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Cited by 139Pneumonia and Respiratory InfectionsStatistical Methods in EpidemiologyStatistical Methods in Clinical Trials

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How to handle mortality when investigating length of hospital stay and time to clinical stability

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Brock, Guy N, Barnes, Christopher, Ramirez, Julio A, Myers, John·2011·BMC Medical Research Methodology
DOI 10.1186/1471-2288-11-144PMC PMC3269825
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Abstract

BACKGROUND: Hospital length of stay (LOS) and time for a patient to reach clinical stability (TCS) have increasingly become important outcomes when investigating ways in which to combat Community Acquired Pneumonia (CAP). Difficulties arise when deciding how to handle in-hospital mortality. Ad-hoc approaches that are commonly used to handle time to event outcomes with mortality can give disparate results and provide conflicting conclusions based on the same data. To ensure compatibility among studies investigating these outcomes, this type of data should be handled in a consistent and appropriate fashion. METHODS: Using both simulated data and data from the international Community Acquired Pneumonia Organization (CAPO) database, we evaluate two ad-hoc approaches for handling mortality when estimating the probability of hospital discharge and clinical stability: 1) restricting analysis to those patients who lived, and 2) assigning individuals who die the "worst" outcome (right-censoring them at the longest recorded LOS or TCS). Estimated probability distributions based on these approaches are compared with right-censoring the individuals who died at time of death (the complement of the Kaplan-Meier (KM) estimator), and treating death as a competing risk (the cumulative incidence estimator). Tests for differences in probability distributions based on the four methods are also contrasted. RESULTS: The two ad-hoc approaches give different estimates of the probability of discharge and clinical stability. Analysis restricted to patients who survived is conceptually problematic, as estimation is conditioned on events that happen at a future time. Estimation based on assigning those patients who died the worst outcome (longest LOS and TCS) coincides with the complement of the KM estimator based on the subdistribution hazard, which has been previously shown to be equivalent to the cumulative incidence estimator. However, in either case the time to in-hospital mortality is ignored, preventing simultaneous assessment of patient mortality in addition to LOS and/or TCS. The power to detect differences in underlying hazards of discharge between patient populations differs for test statistics based on the four approaches, and depends on the underlying hazard ratio of mortality between the patient groups. CONCLUSIONS: Treating death as a competing risk gives estimators which address the clinical questions of interest, and allows for simultaneous modelling of both in-hospital mortality and TCS / LOS. This article advocates treating mortality as a competing risk when investigating other time related outcomes.

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Figure 1 Competing risks framework for discharge and in-hospital mortality. Diagram illustrating the competing risks framework, with discharge and in-hospital mortality as the two competing events with transition hazards α01(t) and α02(t), respectively.
Figure 1 Competing risks framework for discharge and in-hospital mortality. Diagram illustrating the competing risks framework, with discharge and in-hospital mortality as the two competing events with transition hazards α01(t) and α02(t), respectively.CC BY · PubMed Central
Figure 2 Estimates for probability of hospital discharge. Four different estimators for the probability of hospital discharge, for elderly patients hospitalized with CAP with PSI Risk Class V. The four approaches outlined in the text were used: cumulative incidence estimator and complement of the Kaplan-Meier estimator when patients who died were censored at the longest LOS value of 30 days (CI^dis(t) and 1-Ŝdis^W(t), purple line), complement of the Kaplan-Meier estimator (1-Ŝdis(t), green line), and complement of the Kaplan-Meier estimator restricted to only patients who survived (1-Ŝdis^R(t), orange line).
Figure 2 Estimates for probability of hospital discharge. Four different estimators for the probability of hospital discharge, for elderly patients hospitalized with CAP with PSI Risk Class V. The four approaches outlined in the text were used: cumulative incidence estimator and complement of the Kaplan-Meier estimator when patients who died were censored at the longest LOS value of 30 days (CI^dis(t) and 1-Ŝdis^W(t), purple line), complement of the Kaplan-Meier estimator (1-Ŝdis(t), green line), and complement of the Kaplan-Meier estimator restricted to only patients who survived (1-Ŝdis^R(t), orange line).CC BY · PubMed Central
Figure 3 Cumulative incidence curves for discharge and in-hospital mortality. Estimated cumulative incidence curves for hospital discharge and in-hospital mortality, for elderly patients hospitalized with CAP with PSI Risk Class of IV or V.
Figure 3 Cumulative incidence curves for discharge and in-hospital mortality. Estimated cumulative incidence curves for hospital discharge and in-hospital mortality, for elderly patients hospitalized with CAP with PSI Risk Class of IV or V.CC BY · PubMed Central
Figure 4 Probability of hospital discharge from simulated data. Median values of each estimation method for the probability of hospital discharge, based on 1,000 simulations, as detailed in the 'Simulated Data' section of the Methods. The underlying cumulative incidence curves are shown in solid black lines. Median estimates of the restricted analysis estimator 1-Ŝdis^R(t) (top left panel, orange curve) and the complement of the Kaplan-Meier estimator 1-Ŝdis^W(t) (top right panel, green curve) each overestimate the probability of discharge. Median estimates from the cumulative incidence estimator CI^dis(t) (purple, lower left panel) and the worst outcome estimator 1-Ŝdis^W(t) (blue, lower right panel) coincided exactly with the true cumulative incidence function, as was expected. Shaded polygons give the 97.5% and 2.5% percentiles of the estimates from the simulations, for each time point.
Figure 4 Probability of hospital discharge from simulated data. Median values of each estimation method for the probability of hospital discharge, based on 1,000 simulations, as detailed in the 'Simulated Data' section of the Methods. The underlying cumulative incidence curves are shown in solid black lines. Median estimates of the restricted analysis estimator 1-Ŝdis^R(t) (top left panel, orange curve) and the complement of the Kaplan-Meier estimator 1-Ŝdis^W(t) (top right panel, green curve) each overestimate the probability of discharge. Median estimates from the cumulative incidence estimator CI^dis(t) (purple, lower left panel) and the worst outcome estimator 1-Ŝdis^W(t) (blue, lower right panel) coincided exactly with the true cumulative incidence function, as was expected. Shaded polygons give the 97.5% and 2.5% percentiles of the estimates from the simulations, for each time point.CC BY · PubMed Central

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Metadata

Authors
Brock, G. N., Barnes, C., Ramirez, J. A., & Myers, J.
Affiliations
University of Louisville (US)
Corresponding author
  • Brock, Guy N
  • Myers, John
ORCID
Venue
BMC Medical Research Methodology
Publisher
Springer Science and Business Media LLC
Published
2011-10-26
Volume
11
Issue
1
Pages
144-144
ISSN
1471-2288 (ISSN-L)
DOI
10.1186/1471-2288-11-144
PMC
PMC3269825
OpenAlex
W1965493147
Cited by
138
References
58
Citations by year
2026: 6 · 2025: 10 · 2024: 12 · 2023: 10 · 2022: 24 · 2021: 19 · 2020: 17 · 2019: 8 · 2018: 8 · 2017: 13 · 2016: 5 · 2015: 5
FWCI
0.00
Type
journal article
Language
en
Open access
Licence
Locations
  • BMC Medical Research Methodology (publishedVersion, cc-by)
  • Europe PMC (PubMed Central) (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
Funders
  • National Institutes of Health (ES014443)
  • U.S. Public Health Service (P02 728 0800015499, RSGHP-09-099-01)
  • National Institute of Environmental Health Sciences (P30ES014443)
  • National Institute of Dental and Craniofacial Research (P20-RR/DE177702)
  • National Institute for Occupational Safety and Health (1r03oh008957-01a2)
Topics
  • Health Sciences › Medicine › Epidemiology › Pneumonia and Respiratory Infections
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
Keywords
community-acquired pneumonia, length of hospital stay, time to clinical stability, in-hospital mortality, competing risks, right censoring, hospital discharge, time-to-event outcomes, Kaplan-Meier estimator, statistical power
MeSH terms
Algorithms, Computer Simulation, Follow-Up Studies, Humans, Length of Stay, Patient Discharge, Pneumonia, Risk Factors, Time Factors, Models, Statistical, Treatment Outcome, Hospital Mortality, Community-Acquired Infections, Kaplan-Meier Estimate

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