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General Departmental Seminar Series

Prevalent Cohorts

Niels Keiding, PhD
Department of Biostatistics, Institute of Public Health
University of Copenhagen

February 9, 2005, 4-5 pm in room 140 Bardeen Medical Laboratories (1300 University Ave.)


Individuals move between states with calendar time and duration since some time origin (birth, disease onset, treatment assignment, initiating time for attempting to get pregnant). At a certain point in calendar time all or a sample of individuals in a particular state are identified (the prevalent cohort). Information on incidence and mortality may be obtained from information in the cross-section alone, or from various combinations of prospective or retrospective follow-up. The Lexis diagram (Keiding, 1990, 1991, 2000, Lund, 2000) is helpful here.

Cross-section only:

-- current status data (application: rubella incidence based on seroprevalence data). Keiding et al. (1996)

Retrospective follow-up:

-- current duration (application: time to pregnancy). Keiding et al. (2002)

-- retrospective estimation of incidence, invoking Horvitz-Thompson type weights from additional survival information (application: diabetes incidence in Fyn 1933-73 based on prevalent sample in 1973). Keiding et al. (1989), Ogata et al. (2000)

-- retrospectively observed interaction between two life history events, allowing non-symmetric dependence concepts (application: pustulosis palmo-plantaris and menopause). Aalen et al. (1980)

Prospective follow-up:

-- mortality estimation from prevalent cohort studies from forward recurrence times, length-biased data or delayed entry analysis (application: survival of diabetics based on follow-up of the prevalent sample from 1973). Keiding (1992)

-- confirmatory analysis of a possible chance finding at an interim analysis of a clinical trial with staggered entry, obtaining by reusing, with delayed entry, the survivors from the interim analysis (application: breast cancer trial). Keiding et al. (1987), Parner and Keiding (2001)

-- estimation of incidence and prevalence from pharmacoepidemiological databases (Hallas et al. 1997)


Aalen, O.O., Borgan, Ø., Keiding, N. & Thormann, J. (1980). Interaction between life history events. Nonparametric analysis for prospective and retrospective data in the presence of censoring. Scand.J.Statist. 7, 161-171.

Andersen, P.K., Borgan, Ø., Gill, R.D. & Keiding, N. (1993). Statistical Models Based on Counting Processes. New York: Springer, 767 pp.

Andersen, P.K. & Keiding, N. (2001). Event history analysis in continuous time. Internat.Encycl. Social & Behavioral Sciences (ed. N.J. Smelser & P.B. Baltes) 7, 4946-4956. Oxford: Elsevier.

Hallas, J., Gaist, D. & Bjerrum, L. (1997). The waiting time distribution as a graphical approach to epidemiological measures of drug utilization. Epidemiology 8, 666-670.

Keiding, N. (1990). Statistical inference in the Lexis diagram. Phil.Trans.Roy.Soc.Land. A 332, 487-509.

Keiding, N. (1991). Age-specific incidence and prevalence: a statistical perspective (with discussion). J.Roy.Statist.Soc. A 154, 371-412.

Keiding, N. (1992). Independent delayed entry (with discussion). Survival Analysis: State of the Art (eds. J.P. Klein & P.K. Goel). Kluwer, Dordrecht, 309-326.

Keiding, N. (2000). Graphical representations in mortality measurement: Knapp, Zeuner, Becker, Lexis. Research Report 00/8, Department of Biostatistics, University of Copenhagen.

Keiding, N., Bayer, T. & Watt-Boolsen, S. (1987). Confirmatory analysis of survival data using left truncation of the life times of primary survivors. Statist. in Medicine 6, 939-944.

Keiding, N., Begtrup, K., Scheike, T.H. & Hasibeder, G. (1996). Estimation from current-status data in continuous time. Lifetime Data Analysis 2, 119-129.

Keiding, N. & Gill, R.D. (1990). Random truncation models and Markov processes. Ann.Statist. 18, 582-602.

Keiding, N., Holst, C. & Green, A. (1989). Retrospective estimation of diabetes incidence from information in a current prevalent population and historical mortality. Amer.J.Epid. 130, 588-600.

Keiding, N., Kvist, K., Hartvig, H., Tvede, M. & Juul, S. (2002). Estimating time to pregnancy from current durations in a cross-sectional sample. Biostatistics 3, 565-578.

Lund, J. (2000). Sampling bias in population studies how to use the Lexis diagram. Scand.J.Statist. 27, 589-604.

Ogata, Y., Katsura, K., Keiding, N., Holst, C. & Green, A. (2000). Empirical Bayes age-period-cohort analysis of retrospective incidence data. Scand.J.Statist. 27, 415-432.

Parner, E.T. & Keiding, N. (2001). Misspecified proportional hazard models and confirmatory analysis of survival data. Biometrika 88, 459-468.

Wang, M.-C. (1991). Nonparametric estimation from cross-sectional survival data. J.Amer.Statist.Assoc. 86, 130-143.

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