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Age‐Specific Incidence and Prevalence: A Statistical Perspective

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  • Niels Keiding

Abstract

In epidemiology incidence denotes the rate of occurrence of new cases (of disease), while prevalence is the frequency in the population (of diseased people). From a statistical point of view it is useful to understand incidence and prevalence in the parameter space, incidence as intensity (hazard) and prevalence as probability, and to relate observable quantities to these via a statistical model. In this paper such a framework is based on modelling each individual's dynamics in the Lexis diagram by a simple three‐state stochastic process in the age direction and recruiting individuals from a Poisson process in the time direction. The resulting distributions in the cross‐sectional population allow a rigorous discussion of the interplay between age‐specific incidence and prevalence as well as of the statistical analysis of epidemiological cross‐sectional data. For the latter, this paper focuses on methods from modern nonparametric continuous time survival analysis, including random censoring and truncation models and estimation under monotonicity constraints. The exposition is illustrated by examples, primarily from the author's epidemiological experience.

Suggested Citation

  • Niels Keiding, 1991. "Age‐Specific Incidence and Prevalence: A Statistical Perspective," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 154(3), pages 371-396, May.
    • Handle: RePEc:bla:jorssa:v:154:y:1991:i:3:p:371-396
    DOI: 10.2307/2983150
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    Cited by:

    1. Limin X. Clegg & Mitchell H. Gail & Eric J. Feuer, 2002. "Estimating the Variance of Disease-Prevalence Estimates from Population-Based Registries," Biometrics, The International Biometric Society, vol. 58(3), pages 684-688, September.
    2. Marcia C Castro & Mathieu Maheu-Giroux & Christinah Chiyaka & Burton H Singer, 2016. "Malaria Incidence Rates from Time Series of 2-Wave Panel Surveys," PLOS Computational Biology, Public Library of Science, vol. 12(8), pages 1-26, August.
    3. Sungwook Kim & Michael P. Fay & Michael A. Proschan, 2021. "Valid and approximately valid confidence intervals for current status data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(3), pages 438-452, July.
    4. Mitchell H. Gail & Larry Kessler & Douglas Midthune & Steven Scoppa, 1999. "Two Approaches for Estimating Disease Prevalence from Population-Based Registries of Incidence and Total Mortality," Biometrics, The International Biometric Society, vol. 55(4), pages 1137-1144, December.
    5. Chantal Guihenneuc-Jouyaux & Sylvia Richardson & Ira M. Longini Jr., 2000. "Modeling Markers of Disease Progression by a Hidden Markov Process: Application to Characterizing CD4 Cell Decline," Biometrics, The International Biometric Society, vol. 56(3), pages 733-741, September.

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