accelerated failure time models for survival analysis in studies with time-varying treatments. Pharmacoepidemiol Drug Saf 14(7):477–491\nHess KR (1994) Assessing time-by-covariate interactions in proportional hazards regression models using cubic spline functions. Stat Med 13(10):1045–1062\nMartinussen T, Vansteelandt S (2013) On collapsibility and confounding bias in Cox and Aalen regression models. Lifetime Data Anal 19(3):279–296\nMartinussen T, Vansteelandt S, Andersen P (2020) Subtleties in the interpretation of hazard contrasts. Lifetime Data Anal 26(4):833–855\nNelsen RB (2006) An Introduction to Copulas, 2nd edn. Springer\nNeyman J (1990) On the Application of Probability Theory to Agricultural Experiments. Essay on Principles. Section 9. Stat Sci 5(4):465–472\nPearl J (2009) Causality: Models, reasoning, and inference, 2nd edn. Cambridge University Press, Cambridge\nPeters J, Janzing D, Schölkopf B (2018) Elements of causal inference: foundations and learning algorithms. The MIT Press, Cambridge, Massachusetts\nPost RAJ, van den Heuvel ER, Putter H (2024) Bias of the additive hazard model in the presence of causal effect heterogeneity. Lifetime Data Anal. https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs10985-024-09616-z\nRubin DB (1974) Estimating causal effects of treatments in randomized and nonrandomized studies. J Educ Psychol 66(5):688–701\nRyalen PC, Stensrud MJ, Røysland K (2018) Transforming cumulative hazard estimates. 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