IDEAS home Printed from https://ideas.repec.org/a/bpj/apjrin/v7y2012i1p1-24n6.html
   My bibliography  Save this article

Survival Analysis of Left Truncated Income Protection Insurance Data

Author

Listed:
  • LIU QING

    (The University of Melbourne)

  • Pitt David

    (Macquarie University)

  • Wang Yan

    (RMIT)

  • Wu Xueyuan

    (The University of Melbourne)

Abstract

One of the main characteristics of Income Protection Insurance (IPI) claim duration data, which has not been considered in the actuarial literature on the topic, is left-truncation. Claimants that are observed are those whose sickness durations are longer than the deferred periods specified in the policies, and hence left-truncation exists in these data. This paper investigates a series of conditional mixture models when applying survival analysis to model sickness durations of IPI claimants, and examines the consequence of treating the IPI data with lengthy deferred periods as complete data and therefore ignoring the left-truncation by fitting the corresponding unconditional distributions. It also quantifies the extent of the bias in the resulting parameter estimates when ignoring the left-truncation in the data. Using the UK Continuous Mortality Investigation (CMI) sickness duration data, some well-fitting survival model results are estimated. It is demonstrated that ignoring the left-truncation in certain IPI data can lead to substantially different statistical estimates. We therefore suggest taking left-truncation into account by fitting conditional mixture distributions to IPI data. Furthermore, the best fitting model is extended by introducing a number of covariates into the conditional part to do regression analysis.

Suggested Citation

  • LIU QING & Pitt David & Wang Yan & Wu Xueyuan, 2012. "Survival Analysis of Left Truncated Income Protection Insurance Data," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 7(1), pages 1-24, December.
    • Handle: RePEc:bpj:apjrin:v:7:y:2012:i:1:p:1-24:n:6
    DOI: 10.1515/2153-3792.1165
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/2153-3792.1165
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/2153-3792.1165?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Anna Chernobai & Krzysztof Burnecki & Svetlozar Rachev & Stefan Trück & Rafał Weron, 2006. "Modelling catastrophe claims with left-truncated severity distributions," Computational Statistics, Springer, vol. 21(3), pages 537-555, December.
    2. Pitt, D. G. W., 2007. "Modelling the Claim Duration of Income Protection Insurance Policyholders using Parametric Mixture Models," Annals of Actuarial Science, Cambridge University Press, vol. 2(1), pages 1-24, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Härdle, Wolfgang Karl & Burnecki, Krzysztof & Weron, Rafał, 2004. "Simulation of risk processes," Papers 2004,01, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    2. Keighley, Tim & Longden, Thomas & Mathew, Supriya & Trück, Stefan, 2014. "Quantifying Catastrophic and Climate Impacted Hazards Based on Local Expert Opinions," Climate Change and Sustainable Development 189171, Fondazione Eni Enrico Mattei (FEEM).
    3. Krzysztof Burnecki & Rafal Weron, 2006. "Visualization tools for insurance risk processes," HSC Research Reports HSC/06/06, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    4. Burnecki, Krzysztof & Janczura, Joanna & Weron, Rafal, 2010. "Building Loss Models," MPRA Paper 25492, University Library of Munich, Germany.
    5. Burnecki, Krzysztof & Misiorek, Adam & Weron, Rafal, 2010. "Loss Distributions," MPRA Paper 22163, University Library of Munich, Germany.
    6. Giuricich, Mario Nicoló & Burnecki, Krzysztof, 2019. "Modelling of left-truncated heavy-tailed data with application to catastrophe bond pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 498-513.
    7. Jo†Yu Wang & Wen†Lin Wu & Yang†Che Wu & Ming Jing Yang, 2017. "How To Manage Long†term Financial Self†sufficiency of a National Catastrophe Insurance Fund? The Feasibility of Three Bailout Programmes," European Financial Management, European Financial Management Association, vol. 23(5), pages 951-974, October.
    8. Martel-Escobar, M. & Hernández-Bastida, A. & Vázquez-Polo, F.J., 2012. "On the independence between risk profiles in the compound collective risk actuarial model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(8), pages 1419-1431.
    9. Yang‐Che Wu & Ming Jing Yang, 2018. "The effectiveness of asset, liability and equity hedging against catastrophe risk: the cases of winter storms in North America and Europe," European Financial Management, European Financial Management Association, vol. 24(5), pages 893-918, November.
    10. Riza Andrian Ibrahim & Sukono & Herlina Napitupulu, 2022. "Multiple-Trigger Catastrophe Bond Pricing Model and Its Simulation Using Numerical Methods," Mathematics, MDPI, vol. 10(9), pages 1-17, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:apjrin:v:7:y:2012:i:1:p:1-24:n:6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.