title: Flexible parametric modelling of cause-specific hazards to estimate cumulative incidence functions.
abstract: BACKGROUND
  Competing risks are a common occurrence in survival analysis. They arise when a patient is at risk of more than one mutually exclusive event, such as death from different causes, and the occurrence of one of these may prevent any other event from ever happening.
  
  
  METHODS
  There are two main approaches to modelling competing risks: the first is to model the cause-specific hazards and transform these to the cumulative incidence function; the second is to model directly on a transformation of the cumulative incidence function. We focus on the first approach in this paper. This paper advocates the use of the flexible parametric survival model in this competing risk framework.
  
  
  RESULTS
  An illustrative example on the survival of breast cancer patients has shown that the flexible parametric proportional hazards model has almost perfect agreement with the Cox proportional hazards model. However, the large epidemiological data set used here shows clear evidence of non-proportional hazards. The flexible parametric model is able to adequately account for these through the incorporation of time-dependent effects.
  
  
  CONCLUSIONS
  A key advantage of using this approach is that smooth estimates of both the cause-specific hazard rates and the cumulative incidence functions can be obtained. It is also relatively easy to incorporate time-dependent effects which are commonly seen in epidemiological studies.
authors: Department of Health Sciences, Centre for Biostatistics and Genetic Epidemiology, University of Leicester, Leicester, UK. srh20@leicester.ac.uk.
authors: Sally R
authors: SR
authors: Hinchliffe
authors: Paul C
authors: PC
authors: Lambert
mesh_terms: D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D001943:Breast Neoplasms / Q000401:mortality*; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D015994:Incidence; D008875:Middle Aged; D008962:Models, Theoretical; D009367:Neoplasm Staging; D016016:Proportional Hazards Models; D018570:Risk Assessment; D016019:Survival Analysis; D015996:Survival Rate; D055815:Young Adult
references: Biometrics. 2011 Mar;67(1):39-49
references: 20377575
references: Stat Med. 2010 May 20;29(11):1190-205
references: 20099244
references: Am J Epidemiol. 2005 Nov 15;162(10):975-82
references: 16207808
references: Stat Med. 2010 Mar 30;29(7-8):885-95
references: 20213719
references: Stat Med. 2007 Dec 30;26(30):5486-98
references: 17893893
references: Ann Oncol. 2006 Jun;17(6):935-44
references: 16603601
references: J Clin Oncol. 2011 Oct 20;29(30):4014-21
references: 21911717
references: BMC Med Res Methodol. 2012 Jun 24;12:86
references: 22726307
references: Stat Med. 1989 May;8(5):551-61
references: 2657958
references: Stat Med. 2012 May 20;31(11-12):1089-97
references: 21953401
references: J Clin Oncol. 2007 Sep 1;25(25):3808-15
references: 17664460
references: J Am Coll Cardiol. 2011 Jan 25;57(4):445-52
references: 21251585
references: N Engl J Med. 2012 Apr 5;366(14):1310-8
references: 22475594
references: Biometrics. 1995 Jun;51(2):524-32
references: 7662841
references: Stat Med. 2007 Feb 28;26(5):1170-80
references: 16900556
references: Am J Epidemiol. 2009 Jul 15;170(2):244-56
references: 19494242
references: J Clin Oncol. 2010 Jan 10;28(2):311-7
references: 19933918
references: Stat Med. 2002 Aug 15;21(15):2175-97
references: 12210632
references: Cancer. 2011 Mar 1;117(5):1089-96
references: 20960504
references: Cancer Epidemiol. 2011 Dec;35(6):526-33
references: 21606014
references: Radiother Oncol. 2011 Aug;100(2):167-75
references: 21752480
references: J Clin Oncol. 2011 Jun 10;29(17):2301-4
references: 21555693
references: Biometrics. 1978 Dec;34(4):541-54
references: 373811
references: Biometrics. 1998 Mar;54(1):219-28
references: 9544517
references: J Natl Cancer Inst. 2007 Mar 7;99(5):365-75
references: 17341728
references: J Clin Oncol. 2009 Sep 10;27(26):4239-46
references: 19667275
references: Int J Epidemiol. 2012 Jun;41(3):861-70
references: 22253319
references: Br J Cancer. 2004 Oct 4;91(7):1229-35
references: 15305188
references: Am J Epidemiol. 2009 Aug 15;170(4):472-83
references: 19596711
references: Am J Epidemiol. 2011 Feb 1;173(3):319-29
references: 21135028