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

ISARIC4C Investigators; Ruth Keogh; Karla Diaz-Ordaz; Nicholas P. Jewell; Malcolm G. Semple; Liesbeth C. de Wreede; Hein Putter

doi:10.1007/s10985-022-09586-0

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

ISARIC4C Investigators, Ruth Keogh^*, Karla Diaz-Ordaz, Nicholas P. Jewell, Malcolm G. Semple, Liesbeth C. de Wreede, Hein Putter

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	288–317
Number of pages	30
Journal	Lifetime Data Analysis
Volume	29
Early online date	8 Feb 2023
DOIs	https://doi.org/10.1007/s10985-022-09586-0
Publication status	Published - Apr 2023

Bibliographical note

Funding:
RHK is funded by A UK Research and Innovation Future Leaders Fellowship (MR/S017968/1). KDO is supported by a Royal Society-Wellcome Trust Sir Henry Dale Fellowship (218554/Z/19/Z). ISARIC CCP UK is supported by grants from: the National Institute for Health Research (NIHR; award CO-CIN-01), the Medical Research Council (MRC; grant MC_PC_19059), and by the NIHR Health Protection Research Unit (HPRU) in Emerging and Zoonotic Infections at University of Liverpool in partnership with Public Health England (PHE), in collaboration with Liverpool School of Tropical Medicine and the University of Oxford (award 200907), NIHR HPRU in Respiratory Infections at Imperial College London with PHE (award 200927), and NIHR Clinical Research Network for providing infrastructure support for this research. The views expressed are those of the authors and not necessarily those of the NIHR, MRC, or PHE.

Keywords

Multi-state model
Length of stay
Covid-19
Illness-death model
State occupation

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10.1007/s10985-022-09586-0

https://livrepository.liverpool.ac.uk/3168919/

Cite this

@article{19e92b5cd29743c78c74d80cc6012b53,

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

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 {\textquoteleft}length of stay{\textquoteright}, 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 {\textquoteleft}conditional length of stay{\textquoteright}. 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{\textquoteright} 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.",

keywords = "Multi-state model, Length of stay, Covid-19, Illness-death model, State occupation",

author = "{ISARIC4C Investigators} and Ruth Keogh and Karla Diaz-Ordaz and Jewell, {Nicholas P.} and Semple, {Malcolm G.} and Wreede, {Liesbeth C. de} and Hein Putter and Christopher Green",

note = "Funding: RHK is funded by A UK Research and Innovation Future Leaders Fellowship (MR/S017968/1). KDO is supported by a Royal Society-Wellcome Trust Sir Henry Dale Fellowship (218554/Z/19/Z). ISARIC CCP UK is supported by grants from: the National Institute for Health Research (NIHR; award CO-CIN-01), the Medical Research Council (MRC; grant MC_PC_19059), and by the NIHR Health Protection Research Unit (HPRU) in Emerging and Zoonotic Infections at University of Liverpool in partnership with Public Health England (PHE), in collaboration with Liverpool School of Tropical Medicine and the University of Oxford (award 200907), NIHR HPRU in Respiratory Infections at Imperial College London with PHE (award 200927), and NIHR Clinical Research Network for providing infrastructure support for this research. The views expressed are those of the authors and not necessarily those of the NIHR, MRC, or PHE.",

year = "2023",

month = apr,

doi = "10.1007/s10985-022-09586-0",

language = "English",

volume = "29",

pages = "288–317",

journal = "Lifetime Data Analysis",

issn = "1380-7870",

publisher = "Springer",

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AU - ISARIC4C Investigators

AU - Keogh, Ruth

AU - Diaz-Ordaz, Karla

AU - Jewell, Nicholas P.

AU - Semple, Malcolm G.

AU - Wreede, Liesbeth C. de

AU - Putter, Hein

AU - Green, Christopher

N1 - Funding: RHK is funded by A UK Research and Innovation Future Leaders Fellowship (MR/S017968/1). KDO is supported by a Royal Society-Wellcome Trust Sir Henry Dale Fellowship (218554/Z/19/Z). ISARIC CCP UK is supported by grants from: the National Institute for Health Research (NIHR; award CO-CIN-01), the Medical Research Council (MRC; grant MC_PC_19059), and by the NIHR Health Protection Research Unit (HPRU) in Emerging and Zoonotic Infections at University of Liverpool in partnership with Public Health England (PHE), in collaboration with Liverpool School of Tropical Medicine and the University of Oxford (award 200907), NIHR HPRU in Respiratory Infections at Imperial College London with PHE (award 200927), and NIHR Clinical Research Network for providing infrastructure support for this research. The views expressed are those of the authors and not necessarily those of the NIHR, MRC, or PHE.

PY - 2023/4

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N2 - 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.

AB - 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.

KW - Multi-state model

KW - Length of stay

KW - Covid-19

KW - Illness-death model

KW - State occupation

U2 - 10.1007/s10985-022-09586-0

DO - 10.1007/s10985-022-09586-0

M3 - Article

SN - 1380-7870

VL - 29

SP - 288

EP - 317

JO - Lifetime Data Analysis

JF - Lifetime Data Analysis

ER -

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

Abstract

Bibliographical note

Keywords

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