Abstract
I first discuss the main assumptions which can be made for multi-state models: the time-homogeneity and semi-Markov assumptions, the problem of choice of the time scale, the assumption of homogeneity of the population and also assumptions about the way the observations are incomplete, leading to truncation and censoring. The influence of covariates and different durations and time-dependent variables are synthesized using explanatory processes, and a general additive model for transition intensities presented. Different inference approaches, including penalized likelihood, are considered. Finally three examples of application in epidemiology are presented and some references to other works are given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
O. O. Aalen, "Nonparametric inference for a family of counting processes," Annals of Statistics vol. 6 pp. 701–726, 1978.
O. O. Aalen, "Heterogeneity in survival analysis," Statist. Med. vol. 7 pp. 1121–113, 1988.
O. O. Aalen, V. T. Farewell, D. De Angelis, N. E. Day and O. N. Gill, "AMarkov model for HIV disease progression including the effect of HIV diagnosis and treatment: application to AIDS prediction in England and Wales," Stat Med vol. 16 pp. 2191–2210, 1997.
O. O. Aalen and S. Johansen, "An empirical transition matrix for nonhomogeneous Markov chains based on censored observations," Scandinavian Journal of Statistics vol. 5 pp. 141–150, 1978.
A. Alioum, V. Leroy, D. Commenges, F. Dabis, and R. Salamon, "Effect of gender, age, transmission category and antiretroviral therapy on the progression of HIV infection using multi-state Markov models: a prevalent cohort study, Bordeaux, France, 1985–1996," Epidemiology vol. 9 pp. 605–612, 1998a.
A. Alioum, C. Verret, D. Commenges and P. Barberger-Gateau, "Multi-state models for analysing the disablement process in the elderly," The XIXth International Biometric Conference, Cape Town, 14–18 December 1998b, pp. 6.
P. Barberger-Gateau, C. Rainville, L. Letenneur and JF. Dartigues, "A hierarchical model for description of the disablement process," Disabil Rehabil (in press) 1999.
P.K. Andersen, "Multistate models in survival analysis: a study of nephropathy and mortality in diabetes," Stat Med vol. 7 pp. 661–670, 1988.
P. K. Andersen, Ø. Borgan, R. D. Gill and N. Keiding, Statistical Models Based on Counting Processes, Springer-Verlag: New-York, 1993.
D. Commenges, L. Letenneur, P. Joly, A. Alioum and JF. Dartigues "Modelling age-specific risk: application to dementia," Stat Med vol. 17 pp. 1973–1988, 1998.
V. De Gruttola and S. W. Lagakos, "Analysis of doubly-censored survival data, with application to AIDS," Biometrics vol. 45 pp. 1–11, 1989.
H. Frydman, "A non-parametric estimation procedure for a periodically observed three-state Markov process, with application to Aids," Journal of the Royal Statistical Society, Series B vol. 54 pp. 853–866, 1992.
H. Frydman, "Semi-parametric estimation in a three-state duration-dependent Markov model from intervalcensored observations with application to AIDS," Biometrics vol. 51 pp. 502–511, 1995.
F. Ga¨uzere, D. Commenges, P. Barberger-Gateau, L. Letenneur and JF. Dartigues, "Etude de la d´ependance lourde," Population vol. 54 pp. 205–222, 1999.
R. C. Gentleman, J. F. Lawless, J. C. Lindsey and P. Yan, "Multi-state Markov models for analysing incomplete disease history data with illustrations for HIV disease," Stat Med vol. 13 pp. 805–821, 1994.
C. Gu, "Penalized likelihood hazard estimation: a general procedure," Statistica Sinica vol. 6 pp. 861–876, 1996.
S. Haberman and E. Pitacco, Actuarial models for disability insurance. Chapman & Hall/CRC: New-York, 1999.
T. J. Hastie and R. J. Tibshirani, Generalized Additive Models, Monographs on Statistics and Applied Probability 43, Chapman and Hall: London etc., 1990.
P. Hougaard, "Multi-state models. A review," Life Time Data Analysis vol. 5 pp. 239–264, 1999.
P. Joly, D. Commenges and L. Letenneur, "A penalized likelihood approach for arbitrarily censored and truncated data: application to age-specific incidence of dementia," Biometrics vol. 54 pp. 203–212, 1998.
P. Joly, D. Commenges and L. Letenneur, "Penalized likelihood approach in three-sate models: application to dementia," The XIXth International Biometric Conference, Cape Town, 14–18 December 1998, pp. 159.
P. Joly and D. Commenges, "A penalized likelihood approach for a progressive three-state model with censored and truncated data: Application to AIDS," Biometrics vol. 55 (in press) 1999.
S. Katz, T. D. Downs, H. R. Cash and R. C. Grotz, "Progress in development of the index of ADL," Gerontologist vol. 10 pp. 20–30, 1970.
R. Kay, "Multistate survival analysis: an application in breast cancer," Methods Inform Med vol. 23 pp. 157–162, 1984.
N. Keiding, "Age-specific incidence and prevalence: A statistical perspective," J. R. Statist. Soc. A vol. 154 pp. 371–396, 1991.
J. P. Klein, N. Keiding and E. A. Copelan, "Plotting summary predictions in multistate survival models: Probabilities of relapse and death in remission for bone marrow transplantation patients," Stat Med vol. 12 pp. 2315–2332, 1994.
J. P. Klein and M. L. Moeshberger, Survival Analysis, Springer, 1997.
C. Kooperberg, C. J. Stone and Y. K. Truong, "Hazard regression," J Am Stat Assoc vol. 90 pp. 78–94, 1995.
I. M. Longini, W. S. Clark, R. H. Byers, J. W. Ward, W. W. Darrow, G. F. Lemp and H. W. Hethcote, "Statistical analysis of the stages of HIV infection using a Markov model," Stat Med vol. 8 pp. 831–843, 1989.
G. Marshall and R. H. Jones, "Multi-state models and diabetic retinopathy," Stat Med vol. 14 pp. 1975–1983, 1995a.
G. Marshall and R.H.Jones, "MARKOV: A computer program for multi-state Markov models with covariables" Comp Meth Prog Biomed vol. 47 pp. 147–156, 1995b.
G. A. Satten and I. M. Longini, "Markov chains with measurement error: Estimating the "true" course of a marker of the progression of human immunodeficiency virus disease," (With discussion) J R Stat Soc, Ser C vol. 45 pp. 275–309, 1996.
G. Schulgen and M. Schumacher, "Estimation of prolongation of hospital stay attributable to nosocomial infections: New approaches based on multistate models," Lifetime Data Anal vol. 2 pp. 219–240, 1996.
F. O'Sullivan, "Fast computation of fully automated log-density and log-hazard estimators," SIAM Journal on Scientific and Statistical Computing vol. 9 pp. 363–379, 1988.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Commenges, D. Multi-state Models in Epidemiology. Lifetime Data Anal 5, 315–327 (1999). https://doi.org/10.1023/A:1009636125294
Issue Date:
DOI: https://doi.org/10.1023/A:1009636125294