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Estimating distribution of length of stay in a multi-state model conditional on the pathway, with an application to patients hospitalised with Covid-19

Author

Listed:
  • Ruth H. Keogh

    (London School of Hygiene and Tropical Medicine)

  • Karla Diaz-Ordaz

    (London School of Hygiene and Tropical Medicine)

  • Nicholas P. Jewell

    (London School of Hygiene and Tropical Medicine)

  • Malcolm G. Semple

    (University of Liverpool)

  • Liesbeth C. de Wreede

    (Leiden University Medical Center)

  • Hein Putter

    (Leiden University Medical Center)

Abstract

Multi-state models are used to describe how individuals transition through different states over time. The distribution of the time spent in different states, referred to as ‘length of stay’, is often of interest. Methods for estimating expected length of stay in a given state are well established. The focus of this paper is on the distribution of the time spent in different states conditional on the complete pathway taken through the states, which we call ‘conditional length of stay’. This work is motivated by questions about length of stay in hospital wards and intensive care units among patients hospitalised due to Covid-19. Conditional length of stay estimates are useful as a way of summarising individuals’ transitions through the multi-state model, and also as inputs to mathematical models used in planning hospital capacity requirements. We describe non-parametric methods for estimating conditional length of stay distributions in a multi-state model in the presence of censoring, including conditional expected length of stay (CELOS). Methods are described for an illness-death model and then for the more complex motivating example. The methods are assessed using a simulation study and shown to give unbiased estimates of CELOS, whereas naive estimates of CELOS based on empirical averages are biased in the presence of censoring. The methods are applied to estimate conditional length of stay distributions for individuals hospitalised due to Covid-19 in the UK, using data on 42,980 individuals hospitalised from March to July 2020 from the COVID19 Clinical Information Network.

Suggested Citation

  • Ruth H. Keogh & Karla Diaz-Ordaz & Nicholas P. Jewell & Malcolm G. Semple & Liesbeth C. de Wreede & Hein Putter, 2023. "Estimating distribution of length of stay in a multi-state model conditional on the pathway, with an application to patients hospitalised with Covid-19," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(2), pages 288-317, April.
    • Handle: RePEc:spr:lifeda:v:29:y:2023:i:2:d:10.1007_s10985-022-09586-0
    DOI: 10.1007/s10985-022-09586-0
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    References listed on IDEAS

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    1. de Wreede, Liesbeth C. & Fiocco, Marta & Putter, Hein, 2011. "mstate: An R Package for the Analysis of Competing Risks and Multi-State Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 38(i07).
    2. Jan Beyersmann & Hein Putter, 2014. "A note on computing average state occupation times," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 30(62), pages 1681-1696.
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