Abstract
A natural stochastic process framework for studying disease incidence is the simple illness-death model
where the incidence α(a) and the mortality μ(a) of healthy individuals depend on age a only whereas the mortality ν(a, d) of diseased individuals may in addition depend on d, the duration in the diseased state (Keiding, 1986a,b, 1989; Newman, 1988)
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aalen, O.O., Nonparametric inference for a family of counting processes, Ann. Statist. 6 (1978), 701-726.
Andersen, P.K., Borch-Johnsen, K., Deckert, T., Green, A., Hougaard, P., Keiding, N. and Kreiner, S., A Cox regression model for the relative mortality and its application to diabetes mellitus survivial data, Biometrics 41 (1985), 921 - 932.
Andersen, P.K. and Borgan, 0., Counting process models for life history data: A review (with discussion), Scand. J. Statist. 12 (1985), 97 - 158.
Brillinger, D.R., The natural variability of vital rates and associated statistics {with discussion),
Biometrics 42 (1986), 693-734.
Dempster, A.P., Laird, N.M. and Rubin, D.B., Maximum likelihood from incomplete data via the EM algorithm (with discussion), J. Roy. Statist. Soc. B 39 (1977), 1 - 38.
Green, A., Borch-Johnsen, K., Andersen, P.K., Hougaard, P., Keiding, N., Kreiner, S. and Deckert, T., Relative mortality of type 1 (insulin dependent) diabetes in Denmark: 1933-1981, Diabetologia 28 (1985), 339 - 342.
Green, A., Hauge, M., Holm, N.V., and Rasch, L.L., Epidemiological studies of diabetes mellitus in Denmark: II. A prevalence study based on insulin prescriptions, Diabetologia 20 (1981), 468 - 470.
Green, A. and Hougaard, P., Epidemiological studies of diabetes mellitus in Denmark: 5. Mortality and causes of death among insulin-treated diabetic patients, Diabetologia 26 (1984), 190 - 194.
Groeneboom, P., Asymptotics for incomplete censored observations, Department of Mathematics, University of Amsterdam, Report 87 - 18 (1987).
Keiding, N., The epidemiological information in a cross-sectional sample: A statistical perspective, Statistical Research Unit, University of Copenhagen, Research Report 86 /3 (1986a).
Keiding, N., Discussion of D.R. Brillinger: The natural variability of vital rates and associated statistics, Biometrics 42 (1986b), 721 - 724.
Keiding, N., Estimation of age-specific incidence from cross-sectional data, In preparation.
Keiding, N. and Gill, R.D., Random truncation models and Markov processes, Ann. Statist. (to appear ). (1989).
Keiding, N., Holst, C. and Green, A., Retrospective estimation of diabetes incidence from information in a current prevalent population and historical mortality, Amer. J. Epidemiol. (to appear ). (1989).
Newman, S.C., Odds ratio estimation in a steady-state population, J. Clin. Epidemiol. 41 (1988), 59 - 65.
Ramlau-Hansen, H., Smoothing counting process intensities by means of kernel functions, Ann. Statist. 11 (1983), 453 - 466.
Ramlau-Hansen, H., Jespersen, N.C.B., Andersen, P.K., Borch-Johnsen. I\., and Deckert, T., Life insurance for insulin-dependent diabetics, Scand. Act. J. 1-2 (1987), 19 - 36.
Turnbull, B.W., The empirical distribution function with arbitrarily grouped, censored and truncated data, J. Roy. Statist. Soc. B 38 (1976), 290 - 295.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Keiding, N., Hansen, B.E., Holst, C. (1990). Nonparametric estimation of disease incidence from a cross-sectional sample of a stationary population. In: Gabriel, JP., Lefèvre, C., Picard, P. (eds) Stochastic Processes in Epidemic Theory. Lecture Notes in Biomathematics, vol 86. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10067-7_4
Download citation
DOI: https://doi.org/10.1007/978-3-662-10067-7_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-52571-4
Online ISBN: 978-3-662-10067-7
eBook Packages: Springer Book Archive