Modelling healthcare systems with phase-type distributions

Health Care Management Science

Volumn 12, Issue 1, 2009, Pages 11-26

  Fackrell, Mark ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Coxian distribution; Healthcare modelling; Markov chain; Patient flow; Phase type distribution

Indexed keywords

ARTICLE; HEALTH CARE DELIVERY; HEALTH CARE SURVEY; NONBIOLOGICAL MODEL; PATIENT TRANSPORT; PROBABILITY; STATISTICS; STATISTICS AND NUMERICAL DATA;

DELIVERY OF HEALTH CARE; HEALTH CARE SURVEYS; MARKOV CHAINS; MODELS, ORGANIZATIONAL; PATIENT TRANSFER;

EID: 59149090726     PISSN: 13869620     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10729-008-9070-y     Document Type: Article

References (52)

1. S Asmussen 1997
2. Asmussen S (2003) Applied probability and queues, 2nd edn. Springer, Berlin Heidelberg New York
3. S Asmussen O Nerman M Olsson 1996 Fitting phase-type distributions via the EM algorithm Scand J Statist 23 419 441
4. S Asmussen M Olsson 1998
5. Au L, Byrnes GB, Bain CA, Fackrell M, Brand C, Campbell DA, Taylor PG (2008) Predicting overflow in an emergency department. IMA J Manag Math (in press)
6. Bini DA, Latouche G, Meini B (2005) Numerical methods for structured Markov chains. Oxford University Press, Oxford
7. A Bobbio A Cumani 1992
8. DR Cox 1955 A use of complex probabilities in the theory of stochastic processes Proc Camb Philos Soc 5 313 319
9. A Cumani 1982 On the canonical representation of homogeneous Markov processes modelling failure-time distributions Microelectron Reliab 22 583 602
10. AP Dempster NL Laird DB Rubin 1977 Maximum likelihood from incomplete data via the EM algorithm With discussion. J R Stat Soc Ser B 39 1 38
11. AK Erlang 1917-1918 Solution of some problems in the theory of probabilities of significance in automatic telephone exchanges Post Off Electr Eng J 10 189 197
12. Fackrell M (2003) Characterization of matrix-exponential distributions. PhD thesis, School of Applied Mathematics, University of Adelaide, South Australia
13. MJ Faddy 1990 Compartmental models with phase-type residence-time distributions Appl Stoch Models Data Anal 6 121 127
14. MJ Faddy 1993 A structured compartmental model for drug kinetics Biometrics 49 243 248
15. MJ Faddy 1994 Examples of fitting structured phase-type distributions Appl Stoch Models Data Anal 10 247 255
16. MJ Faddy 1995 Phase-type distributions for failure times Math Comput Model 22 63 70
17. MJ Faddy 1998 On inferring the number of phases in a Coxian phase-type distribution Commun Stat Stoch Models 14 407 417
18. MJ Faddy 2002
19. MJ Faddy SI McClean 1999 Analysing data on lengths of stay of hospital patients using phase-type distributions Appl Stoch Models Bus Ind 15 311 317
20. MJ Faddy SI McClean 2005 Markov chain modelling for geriatric patient care Methods Inf Med 44 369 373
21. MJ Faddy GT Taylor 2003 Stochastic modelling of the onset of bronchiolitis obliterans syndrome following lung transplantations: an analysis of risk factors Math Comput Model 38 1185 1189
22. F Gorunescu SI McClean PH Millard 2002 A queueing model for bed-occupancy management and planning of hospitals J Oper Res Soc 53 19 24
23. JO Gribbin SI McClean 1990 Modelling the duration of spells of withdrawal from a female dominated labour force J Appl Stat 17 369 381
24. Hampel K (1997) Modelling phase-type distributions. Honours Thesis, Department of Statistics, University of Adelaide, South Australia
25. Q-M He H Zhang 2005 A note on unicyclic representations of phase type distributions Stoch Models 21 465 483
26. A Horváth M Telek 2000
27. A Horváth M Telek 2007
28. MA Johnson 1993 Selecting parameters of phase distributions: combining nonlinear programming, heuristics, and Erlang distributions ORSA J Comput 5 69 83
29. Latouche G, Ramaswami V (1999) Introduction to matrix analytic methods in stochastic models. SIAM, Philadelphia
30. AH Marshall SI McClean 2003 Conditional phase-type distributions for modelling length of stay in hospital Int Trans Oper Res 10 565 576
31. AH Marshall C Vasilakis E El-Darzi 2005 Length of stay-based patient flow models: recent developments and future directions Health Care Manage Sci 8 213 220
32. SI McClean 1976 The two-stage model of personnel behaviour J R Stat Soc Ser A 139 205 217
33. SI McClean MJ Faddy PH Millard 2005
34. SI McClean JO Gribbin 1987 Estimation for incomplete manpower data Appl Stoch Models Data Anal 3 13 25
35. SI McClean PH Millard 1993 Patterns of length of stay after admission in geriatric medicine: an event history approach Statistician 42 263 274
36. McLachlan GJ, Krishnan T (1997) The EM algorithm and extensions. Wiley, New York
37. JA Nelder R Mead 1965 A simplex method for function minimization Comput J 7 308 313
38. Neuts MF (1975) Probability distributions of phase-type. In: Liber amicorum Prof. Emeritus H. Florin, Department of Mathematics, University of Louvain, Louvain, pp 173-206
39. Neuts MF (1981) Matrix-geometric solutions in stochastic models: an algorithmic approach. The John Hopkins University Press, Baltimore
40. MF Neuts 1984 The abscissa of convergence of the Laplace-Stieltjes transform of a PH distribution Commun Stat Simul Comput 13 367 373
41. Neuts MF (1989) Structured stochastic matrices of M/G/1 type and their applications. Marcel Dekkar, New York
42. Neuts MF (1995) Algorithmic probability. Chapman and Hall, London
43. Norris JR (1997) Markov chains. Cambridge University Press, Cambridge
44. CA O'Cinneide 1989 On non-uniqueness of representations of phase-type distributions Commun Stat Stoch Models 5 247 259
45. CA O'Cinneide 1999 Phase-type distributions: open problems and a few properties Commun Stat Stoch Models 15 731 757
46. M Olsson 1996 Estimation of phase-type distributions from censored data Scand J Statist 23 443 460
47. Ross SM (1993) Introduction to probability models, 5th edn. Academic, San Diego
48. L Schmickler 1992 MEDA: mixed Erlang distributions as phase-type representations of empirical distribution functions Commun Stat Stoch Models 8 131 156
49. Seneta E (2006) Non-negative matrices and markov chains, revised printing. Springer, New York
50. M Shaked JG Shanthikumar 1985
51. C Vasilakis AH Marshall 2005 Modelling nationwide hospital length of stay: opening the black box J Oper Res Soc 56 862 869
52. H Xie TJ Chaussalet PH Millard 2005 A continuous time Markov model for the length of stay of elderly people in institutional long-term care J R Stat Soc Ser A 168 51 61