Bayesian analysis of survival on multiple time scales
Abstract
We propose a Bayesian approach to the analysis of survival data on multiple time scales. Non‐parametric modelling of variation of rates with more than one time scale is achieved using priors which specify smooth variation. Computations are conveniently carried out using Gibbs sampling. We discuss the extension of the method to Bayesian forecasting of rates. Numerical experience of two examples is described.
Citing Literature
Number of times cited according to CrossRef: 70
- Nicholas DeVogel, Anjishnu Banerjee, Narayan Yoganandan, Application of resampling techniques to improve the quality of survival analysis risk curves for human frontal bone fracture, Clinical Biomechanics, 10.1016/j.clinbiomech.2018.04.013, 64, (28-34), (2019).
- Hajar Saoud, Abderrahim Ghadi, Mohamed Ghailani, Analysis of Evolutionary Trends of Incidence and Mortality by Cancers, Innovations in Smart Cities and Applications, 10.1007/978-3-319-74500-8_71, (778-788), (2018).
- Gen Li, Jianhua Z. Huang, Haipeng Shen, To Wait or Not to Wait: Two-Way Functional Hazards Model for Understanding Waiting in Call Centers, Journal of the American Statistical Association, 10.1080/01621459.2018.1423985, 113, 524, (1503-1514), (2018).
- Andrea Riebler, Leonhard Held, Projecting the future burden of cancer: Bayesian age–period–cohort analysis with integrated nested Laplace approximations, Biometrical Journal, 10.1002/bimj.201500263, 59, 3, (531-549), (2017).
- Zhengyi Zhou, David S. Matteson, Hui Yang, Eva K. Lee, Temporal and Spatiotemporal Models for Ambulance Demand, Healthcare Analytics, 10.1002/9781118919408, (389-412), (2016).
- Naoru Koizumi, Monica Gentili, Rajesh Ganesan, Debasree DasGupta, Amit Patel, Chun‐Hung Chen, Nigel Waters, Keith Melancon, Hui Yang, Eva K. Lee, Mathematical Optimization and Simulation Analyses for Optimal Liver Allocation Boundaries, Healthcare Analytics, 10.1002/9781118919408, (413-437), (2016).
- Kyoji Furukawa, Munechika Misumi, John B. Cologne, Harry M. Cullings, A Bayesian Semiparametric Model for Radiation Dose‐Response Estimation, Risk Analysis, 10.1111/risa.12513, 36, 6, (1211-1223), (2015).
- Christian Kuehn, Christian Kuehn, Stochastic Systems, Multiple Time Scale Dynamics, 10.1007/978-3-319-12316-5_15, (477-524), (2015).
- Frank E. Harrell, Frank E. Harrell ,, Introduction to Survival Analysis, Regression Modeling Strategies, 10.1007/978-3-319-19425-7_17, (399-422), (2015).
- Olli Saarela, Elja Arjas, Non‐parametric Bayesian Hazard Regression for Chronic Disease Risk Assessment, Scandinavian Journal of Statistics, 10.1111/sjos.12125, 42, 2, (609-626), (2014).
- Carl Schmertmann, Emilio Zagheni, Joshua R. Goldstein, Mikko Myrskylä, Bayesian Forecasting of Cohort Fertility, Journal of the American Statistical Association, 10.1080/01621459.2014.881738, 109, 506, (500-513), (2014).
- Bent Nielsen, Jens P. Nielsen, Identification and Forecasting in Mortality Models, The Scientific World Journal, 10.1155/2014/347043, 2014, (1-24), (2014).
- Freddie Bray, D. Maxwell Parkin, Descriptive Studies, Handbook of Epidemiology, 10.1007/978-0-387-09834-0, (187-258), (2014).
- Niels Keiding, Lexis Diagram, Wiley StatsRef: Statistics Reference Online, 10.1002/9781118445112, (2014).
- Joseph G. Ibrahim, Ming‐Hui Chen, Debajyoti Sinha, Bayesian Survival Analysis, Wiley StatsRef: Statistics Reference Online, 10.1002/9781118445112, (2014).
- Theodore R. Holford, Age–Period–Cohort Analysis, Wiley StatsRef: Statistics Reference Online, 10.1002/9781118445112, (2014).
- Theodore R. Holford, Age–Period–Cohort Analysis, Wiley StatsRef: Statistics Reference Online, 10.1002/9781118445112, (1-25), (2014).
- Leonardo Ventura, Maura Mezzetti, Estimating cancer incidence using a Bayesian back‐calculation approach, Statistics in Medicine, 10.1002/sim.6240, 33, 25, (4453-4468), (2014).
- Ramon Clèries, Jose Miguel Martínez, Victor Moreno, Yutaka Yasui, Josepa Ribes, Josep Maria Borràs, Predicting the Change in Breast Cancer Deaths in Spain by 2019, Epidemiology, 10.1097/EDE.0b013e31828b0866, 24, 3, (454-460), (2013).
- Giulia Carreras, Giuseppe Gorini, Time Trends of Italian Former Smokers 1980–2009 and 2010–2030 Projections Using a Bayesian Age Period Cohort Model, International Journal of Environmental Research and Public Health, 10.3390/ijerph110100001, 11, 1, (1-12), (2013).
- Daniel Eilstein, Kanwal Eshai, Lung and breast cancer mortality among women in France: Future trends, Cancer Epidemiology, 10.1016/j.canep.2012.07.008, 36, 6, (e341-e348), (2012).
- Katherine M. Keyes, Guohua Li, Age–Period–Cohort Modeling, Injury Research, 10.1007/978-1-4614-1599-2, (409-426), (2012).
- Ramon Clèries, Josepa Ribes, Maria Buxo, Alberto Ameijide, Rafael Marcos‐Gragera, Jaume Galceran, José Miguel Martínez, Yutaka Yasui, Bayesian approach to predicting cancer incidence for an area without cancer registration by using cancer incidence data from nearby areas, Statistics in Medicine, 10.1002/sim.4463, 31, 10, (978-987), (2012).
- Leonhard Held, Andrea Riebler, A conditional approach for inference in multivariate age-period-cohort models, Statistical Methods in Medical Research, 10.1177/0962280210379761, 21, 4, (311-329), (2010).
- Birgit Schrödle, Leonhard Held, A primer on disease mapping and ecological regression using $${\texttt{INLA}}$$, Computational Statistics, 10.1007/s00180-010-0208-2, 26, 2, (241-258), (2010).
- Di Kuang, Bent Nielsen, Jens Perch Nielsen, Forecasting in an Extended Chain‐Ladder‐Type Model, Journal of Risk and Insurance, 10.1111/j.1539-6975.2010.01395.x, 78, 2, (345-359), (2010).
- Peter Congdon, References, Applied Bayesian Hierarchical Methods, 10.1201/9781584887218, (495-500), (2010).
- Karri Seppä, Timo Hakulinen, Hyon‐Jung Kim, Esa Läärä, Cure fraction model with random effects for regional variation in cancer survival, Statistics in Medicine, 10.1002/sim.4046, 29, 27, (2781-2793), (2010).
- Andrea Riebler, Leonhard Held, The analysis of heterogeneous time trends in multivariate age–period–cohort models, Biostatistics, 10.1093/biostatistics/kxp037, 11, 1, (57-69), (2009).
- O. Saarela, S. Kulathinal, J. Karvanen, Joint analysis of prevalence and incidence data using conditional likelihood, Biostatistics, 10.1093/biostatistics/kxp013, 10, 3, (575-587), (2009).
- Peter Congdon, Adaptive autoregressive priors for area and time structured mortality data, Journal of Statistical Planning and Inference, 10.1016/j.jspi.2009.01.011, 139, 9, (2870-2884), (2009).
- R. Cleries, J.M. Martínez, J. Valls, L. Pareja, L. Esteban, R. Gispert, V. Moreno, J. Ribes, J.M. Borràs, Life expectancy and age–period–cohort effects: analysis and projections of mortality in Spain between 1977 and 2016, Public Health, 10.1016/j.puhe.2008.10.026, 123, 2, (156-162), (2009).
- Kyoji Furukawa, John B. Cologne, Yukiko Shimizu, N. Phillip Ross, Predicting Future Excess Events in Risk Assessment, Risk Analysis, 10.1111/j.1539-6924.2009.01197.x, 29, 6, (885-899), (2009).
- Jing Cao, Chong Z. He, Kimberly M. Suedkamp Wells, Joshua J. Millspaugh, Mark R. Ryan, Modeling Age and Nest‐Specific Survival Using a Hierarchical Bayesian Approach, Biometrics, 10.1111/j.1541-0420.2009.01204.x, 65, 4, (1052-1062), (2009).
- Peter Congdon, Life Expectancies for Small Areas: A Bayesian Random Effects Methodology, International Statistical Review, 10.1111/j.1751-5823.2009.00080.x, 77, 2, (222-240), (2009).
- Daniel Eilstein, Zoé Uhry, Tek-Ang Lim, Juliette Bloch, Lung cancer mortality in France, Lung Cancer, 10.1016/j.lungcan.2007.10.012, 59, 3, (282-290), (2008).
- Olli Saarela, Sangita Kulathinal, Elja Arjas, Esa Läärä, Nested case–control data utilized for multiple outcomes: a likelihood approach and alternatives, Statistics in Medicine, 10.1002/sim.3416, 27, 28, (5991-6008), (2008).
- Ludwig Fahrmeir, Leonhard Knorr‐Held, Dynamic Discrete‐time Duration Models: Estimation via Markov Chain Monte Carlo, Sociological Methodology, 10.1111/1467-9531.271033, 27, 1, (417-452), (2008).
- D. Kuang, B. Nielsen, J. P. Nielsen, Forecasting with the age-period-cohort model and the extended chain-ladder model, Biometrika, 10.1093/biomet/asn038, 95, 4, (987-991), (2008).
- D. Eilstein, É. Quoix, G. Hédelin, Incidence du cancer du poumon dans le Bas-Rhin : tendance et projections en 2014, Revue des Maladies Respiratoires, 10.1016/S0761-8425(06)71474-7, 23, 2, (117-125), (2006).
- Isabelle Bray, Paul Waraich, Wayne Jones, Serena Slater, Elliot M. Goldner, Julian Somers, Increase in schizophrenia incidence rates: findings in a Canadian cohort born 1975–1985, Social Psychiatry and Psychiatric Epidemiology, 10.1007/s00127-006-0073-z, 41, 8, (611-618), (2006).
- D. Max Parkin, Burden of Breast Cancer in Developing and Developed Countries, Breast Cancer in Women of African Descent, 10.1007/978-1-4020-3664-4, (1-22), (2006).
- Deborah Ashby, Bayesian statistics in medicine: a 25 year review, Statistics in Medicine, 10.1002/sim.2672, 25, 21, (3589-3631), (2006).
- R. Clèries, J. Ribes, L. Esteban, J.M. Martinez, J.M. Borràs, Time trends of breast cancer mortality in Spain during the period 1977–2001 and Bayesian approach for projections during 2002–2016, Annals of Oncology, 10.1093/annonc/mdl303, 17, 12, (1783-1791), (2006).
- Freddie Bray, Bjørn Møller, Predicting the future burden of cancer, Nature Reviews Cancer, 10.1038/nrc1781, 6, 1, (63-74), (2005).
- A. Baker, I. Bray, Bayesian Projections: What Are the Effects of Excluding Data from Younger Age Groups?, American Journal of Epidemiology, 10.1093/aje/kwi273, 162, 8, (798-805), (2005).
- D. Eilstein, Z. Uhry, L. Cherie-Challine, H. Isnard, Mortalité par cancer du poumon chez les femmes françaises. Analyse de tendance et projection à l’aide d’un modèle âge-cohorte bayésien, de 1975 à 2014, Revue d'Épidémiologie et de Santé Publique, 10.1016/S0398-7620(05)84586-9, 53, 2, (167-181), (2005).
- Theodore R. Holford, Age–Period–Cohort Analysis, Encyclopedia of Biostatistics, 10.1002/0470011815, (2005).
- Joseph G. Ibrahim, Ming‐Hui Chen, Debajyoti Sinha, Bayesian Survival Analysis, Encyclopedia of Biostatistics, 10.1002/0470011815, (2005).
- Niels Keiding, Lexis Diagram, Encyclopedia of Biostatistics, 10.1002/0470011815, (2005).
- Olivier Catelinois, Pierre Verger, Marc Colonna, Agn??s Rogel, Denis Hemon, Margot Tirmarche, PROJECTING THE TIME TREND OF THYROID CANCERS: ITS IMPACT ON ASSESSMENT OF RADIATION-INDUCED CANCER RISKS, Health Physics, 10.1097/01.HP.0000138587.93203.c5, 87, 6, (606-614), (2004).
- Niels Keiding, Samuel Kotz, Campbell B. Read, N. Balakrishnan, Brani Vidakovic, Norman L. Johnson, Lexis Diagram, Encyclopedia of Statistical Sciences, 10.1002/0471667196, (2004).
- Isabel Natário, Leonhard Knorr‐Held, Non‐Parametric Ecological Regression and Spatial Variation, Biometrical Journal, 10.1002/bimj.200390041, 45, 6, (670-688), (2003).
- Corrado Lagazio, Annibale Biggeri, Emanuela Dreassi, Age–period–cohort models and disease mapping, Environmetrics, 10.1002/env.600, 14, 5, (475-490), (2003).
- Bjørn Møller, Harald Fekjær, Timo Hakulinen, Helgi Sigvaldason, Hans H. Storm, Mats Talbäck, Tor Haldorsen, Prediction of cancer incidence in the Nordic countries: empirical comparison of different approaches, Statistics in Medicine, 10.1002/sim.1481, 22, 17, (2751-2766), (2003).
- P Brennan, I Bray, Recent trends and future directions for lung cancer mortality in Europe, British Journal of Cancer, 10.1038/sj.bjc.6600352, 87, 1, (43-48), (2002).
- W.M. Mason, N.H. Wolfinger, Cohort Analysis, International Encyclopedia of the Social & Behavioral Sciences, 10.1016/B0-08-043076-7/00401-0, (2189-2194), (2001).
- D.M Parkin, F.I Bray, S.S Devesa, Cancer burden in the year 2000. The global picture, European Journal of Cancer, 10.1016/S0959-8049(01)00267-2, 37, (4-66), (2001).
- Nobutane Hanayama, A simple two‐stage model for cancer risk in the environment, Environmetrics, 10.1002/env.498, 12, 8, (757-773), (2001).
- Isabelle Bray, Paul Brennan, Paolo Boffetta, Projections of alcohol‐ and tobacco‐related cancer mortality in Central Europe, International Journal of Cancer, 10.1002/1097-0215(20000701)87:1<122::AID-IJC18>3.0.CO;2-W, 87, 1, (122-128), (2000).
- Tadeusz Dyba, Timo Hakulinen, Comparison of different approaches to incidence prediction based on simple interpolation techniques, Statistics in Medicine, 10.1002/1097-0258(20000715)19:13<1741::AID-SIM496>3.0.CO;2-O, 19, 13, (1741-1752), (2000).
- Leonhard Knorr‐Held, Bayesian modelling of inseparable space‐time variation in disease risk, Statistics in Medicine, 10.1002/1097-0258(20000915/30)19:17/18<2555::AID-SIM587>3.0.CO;2-#, 19, 17‐18, (2555-2567), (2000).
- Nico Nagelkerke, Siem Heisterkamp, Martien Borgdorff, Jaap Broekmans, Hans Van Houwelingen, Semi‐parametric estimation of age–time specific infection incidence from serial prevalence data, Statistics in Medicine, 10.1002/(SICI)1097-0258(19990215)18:3<307::AID-SIM15>3.0.CO;2-Z, 18, 3, (307-320), (1999).
- Maura Mezzetti, Chris Robertson, A hierarchical Bayesian approach to age‐specific back‐calculation of cancer incidence rates, Statistics in Medicine, 10.1002/(SICI)1097-0258(19990430)18:8<919::AID-SIM89>3.0.CO;2-7, 18, 8, (919-933), (1999).
- Chris Robertson, Peter Boyle, Age–period–cohort analysis of chronic disease rates. I: modelling approach, Statistics in Medicine, 10.1002/(SICI)1097-0258(19980630)17:12<1305::AID-SIM853>3.0.CO;2-W, 17, 12, (1305-1323), (1998).
- Leonhard Knorr‐Held, Julian Besag, Modelling risk from a disease in time and space, Statistics in Medicine, 10.1002/(SICI)1097-0258(19980930)17:18<2045::AID-SIM943>3.0.CO;2-P, 17, 18, (2045-2060), (1998).
- WEN C. LEE, RUEY S. LIN, AUTOREGRESSIVE AGE–PERIOD–COHORT MODELS, Statistics in Medicine, 10.1002/(SICI)1097-0258(19960215)15:3<273::AID-SIM172>3.0.CO;2-R, 15, 3, (273-281), (1998).
- C. Berzuini, C. Larizza, A unified approach for modeling longitudinal and failure time data, with application in medical monitoring, IEEE Transactions on Pattern Analysis and Machine Intelligence, 10.1109/34.481537, 18, 2, (109-123), (1996).
- C Osmond, An appreciation of "Cohort analysis of mortality rates as an historical or narrative technique" (RAM Case), Journal of Epidemiology & Community Health, 10.1136/jech.50.2.125, 50, 2, (125-126), (1996).
- Medical monitoring, Markov Chain Monte Carlo in Practice, 10.1201/b14835, (339-356), (1995).




