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Sampling Bias in Population Studies—How to Use the Lexis Diagram

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  • Jens Lund

Abstract

Modified versions of the lifetime distribution are often used in survival analysis. The modifications depend on how we choose individuals for the study and on the assumptions on the behaviour of the population. A rigorous point process description of the Lexis diagram is used to make the sampling mechanisms and the preconditions transparent. The point process description gives a framework to handle all possible sampling patterns. The set‐up is generalized so it can handle more complicated life descriptions than just lifetimes, and the diability model is used as an example. Two set‐ups can be used. Conditional on the birthtimes, the lifetime distribution is left truncated and subject to either right censoring or right truncation. Assuming that the birthtimes can be described by a Poisson process the modifications are length bias and the recurrence time distribution known from renewal theory.

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  • Jens Lund, 2000. "Sampling Bias in Population Studies—How to Use the Lexis Diagram," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 589-604, December.
    • Handle: RePEc:bla:scjsta:v:27:y:2000:i:4:p:589-604
    DOI: 10.1111/1467-9469.00210
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    Cited by:

    1. Elodie Brunel & Fabienne Comte & Agathe Guilloux, 2008. "Estimation Strategies for Censored Lifetimes with a Lexis‐Diagram Type Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 557-576, September.
    2. Jean-Yves Dauxois & Agathe Guilloux, 2004. "Estimating the Cumulative incidence Functions under Length-biased Sampling," Working Papers 2004-01, Center for Research in Economics and Statistics.
    3. van Santen, Eric, 2010. "Predictors of exit type and length of stay in non-kinship family foster care -- The German experience," Children and Youth Services Review, Elsevier, vol. 32(10), pages 1211-1222, October.
    4. Jean-Yves Dauxois & Agathe Guilloux & Syed N. U. A. Kirmani, 2004. "Estimation in a Competing Risks Proportional Hazards Model Under Length-biased Sampling with Censoring," Working Papers 2004-02, Center for Research in Economics and Statistics.
    5. Dauxois, Jean-Yves & Guilloux, Agathe, 2008. "Nonparametric inference under competing risks and selection-biased sampling," Journal of Multivariate Analysis, Elsevier, vol. 99(4), pages 589-605, April.

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