Marginalized Frailty-Based Illness-Death Model: Application to the UK-Biobank Survival Data

References

• Aalen, O. (1978), “Nonparametric Inference for a Family of Counting Processes,” The Annals of Statistics , 6, 701–726. DOI: 10.1214/aos/1176344247.
   Web of Science ®Google Scholar
• Anders, C. K. , Johnson, R. , Litton, J. , Phillips, M. , and Bleyer, A. (2009), “Breast Cancer Before Age 40 Years,” Seminars in Oncology , 36, 237–249. DOI: 10.1053/j.seminoncol.2009.03.001.
   PubMed Web of Science ®Google Scholar
• Andersen, P. K. (1988), “Multistate Models in Survival Analysis: A Study of Nephropathy and Mortality in Diabetes,” Statistics in Medicine , 7, 661–670. DOI: 10.1002/sim.4780070605.
   PubMed Web of Science ®Google Scholar
• Andersen, P. K. , and Klein, J. P. (2007), “Regression Analysis for Multistate Models Based on a Pseudo-Value Approach, With Applications to Bone Marrow Transplantation Studies,” Scandinavian Journal of Statistics , 34, 3–16. DOI: 10.1111/j.1467-9469.2006.00526.x.
   Web of Science ®Google Scholar
• Bradbury, K. E. , Murphy, N. , and Key, T. J. (2020), “Diet and Colorectal Cancer in UK Biobank: A Prospective Study,” International Journal of Epidemiology , 49, 246–258. DOI: 10.1093/ije/dyz064.
   PubMed Web of Science ®Google Scholar
• Cai, J. , and Zeng, D. (2004), “Sample Size/Power Calculation for Case–Cohort Studies,” Biometrics , 60, 1015–1024. DOI: 10.1111/j.0006-341X.2004.00257.x.
   PubMed Web of Science ®Google Scholar
• Chang, S.-H. , and Tzeng, S.-J. (2006), “Nonparametric Estimation of Sojourn Time Distributions for Truncated Serial Event Data—A Weight-Adjusted Approach,” Lifetime Data Analysis , 12, 53–67. DOI: 10.1007/s10985-005-7220-9.
   PubMed Web of Science ®Google Scholar
• Chen, Y.-H. (2012), “Maximum Likelihood Analysis of Semicompeting Risks Data With Semiparametric Regression Models,” Lifetime Data Analysis , 18, 36–57. DOI: 10.1007/s10985-011-9202-4.
   PubMed Web of Science ®Google Scholar
• Clayton, D. G. (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. DOI: 10.1093/biomet/65.1.141.
   Web of Science ®Google Scholar
• Fine, J. P. , Jiang, H. , and Chappell, R. (2001), “On Semi-Competing Risks Data,” Biometrika , 88, 907–919. DOI: 10.1093/biomet/88.4.907.
   Web of Science ®Google Scholar
• Glidden, D. V. , and Self, S. (1999), “Semiparametric Likelihood Estimation in the Clayton–Oakes Failure Time Model,” Scandinavian Journal of Statistics , 26, 363–372. DOI: 10.1111/1467-9469.00154.
   Web of Science ®Google Scholar
• Gorfine, M. , Zucker, D. M. , and Hsu, L. (2006), “Prospective Survival Analysis With a General Semiparametric Shared Frailty Model: A Pseudo Full Likelihood Approach,” Biometrika , 93, 735–741. DOI: 10.1093/biomet/93.3.735.
   Web of Science ®Google Scholar
• Hougaard, P. (2000), Analysis of Multivariate Survival Data , New York: Springer-Verlag.
   Google Scholar
• Jeon, J. , Du, M. , Schoen, R. E. , Hoffmeister, M. , Newcomb, P. A. , Berndt, S. I. , Caan, B. , Campbell, P. T. , Chan, A. T. , Chang-Claude, J. , and Giles, G. G. (2018), “Determining Risk of Colorectal Cancer and Starting Age of Screening Based on Lifestyle, Environmental, and Genetic Factors,” Gastroenterology , 154, 2152–2164. DOI: 10.1053/j.gastro.2018.02.021.
   PubMed Web of Science ®Google Scholar
• Kalbfleisch, J. D. , and Prentice, R. L. (2011), The Statistical Analysis of Failure Time Data (2nd ed.), Hoboken, NJ: Wiley.
   Google Scholar
• Kendall, M. G. (1938), “A New Measure of Rank Correlation,” Biometrika , 30, 81–93. DOI: 10.1093/biomet/30.1-2.81.
   Web of Science ®Google Scholar
• Klein, J. P. , and Moeschberger, M. L. (2006), Survival Analysis: Techniques for Censored and Truncated Data , New York: Springer.
   Google Scholar
• Kosorok, M. R. , Lee, B. L. , and Fine, J. P. (2004), “Robust Inference for Univariate Proportional Hazards Frailty Regression Models,” The Annals of Statistics , 32, 1448–1491. DOI: 10.1214/009053604000000535.
   Web of Science ®Google Scholar
• Mackenzie, T. (2012), “Survival Curve Estimation With Dependent Left Truncated Data Using Cox’s Model,” The International Journal of Biostatistics , 8, 29. DOI: 10.1515/1557-4679.1312.
   Google Scholar
• Morris, J. S. , Bradbury, K. E. , Cross, A. J. , Gunter, M. J. , and Murphy, N. (2018), “Physical Activity, Sedentary Behaviour and Colorectal Cancer Risk in the UK Biobank,” British Journal of Cancer , 118, 920. DOI: 10.1038/bjc.2017.496.
   PubMed Web of Science ®Google Scholar
• Ouakrim, D. A. , Pizot, C. , Boniol, M. , Malvezzi, M. , Boniol, M. , Negri, E. , Bota, M. , Jenkins, M. A. , Bleiberg, H. , and Autier, P. (2015), “Trends in Colorectal Cancer Mortality in Europe: Retrospective Analysis of the WHO Mortality Database,” BMJ , 351, h4970.
   Web of Science ®Google Scholar
• Saarela, O. , Kulathinal, S. , and Karvanen, J. (2009), “Joint Analysis of Prevalence and Incidence Data Using Conditional Likelihood,” Biostatistics , 10, 575–587. DOI: 10.1093/biostatistics/kxp013.
   PubMed Web of Science ®Google Scholar
• Shen, P.-S. (2017), “Semiparametric Analysis of Transformation Models With Dependently Left-Truncated and Right-Censored Data,” Communications in Statistics—Simulation and Computation , 46, 2474–2487. DOI: 10.1080/03610918.2015.1048879.
   Web of Science ®Google Scholar
• Tsai, W.-Y. (1990), “Testing the Assumption of Independence of Truncation Time and Failure Time,” Biometrika , 77, 169–177. DOI: 10.1093/biomet/77.1.169.
   Web of Science ®Google Scholar
• Vakulenko-Lagun, B. , and Mandel, M. (2016), “Comparing Estimation Approaches for the Illness-Death Model Under Left Truncation and Right Censoring,” Statistics in Medicine , 35, 1533– 1548. DOI: 10.1002/sim.6796.
   PubMed Web of Science ®Google Scholar
• Vakulenko-Lagun, B. , Mandel, M. , and Goldberg, Y. (2017), “Nonparametric Estimation in the Illness-Death Model Using Prevalent Data,” Lifetime Data Analysis , 23, 25–56. DOI: 10.1007/s10985-016-9373-0.
   PubMed Web of Science ®Google Scholar
• Virdee, P. S. , Kirtley, S. , Elhussein, L. , Watkinson, P. J. , Holt, T. A. , and Birks, J. (2019), “Components of the Full Blood Count as Risk Factors for Colorectal Cancer Detection: A Systematic Review Protocol,” BMJ Open , 9, e032759. DOI: 10.1136/bmjopen-2019-032759.
   PubMed Web of Science ®Google Scholar
• Xu, J. , Kalbfleisch, J. D. , and Tai, B. (2010), “Statistical Analysis of Illness-Death Processes and Semicompeting Risks Data,” Biometrics , 66, 716–725. DOI: 10.1111/j.1541-0420.2009.01340.x.
   PubMed Web of Science ®Google Scholar
• Zhou, R. , Zhu, H. , Bondy, M. , and Ning, J. (2016), “Semiparametric Model for Semi-Competing Risks Data With Application to Breast Cancer Study,” Lifetime Data Analysis , 22, 456–471. DOI: 10.1007/s10985-015-9344-x.
   PubMed Web of Science ®Google Scholar