title: Parametric survival densities from phase-type models.
abstract: After a brief historical survey of parametric survival models, from actuarial, biomedical, demographical and engineering sources, this paper discusses the persistent reasons why parametric models still play an important role in exploratory statistical research. The phase-type models are advanced as a flexible family of latent-class models with interpretable components. These models are now supported by computational statistical methods that make numerical calculation of likelihoods and statistical estimation of parameters feasible in theory for quite complicated settings. However, consideration of Fisher Information and likelihood-ratio type tests to discriminate between model families indicates that only the simplest phase-type model topologies can be stably estimated in practice, even on rather large datasets. An example of a parametric model with features of mixtures, multiple stages or 'hits', and a trapping-state is given to illustrate simple computational tools in R, both on simulated data and on a large SEER 1992-2002 breast-cancer dataset.
authors: Census Bureau CSRM, Washington, DC, USA, Eric.V.Slud@census.gov.
authors: Eric V
authors: EV
authors: Slud
authors: Jiraphan
authors: J
authors: Suntornchost
mesh_terms: D001943:Breast Neoplasms / Q000401:mortality; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D008390:Markov Chains; D015233:Models, Statistical; D016019:Survival Analysis
references: Philos Trans R Soc Lond B Biol Sci. 2015 Apr 19;370(1666):
references: 25750242
references: J Natl Cancer Inst. 1980 Jan;64(1):9-16
references: 6928051
references: Breast Cancer Res Treat. 2006 Nov;100(1):121-6
references: 16685588
references: Br J Cancer. 1954 Mar;8(1):1-12
references: 13172380
references: Proc Natl Acad Sci U S A. 1971 Apr;68(4):820-3
references: 5279523
references: Int J Epidemiol. 2004 Dec;33(6):1182-3
references: 15319398
references: Demography. 2005 Feb;42(1):23-49
references: 15782894