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

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.

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 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 (${\widehat{CI}}_{dis}\left(t\right)$ and $1-{Ŝ}_{dis}^W\left(t\right)$, purple line), complement of the Kaplan-Meier estimator ($1-{Ŝ}_{dis}\left(t\right)$, green line), and complement of the Kaplan-Meier estimator restricted to only patients who survived ($1-{Ŝ}_{dis}^R\left(t\right)$, orange line).

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 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 $1-{Ŝ}_{dis}^R\left(t\right)$ (top left panel, orange curve) and the complement of the Kaplan-Meier estimator $1-{Ŝ}_{dis}^W\left(t\right)$ (top right panel, green curve) each overestimate the probability of discharge. Median estimates from the cumulative incidence estimator ${\widehat{CI}}_{dis}\left(t\right)$ (purple, lower left panel) and the worst outcome estimator $1-{Ŝ}_{dis}^W\left(t\right)$ (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.