the role of a step-down unit in improving patient outcomes

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The Role of a Step-Down Unit in Improving PatientOutcomes

Carri W. ChanDecision, Risk, and Operations, Columbia Business School, [email protected]

Linda V. GreenDecision, Risk, and Operations, Columbia Business School, [email protected]

Lijian LuDecision, Risk, and Operations, Columbia Business School, [email protected]

Gabriel EscobarDivision of Research, Kaiser Permanente, [email protected]

This paper examines the role of a hospital Step-Down Unit (SDU) on patient flows and patient outcomes.

An SDU provides an intermediate level of care for semi-critically ill patients who are not sick enough to

require intensive care but not stable enough to be treated in the general medical/surgical ward (ward).

Using data from 10 hospitals from a single hospital network, we use an instrumental variable approach to

estimate the impact on patient outcomes of routing patients to the SDU following Intensive Care Unit (ICU)

discharge. Our empirical findings suggest that SDU care is associated with reduced in-hospital mortality of

6%, shortened hospital length-of-stay of 1.08 days, a reduced ICU readmission rate of 4%, and a reduction in

the hospital readmission rate of 8%. We use our empirical findings to calibrate a simulation model of critical

care patient flows and examine how the size of an SDU may impact patient outcomes, even when there is

ample capacity in the ICU. There is substantial debate in the medical community regarding whether SDU

care is beneficial and, if so, how many SDU beds are needed. This work takes an important first step in

addressing these issues.

Key words : healthcare, empirical operations management, discharge controls, congestion, quality of service

History :

1. Introduction

Hospitals are responsible for the largest component of national health care expenditures and are

therefore under pressure from government and private payers to become more cost efficient. Inten-

sive care units (ICUs), which provide the highest level of care, are the most costly inpatient units

1

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to operate. The estimated annual cost of critical care in the U.S is between $121 and $263 bil-

lion, accounting for 17.4%-39% of total hospital costs (Coopersmith et al. 2012). Step-down units

(SDUs), sometimes called transitional care or intermediate care units, have been used in many

hospitals to mitigate critical care costs without jeopardizing the quality of care. SDUs provide

an intermediate level of care for semi-critically ill patients who are not severe enough to require

intensive care but not stable enough to be treated in the general medical/surgical ward (ward).

SDUs are generally less expensive to operate than ICUs due primarily to lower nurse-to-patient

ratios. While an ICU may have one nurse per one or two patients, an SDU would typically have

one nurse per three to four patients. On the other hand, SDUs are more expensive than general

wards where there are, generally, about 6 patients per nurse.

There is ongoing debate about the role of the SDU in the medical community. Those who advo-

cate the use of SDUs see them as an alternative to either maintaining larger ICUs or jeopardizing

patient care due to premature, demand-driven, discharge of patients from ICUs to general care

units. As the name suggests, the initial role of SDUs was to serve as a transition for patients after

being discharged from the ICU and our study will focus on this particular use. In practice, SDUs

are often used to treat other patients, for example, those who might have gone to an ICU but were

blocked because the ICU was full. In general, the use of SDUs has evolved without substantial

evidence as to their benefits and what their role should be. Some studies argue that these units

provide a safe and cost-effective environment for semi-critical patients and can serve as a “bridge

from hospital to home” thereby improving patient outcomes and efficiency (Byrick et al. 1986,

Harding 2009, and Stacy 2011). Other studies argue that SDUs should not be used as there is not

enough evidence of their cost-effectiveness (Keenan et al. 1998 and Hanson et al. 1999). Despite

the lack of consensus in the medical community surrounding the use of SDUs, many hospitals have

SDUs and others are considering introducing these units. Even within a single hospital, the use

of SDUs is generally not standardized. Therefore, it is very important to understand their value

and how they can best be used. This paper examines whether or not SDUs are associated with

improved operational and/or clinical outcomes as well as how these outcomes may be affected by

SDU size. As SDUs are much less expensive to operate than ICUs, improvements associated with

SDU care may enable reductions in hospital operating costs without sacrificing patient outcomes.

Given the increasing pressures for hospitals to reduce costs, such insights can be very valuable to

hospital administrators.

To the best of our knowledge, our work is the first to conduct a multi-hospital study to empirically

examine the role of an SDU for patients who are discharged from the ICU. Our analyses are based

on recent data from Kaiser Permanente Northern California, an integrated health care delivery

system serving 3.6 million members that operates 21 hospitals, some of which do and some of

Author: The Role of a Step-Down Unit in Improving Patient OutcomesArticle submitted to Manufacturing & Service Operations Management; manuscript no. (Please, provide the manuscript number!) 3

which do not have SDUs. The cohort and type of data we employ have been described in previous

studies (see Escobar et al. (2008), Kim et al. (2014) among others). Our data source is based on

nearly 170,000 hospitalizations in a total of 10 hospitals over a course of one and half years. Each

of the 10 hospitals in our study has an ICU and SDU, though the number of beds in each of the

units varies across hospitals. We focus on patients who are admitted to the ICU and examine how

being discharged from the ICU to the SDU impacts various clinical and operational outcomes. In

conducting this research, we must deal with an important estimation challenge. The routing of a

patient following ICU discharge may be affected by health factors which are known to the physician

at the time of the decision on when and to where the patient is discharged, but are unobservable in

the data. Ignoring this endogeneity could result in biased estimates. So we utilize an instrumental

variable approach to identify the desired effects. Our empirical findings suggest that SDU care is

associated with substantial improvements in various patient outcomes. In particular, on average,

routing to the SDU following ICU discharge is associated with reductions in the likelihood of in-

hospital death by 6%, the remaining hospital length-of-stay by 1.08 days, the likelihood of ICU

readmission by 4%, and the likelihood of hospital readmission by 8%.

Based on our empirical findings, we develop and calibrate a simulation model of critical care

patient flows to gain an understanding of how SDU size may impact patient flows and outcomes. In

our simulation, we assume a critically ill patient receives care in the ICU until he enters one of two

health conditions–semi-critical or stable. A stable patient is transferred to the ward or discharged

out of the hospital, while a semi-critical patient is transferred to an SDU bed if one is available.

Thus, depending on bed availability, a semi-critical patient could have three possible routings:

(1) if an SDU bed is available, the patient is transferred to an SDU bed, (2) if the SDU is full,

but the ICU has available beds, the patient remains in the ICU and is considered reverse access

blocked (RAB), and (3) if both the SDU and the ICU are full, the patient is rerouted to the ward

to make room for new ICU patients. A RAB patient may be subsequently rerouted to the ward

if a critical patient arrives and there are no available ICU or SDU beds. Having a large number

of RAB patients and/or having these patients blocked in the ICU for long periods of time can

be very costly and may indicate a mismatch of capacity between the ICU and SDU. Semi-critical

patients who are rerouted to the ward may have worse outcomes: a higher likelihood of in-hospital

death and ICU readmission. While our simulation model does not capture every possible flow of

patients through the ICU and SDU, it provides insight into the role of SDUs, especially in the case

where an SDU is utilized as a true step-down unit (i.e. patients are only admitted to the SDU

from the ICU). Our simulation reveals that SDU size is a very important factor in achieving better

patient outcomes–a larger SDU results in improved patient outcomes even when there is ample ICU

capacity. However, the marginal gains decrease for each additional SDU bed. Our findings suggest


that a moderately sized SDU, e.g., 70% of ICU size, is sufficient to achieve patient outcomes as

good as those associated with a much larger SDU.

Our main contributions are summarized as follows:

• Quantifying the impact of SDU care on patient outcomes: We develop an econometric

model to estimate the impact of discharging ICU patients to the SDU on patient outcomes. We

find statistical evidence of reduced mortality, readmissions, and LOS when a patient is sent to the

SDU following ICU discharge.

• Understanding how SDU size affects patient outcomes: We develop a patient flow

model, with parameters calibrated using our empirical results, to quantify the impact of the SDU

size on patient outcomes. Our results show that increasing the SDU size improves patient outcomes

but the marginal improvement decreases as the SDU size increases. Our model provides insight for

hospital administrators when determining 1) how many SDU beds to have and 2) how to allocate

resources between the ICU and SDU.

The rest of the paper is organized as follows. Section 2 reviews related papers in the literature.

In Section 3, we present our econometric models and estimation results for the decision of where

to transfer patients following ICU discharge. We present a general patient flow model in Section

4. Section 5 provides our simulation results and provides numerous robustness tests. Section 6

summarizes our results and provides directions for future research.

2. Literature Review

Our work is related to existing literature in both the medical and operations management commu-

nities.

First, our work contributes to the ongoing debate in the medical community about the role of

SDUs. On one hand, some studies argue that SDUs are a cost-effective approach to treat patients

by providing a safe and less expensive environment for patients who are not quite sick enough to

require treatment in the ICU, but not quite stable enough to be treated in the ward. Without

an SDU, most of these patients end up being cared for in the ICU. Byrick et al. (1986) suggests

that the use of the SDU could alleviate the ICU congestion by reducing ICU length-of-stay (LOS)

without increasing mortality rates. This reduction is possible because patients do not have to reach

as high a level of stability to be discharged to an SDU rather than to a general medical-surgical

ward. Other studies that have shown the cost-effectiveness of an SDU include Harding (2009), Stacy

(2011), and Tosteson et al. (1996). On the other hand, a survey of studies on SDUs raises doubts

about these benefits and argues that there is not enough evidence of cost-effectiveness (Keenan

et al. 1998). The majority of these studies are conducted exclusively within a single hospital,

whereas our study utilizes data from 10 different hospitals. Additionally, rather than conducting a


before-and-after study, which may be limited by the inability to control for temporal changes such

as staffing changes or closures of nearby hospitals, we utilize an instrumental variable approach

to identify the impact of different care pathways (going to the SDU versus ward following ICU

discharge). Our multi-center study provides compelling evidence that SDUs are associated with

improved patient outcomes.

Our work is also related to the body of literature in the operations management community

regarding ICU care. There are a number of papers, including Suter et al. (1994), Azoulay et al.

(2001), Shmueli et al. (2003), Escher et al. (2004), Simchen et al. (2004) and Kim et al. (2014),

which examine the impact of ICU admission decisions on patient outcomes. In contrast, our work

considers the bed transfer decision upon ICU discharge. Kc and Terwiesch (2012) also examines

the ICU discharge process; however, the focus is on early discharges from the ICU due to demand

pressures. This work examines the impact of the type of unit a patient is transferred to following

ICU discharge.

Our estimation model is most related to that considered in Kim et al. (2014). Like Kim et al.

(2014) and Kc and Terwiesch (2012), among others, we utilize an instrumental variable which is

based on an operational measure–congestion in an inpatient unit. While the general methodology

is similar, the question we are considering is wholly different. Our focus is on the role of an SDU

in the care of critical patients, whereas the aforementioned works focus on the ICU.

Our work is also related to the voluminous literature on hospital capacity planning (see Green

2006 for an overview). These papers typically use a queueing approach. For example, Yankovic

and Green (2011) develop a queuing model to identify nurse staffing levels that satisfy a particular

service level. Yom-Tov and Mandelbaum (2014) introduce an Erlang-R model to guide staffing

decisions in the Emergency Department. The work described in this paper complements some

of the results from Armony et al. (2013), which uses fluid and diffusion analysis to study nurse

allocation between the ICU and the SDU. The findings in that paper demonstrate that the nurse

allocation decision depends upon the cost of two undesirable phenomena: The first occurs when

critical patients requiring ICU care experience excessive delays in being admitted to the ICU. In

many of these instances, they are sent to a different unit or hospital for care, or, in the worst

case, die. We refer to this phenomenon of patients who need to be admitted to an ICU but don’t

get admitted as ‘abandonment’ (e.g., in the queueing sense). The second undesirable phenomenon

occurs when RAB semi-critical patients are demand-driven discharged (see, for example, Kc and

Terwiesch (2012) and Chan et al. (2012)) from the ICU to the ward when new, more severe patients

require ICU care. We refer to this phenomenon as ‘bumping’. Armony et al. (2013) find that

the nurse allocation decision depends on the relative costs of bumping and abandonment. The

work described in this paper is a first step towards estimating the impact of bumping on patient


outcomes, which in turn can be used to estimate costs. We utilize these estimates to calibrate

a simulation model to examine the impact of SDU size on patient outcomes. While there are a

number of papers which utilize simulation approaches to examine capacity management (see e.g.,

Ballard and Kuhl 2006, Griffiths et al. 2010, and Zhu et al. 2012), to the best of our knowledge

ours is the first to consider the role of an SDU.

3. Empirical Estimation

In this section, we empirically estimate how SDU admission immediately following ICU discharge

affects patient outcomes. Section 3.1 describes the data we use. Section 3.2 develops the estimation

approach and Section 3.3 reports our empirical results.

3.1. Data

This project was approved by the Kaiser Permanente Northern California Institutional Review

Board for the Protection of Human Subjects, which has jurisdiction over all study hospitals. We

utilize patient data from 10 hospitals from Kaiser Permanente Northern California, containing

165,948 hospitalizations over a course of one and a half years.

Our data contains operational level information, including every unit to which a patient is

admitted during his hospital stay as well as the date and time of admission and discharge for

each unit. For each inpatient unit in each hospital, we use these patient flow data to derive hourly

occupancy levels and we define its capacity as the maximum occupancy level over the time horizon.

Table 1 summarizes the capacity for each of the different levels of inpatient care in each hospital:

the ICU, SDU, and ward. While each level of care may have further divisions based on specific

services, e.g. medical versus surgical ICU, the boundaries are somewhat loose in these hospitals in

the sense that if a critical patient requires ICU care and is under the medical service, but there

are no medical ICU beds available, he will likely be cared for in the surgical ICU. We observe

substantial heterogeneity across these hospitals; the SDU capacity varies from 11 to 32 and the

ICU size ranges from one half to twice of the SDU size.

Our data selection process is depicted in Figure 1. First, we restrict our cohort to the 12 months

in the center of the 1.5 year time period to avoid censored estimation of capacity and occupancy.

A patient’s admission category is defined as a combination of whether or not they were admitted

through the ED, and whether they were a medical or surgical patient resulting in 4 categories:

ED-medical, ED-surgical, non-ED-medical, or non-ED-surgical. Since our goal is to examine the

impact of the ICU to SDU routing on patient outcomes, we only consider patients who are admitted

to the ICU at least once during their hospital stay. Note that within the SDUs at this hospital

network, there are patients who are not admitted via the ICU. Of these, we primarily focus on

patients who are admitted via the ED to a medical service for two major reasons. First, this group


Table 1 Capacity of various impatient units

Hosp ICU SDU Ward1 11 24 612 11 25 763 16 14 774 16 19 765 16 24 786 23 19 1247 24 20 1458 26 27 1109 31 11 18810 32 32 100

is the largest, consisting of about 60% of the patients treated in these hospitals, and is similar to

the cohort considered in Kim et al. (2014). Second, the care pathways of surgical patients tend to

be fairly standardized, especially for non-ED-surgical patients, which is the larger surgical group.

In contrast, the care pathways of ED-medical patients are more variable. For each patient, we

focus on the initial ICU admission. We exclude patients who die in the ICU or are discharged

directly home from the ICU, since there is no decision about whether to route these patients to

the SDU or ward following ICU discharge. In Appendix C, we also consider the three other patient

categories: ED-surgical, non-ED-medical, and non-ED-surgical. We also do some robustness checks

by considering the last ICU admission and all ICU admissions within the hospital stay.

Our dataset contains information about patient characteristics such as age, gender, admitting

diagnosis and three different severity scores. One score is based on lab results taken within the

first 72 hours of hospital admission and the second is based on comorbidities, such as diabetes,

that may complicate patient recovery. These severity scores are assigned at hospital admission and

are not updated during the hospital stay (more details on these scores can be found in Escobar

et al. (2008)). The third severity score is the simplified acute physiology score 3 (SAPS3), which

is a common severity score used for ICU patients. It is updated and assigned each time a patient

is admitted to the ICU. Christensen et al. (2011), Mbongo et al. (2009), and Strand and Flaatte

(2008) provide detailed descriptions and validation of the SAPS3 score. Table 2 provides summary

statistics for these patient characteristics.

3.2. Estimation Approach

We are interested in understanding whether SDU care following ICU discharge is associated with

better patient outcomes and, if so, the magnitude of the improvement. Specifically, our objective

is to determine if ICU patients who are transferred to the SDU have better outcomes than those

transferred to the ward. To accomplish this, we must deal with an estimation challenge which arises

due to the fact that the routing decision following ICU discharge is likely correlated with patient


Figure 1 Data Selection

Patient cohortTotal Hospitalizations:

165,948 *

Admitted during the 1‐year period: 130,698

Admitted as ED‐Medicalpatients: 77,418

Admitted to ICU at least once: 14,996

Admitted as a Surgical or Non‐ED patient: 53,280(40.77%)

Never admitted to ICU: 62,422 (80.63%)

Admitted outside the study period : 35,250 (21.24%)

Admitted to Ward/SDU after 1st ICU : 11,058 **

Out‐of‐hospital or non‐Ward/SDU units : 3,938(26.26%)

* to determine capacity and occupancy** patient cohort used in our econometric model

Table 2 Summary Statistics

Variable mean std min p25 p75 maxAge 68.13 15.91 18 56 78 105Male 0.5513 0.4974 0 0 1 1LAPS2 75.13 49.10 0 29 106 262COPS2 46.63 44.61 0 10 66 267SAPS3 45.41 11.79 15 37 52 100ICU LOS (hrs) 61.87 84.75 0.02 22.02 68.07 2279.17LOS before ICU (hrs) 32.99 108.88 0 0.9 18.52 4877.58

outcomes. That is, sicker patients are more likely to be transferred to the SDU, but also more likely

to have bad outcomes. To overcome this potential endogeneity bias, we utilize an identification

strategy using Instrumental Variables (IVs).

3.2.1. Patient Outcomes We consider four patient outcomes: (1) in-hospital death

(Mortality), (2) ICU readmission (ICUReadm), (3) remaining hospital length-of-stay

(HospRemLOS), and (4) hospital readmission (HospReadm). HospRemLOS measures the

time between discharge from the first ICU admission and hospital discharge. In the model for

HospRemLOS, we include patients with in-hospital death; the results are similar if we exclude

these patients. HospReadm2w is defined as hospital readmission within two weeks after leaving


hospital (e.g., see Doran et al. 2013 and Ouanes et al. 2012 which use these durations), and

ICUReadm2d (ICUReadm5d) indicates ICU readmission within two (five) days following ICU

discharge (Brown et al. 2013 aims to define reasonable time periods for ICU readmission). In calcu-

lating hospital readmission rates, we exclude patients with in-hospital death. Similarly, we did not

include patients who die within 2 days following ICU discharge in the analysis of ICUReadm2d.

Table 3 Summary Statistics for Patient Outcomes

SDU Wardoutcome obs. mean std obs. mean stdMortality 3,832 0.06 - 7,226 0.07 -

ICUReadm - 2 days 3,832 0.04 - 7,226 0.05 -ICUReadm - 5 days 3,832 0.08 - 7,226 0.06 -

HospReadm - 2 weeks 3,585 0.14 - 6,685 0.13 -HospRemLOS (days) 3,832 7.32 15.68 7,226 5.26 10.36

We also do robustness checks for different time windows in Appendix C. Summary statistics of

these outcomes are provided in Table 3 and are grouped by the inpatient unit a patient goes to

after completing ICU service.

3.2.2. Econometric Model We now present our estimation model. For patient i, let yi denote

the patient outcome of interest (e.g., HospRemLOSi) and Xi be a row-vector of covariates includ-

ing age, gender, severity scores, admitting diagnosis, seasonality controls, care before the ICU

admission, and ICU LOS. Table 7 in the Appendix provides detailed descriptions of these control

variables. We also control for the daily average occupancy level, denoted as AvgOccV isitedi, patient

i experiences for all impatient units s/he is admitted to after leaving the ICU and before leaving

hospital. For ICU readmission, we modified AvgOccV isitedi to be the daily average occupancy level

that patient i experiences in all impatient units s/he is admitted to between two consecutive ICU

admissions. Appendix C provides robustness checks for different specifications of AvgOccV isitedi,

as well as with this control excluded. We include such a measure as Kc and Terwiesch (2012) shows

that patient outcomes are affected by congestion; Kim et al. (2014) provides additional discussion.

Define ICU2SDUi as an indicator that equals to 1 if patient i is transferred to the SDU after

completing ICU service and 0 if patient i is routed to the ward, i.e.,

ICU2SDUi =

{1, if patient i is transferred to the SDU from the ICU0, if patient i is transferred to Ward from the ICU

. (1)

The objective is to estimate the impact of the ICU discharge decision ICU2SDUi on patient

outcomes.

Author: The Role of a Step-Down Unit in Improving Patient Outcomes10Article submitted to Manufacturing & Service Operations Management; manuscript no. (Please, provide the manuscript number!)

Instrumental Variable: As discussed earlier, the decision to admit a patient to the SDU following

ICU discharge is endogenous. A common approach to address endogeneity and obtain consistent

estimates is by utilizing an instrumental variable (IV) approach. We use congestion in the SDU

one hour before the ICU discharge as an IV. In particular, we define SDUBusyi as an indicator

variable that equals one when the number of available beds in the SDU one hour prior to patient

i’s discharge from the ICU is less than or equal to two, and zero otherwise1. On average, about

11% patients are discharged from the ICU when the SDU is busy (SDUBusy = 1), though this

varies quite a bit across hospitals (see Table EC.2).

A valid instrument should be 1) correlated with the endogenous variable, which in our case is

the routing at ICU discharge, ICU2SDUi, and 2) unrelated to the unobservable factors captured

in εi which affect patient outcomes. In Figure 2(a), we group patients into 20 groups based on

their SAPS3 scores and compare the percentage of ICU patients who are routed to the SDU when

the SDU is busy versus not busy. We find that with this coarse comparison, SDU congestion is

associated with a reduction in the fraction of patients admitted to the SDU for all severity levels.

When controlling for various patient characteristics in a Probit regression model (results in Table 8

of the Appendix), we also find at the 0.1% significance level that when the SDU is busy, patients are

less likely to go to the SDU. In particular, we estimate that, on average, 21.14% percent of patients

are routed to the SDU if SDUBusy= 1 and this percentage increases to 35.91% if SDUBusy= 0.

Namely, a congested SDU is predicted to result in a 47% reduction in the likelihood of the SDU

admission.

For SDUBusyi to be a valid instrument, it also has to be uncorrelated with unobservable fac-

tors in patient outcomes captured in error εi. Since we cannot examine unobservable measures,

we use patient severity, SAPS3, as a proxy for those unobservable factors. In particular, we per-

form a two-sample Kolmogorov-Smirnov test (see Gibbons and Chakraborti 2011 for details) to

test the hypothesis that the distribution of SAPS3 for patients who are discharged from ICU

when SDUBusy = 1 is not statistically different to that when SDUBusy = 0. The p-value for

the combined Kolmogorov-Smirnov test is 0.136. Thus, we can not reject the null hypothesis and

believe that patients who are discharged from the ICU when SDUBusy = 1 are statistically sim-

ilar to patients who are discharged from the ICU when SDUBusy = 0. Figure 2(b) depicts the

distributions for patients who are discharged from the ICU when SDUBusy = 1 and those when

SDUBusy= 0.

1 We also do robustness checks in Appendix C by considering different specifications of SDU busy: (1) different cutoffsat one, two, three, four available beds; (2) dummy variables using occupancy level with cutoffs at 80th (or 85th, 90th,95th) percentile, i.e., SDUBusyi = 1 if occupancy level is larger than the cutoff percentile and zero otherwise; (3)congestion represented by a continuous piecewise linear spline variable with knots at the 80th (or 85th, 90th, 95th)percentile; and (4) these measures 2 hours (instead of 1) prior to ICU discharge.

Author: The Role of a Step-Down Unit in Improving Patient OutcomesArticle submitted to Manufacturing & Service Operations Management; manuscript no. (Please, provide the manuscript number!)11

020

4060

8010

0O

bser

ved

ICU

2SD

U%

0 5 10 15 2020 Quantiles of SAPS3

SDUBusy=1 SDUBusy=0

(a) Routings of ICU Discharge

0.0

1.0

2.0

3.0

4de

nsity

20 40 60 80 100 120SAPS3

SDUBusy=1SDUBusy=0

(b) Distributions of Patient Severity Scores

Figure 2 IV identification: SDUBusy= 1 vs SDUBusy= 0. (Left (a)) Observed percentage of ICU patients who

are routed to SDU when SDUBusy= 1 vs SDUBusy= 0 with different severity levels characterized by

SAPS3. (Right (b)) Distributions of severity scores for patients who are transferred to the SDU when

SDUBusy= 1 vs SDUBusy= 0.

Kc and Terwiesch 2012 demonstrates that ICU congestion could result in early discharge, which

could, in turn, affect the routing decision of ICU patients. While ICU congestion has been used as

an IV in a number of hospital studies (e.g. Kc and Terwiesch 2012, Kim et al. 2014), we find that

ICU congestion is not a valid IV. This is because the impact of ICU congestion does not exhibit a

consistent effect on ICU routing, i.e., a congested ICU could result in both a higher and a lower

percentage of patients being admitted to the SDU depending on a patient’s severity score.

Joint Estimation of Two Equations. Since the ICU to SDU routing decision, ICU2SDUi, is a

binary variable, we model the ICU discharge decision via a latent variable model:

ICU2SDUi = 1{ICU2SDU∗i > 0} and ICU2SDU∗i =Xiθ+αSDUBusyi +ωh(i) + ξi, (2)

where ICU2SDU∗i is a latent variable which represents the propensity towards SDU admission;

Xi is a vector of control variables for patient information; ωh(i) is the hospital fixed effect (h(i)

is patient i’s hospital); and, ξi represents unobservable factors that affect the routing at ICU

discharge.

For a binary outcome (Mortality,HospReadm,ICUReadm), we model the patient outcome as:

yi = 1{y∗i > 0} and y∗i =Xiβ+ γ · ICU2SDUi + δ ·AvgOccV isitedi + νh(i) + εi, (3)

where y∗i is a latent variable which represents the propensity for the outcome; νh(i) is the hospital

fixed effect; and εi captures unobservable factors that affect patient outcomes. The error terms

(ξi, εi) in the above two equations (2) - (3) may be correlated to model the endogeneity between

the routing at ICU discharge and patient outcomes. We assume that (ξi, εi) follows a Standard


Bivariate Normal distribution with correlation coefficient ρ. This Bivariate Probit model can be

jointly estimated via Full Maximum Likelihood Estimation “FLME” (see Cameron and Trivedi

1998, Greene 2012, and Kim et al. 2014). The presence of endogeneity can be tested through a

likelihood ratio test of null ρ= 0.

For HospRemLOS, which is a continuous variable, equation (3) is replaced by

log(HospRemLOSi) =Xiβ+ γ · ICU2SDUi + δ ·AvgOccV isitedi + νh(i) + εi, (4)

Similar to the binary outcomes, we assume that (ξi, εi) follows a Bivariate Normal distribution with

mean zero and covariance matrix

(σ ρρ 1

). This model can be jointly estimated using a treatment

effect model via FLME ( Greene 2012). Similarly, a likelihood ratio test of null ρ= 0 can be used

to test the presence of endogeneity.

3.3. Estimation Results

This section summarizes our estimation results. We are primarily interested in estimating the effects

of SDU admission on patient outcomes; thus, we report only the coefficient of SDU admission on

the patient outcomes, i.e., γ in (3) and (4). The full estimation results are provided in Appendix

B.

Table 4 Effect of SDU Admission (γ) on Patient Outcomes

With IV Without IV

Outcome γ (SE)Predicted Outcome

ρ (SE)Test

γ (SE)P̂SDU P̂Ward ρ= 0

Mortality -0.60** (0.22) 3.96% 10.26% 0.26+ (0.14) 0.07 -0.18*** (0.05)log(HospRemLOS) -0.35*** (0.10) 0.91 1.27 0.44*** (0.05) 0.00 0.38*** (0.02)

ICUReadm2d -0.51** (0.20) 2.34% 6.62% 0.32* (0.12) 0.02 0.01 (0.05)ICUReadm5d -0.51**(0.18) 3.93% 10.10% 0.36** (0.11) 0.05 0.09* (0.04)HospReadm2w -0.43* (0.21) 8.66% 17.08% 0.21+ (0.12) 0.09 0.05 (0.04)

Note. Standard error in parentheses. +(p < 10%),∗(p < 5%),∗ ∗ (p < 1%),∗ ∗ ∗(p < 0.1%).

Predicted outcome: P̂SDU - Average predicted outcome if all patients could be routed to the SDU

and P̂Ward if no SDU and everyone is rerouted to Ward.

Table 4 summarizes the relationship between SDU admission right after ICU discharge and

patient outcomes. The sign of SDU admission is negative and statistically significant in all outcome

measures, suggesting that routing an ICU discharge to the SDU is associated with improved patient

outcomes. We also use our estimation results to predict patient outcomes under two extreme sce-

narios: (i) the SDU has ample capacity so that all patients will be routed to the SDU (referred to

as P̂SDU) versus (ii) the hospital does not have an SDU and all patients will be routed to the ward

(referred to as P̂Ward). We find that, on average, SDU care is associated with significant improve-

ments in patient outcomes: the relative reduction is 72% in the likelihood of in-hospital death,


34% in the hospital remaining length-of-stay, 67.7% (63.9%) in the likelihood of ICU readmission

within 2 (5) days, and 52% in the likelihood of hospital readmission within 2 weeks.

We note that the large effect on mortality rate could be partially due to “do not resuscitate

(DNR)” orders, which are patients’ end-of life wishes not to undergo Cardiopulmonary resuscitation

(CPR) or advanced cardiac life support if their heart were to stop or they were to stop breathing.

In speaking with intensivists, we learned it is possible that patients with DNRs are more likely to

be sent to the ward, but also may be more likely to die, resulting in an overestimate of the effect

of SDU care. Unfortunately, we do not have access to patients’ DNR status, so cannot control

for this. That said, DNR orders only represent 9% of ICU patients (Jayes et al. 1993), so this is

likely to affect a small percentage of patients. Additionally, there is evidence that DNR orders do

not change the quality of care (Baker et al. 2003). We do not expect DNR orders to impact our

results for hospital readmission since we exclude patients who died in hospital in this model. For

remaining LOS, we find that our results are robust to including and excluding patients who died.

Our empirical findings also suggest strong evidence of an endogeneity bias between the routing

following ICU discharge and patient outcomes. The p-value of the likelihood ratio test with null

hypothesis ρ= 0 is small, as seen in Table 4, implying a strong correlation between the routing at

ICU discharge and patient outcomes. Ignoring this endogeneity tends to result in underestimates

of the benefit of SDU care and could result in a qualitatively different insight; see the column titled

with “Without IV”.

We examine a number of robustness checks including alternative specifications of patient char-

acteristics, different specifications for SDU congestion, and different time windows for readmission.

The results are summarized in Appendix C. We find that the main results hold with slight quanti-

tative changes. For example, the effect of the ICU to SDU routing on hospital readmission is weaker

when the elapsed time between two consecutive hospital stays is longer. This may be because the

complication requiring readmission will be less likely to be related to the routing following ICU dis-

charge and more likely related to post-discharge events. Given our findings indicating the benefits

of SDU care following ICU discharge, we use these empirical results to develop an understanding

of the role of SDU capacity on patient outcomes.

4. Patient Flow Model

We present an ICU patient flow model that we use to explore the impact of SDU capacity on

the percentage of patients routed to the ward following ICU discharge and the associated patient

outcomes such as in-hospital mortality and ICU readmissions. The model is illustrated in Figure

3.


Figure 3 Simulation Model

ICU

��

BICU

SDU

BSDU

pSC: semi-critical

1- pSC

Readmitted

New

Re

ve

rse

Acce

ss B

locke

d

Ward

…

R

SDUp

R

SDUp−1

R

Wardp

R

Wardp−1

Survival

Wardp

Survival

SDUp−1

Survival

SDUp

Survival

Wardp−1

ICU Admissions: New patients arrive at the ICU according to a Poisson process (see e.g. Shmueli

et al. (2003), Kim et al. (2014)) with rate λICU and are assumed to be in a critical state. Their

service times, defined as the duration of time for which they remain critical, are independent and

identically lognormally distributed with mean LOS0ICU and standard deviation σ0

ICU (see Armony

et al. (2011) and Shi et al. (2014) for evidence of lognormal LOS in hospital settings). As will

be described in more detail later, patients may require readmission to the ICU after their initial

stay. The service time of readmitted patients is lognormally distributed with mean LOSRICU and

standard deviation σRICU . If, upon arrival of a new or readmitted ICU patient, there is an available

ICU bed, he will be admitted directly to the unit. If the ICU is full, the patient will join either

the new or readmission queue, depending on how he arrived, to wait for an available bed. When

an ICU bed becomes available, priority is given to readmitted patients. A first-come-first-serve

(FCFS) rule is used within each queue.

Inpatient Unit Routing following ICU Discharge: After service completion in the ICU, a patient

becomes semi-critical following completion of time spent as critical with probability pSC . If a

patient is semi-critical, medical needs would warrant placement in the SDU. Otherwise, with prob-

ability 1−pSC , the patient does not require SDU service. For example, if the patient is sufficiently

stable, he can be sent directly to the ward or home. Alternatively, the patient may die in the ICU.

For newly semi-critical patients, there are three possibilities (1) an SDU bed is available and the

patient is placed in the SDU; (2) the SDU is full and so the patient becomes a RAB patient and


stays in the ICU, or (3) both the ICU and the SDU are full and so the patient is rerouted to the

ward.

Rerouting patients is associated with worse outcomes: a higher likelihood of in-hospital mortal-

ity and a higher readmission rate. In particular, if a semi-critically ill patient is admitted to the

SDU, the patient will die in the SDU with probability pMSDU(= 1−pSurvivalSDU ). If the patient survives

to SDU discharge, with probability pRSDU the patient’s health condition deteriorates and requires

readmission to the ICU. The same process applies to patients who are rerouted to the ward with

pMWard(= 1−pSurvivalWard ) and pRWard denoting the likelihood of in-hospital death and ICU readmission,

respectively. We assume that pRSDU < pRWard and pMSDU < pMWard to reflect the worse outcomes asso-

ciated with rerouting semi-critically ill patients to the ward. We also assume that the service times

of semi-critically ill patients are independent and identically lognormally distributed: with mean

LOSSCSDU and standard deviation σSCSDU for the service time in the SDU, with mean LOSSCWard and

standard deviation σSCWard for the service time at the ward. We assume that there is ample ward

capacity so that there is no possibility of patients discharged to the ward being blocked.

Reverse Access Blocked (RAB) Patients in the ICU: An RAB patient leaves the ICU under the

following scenarios: (1) An SDU bed becomes available. We refer this as a regular discharge. (2)

A new or readmitted critical patient arrives to the ICU and there are no available ICU beds.

The critical patient has priority for ICU care over the semi-critical patient, so the RAB will be

discharged from the ICU. Note that because the SDU is full, this patient must go to the ward.

We call this type of RAB discharge a demand-driven discharge. (3) It is also possible that a RAB

patient leaves the ICU after stablizing in the ICU. For the regular and demand-driven discharge of

RAB patients, we assume that the FCFS rule is used when there are multiple RAB patients in the

ICU, namely, the patient with the longest blocked time in the semi-critical state leaves the ICU

first.

For each RAB patient, we assume that the time spent in the ICU while in a semi-critical state

is perfectly substitutable for the service time in the SDU. This is because the time needed for a

patient to become stable is mainly determined by the physiological state of the patient and this

recovery time does not depend on where the patient is treated (e.g., see Zimmerman et al. 2006).

In particular, at the epoch of entering the RAB state, we sample patient i’s service time LOSi,SDU

as if he were transferred to the SDU and LOSi,Ward as if he were transferred to the ward according

to the corresponding distributions. Let Blocki,ICU be the blocked time in the ICU for RAB patient

i; then, patient i’s remaining service time in the SDU would be LOSi,SDU −Blocki,ICU if patient i

is transferred to the SDU and LOSi,Ward−Blocki,ICU if patient i is transferred to a general ward.

When Blocki,ICU = min{LOSi,SDU ,LOSi,Ward}, a RAB patient i becomes stabilized in the ICU

and either goes directly home or to the ward.


4.1. Operating Regime

There are many operational factors that could impact patient outcomes. For example, patient

outcomes can deteriorate as a result of actions taken by physicians when the ICU becomes congested

(Chan et al. 2012, Kc and Terwiesch 2012, and Kim et al. 2014). Since our objective is to understand

the impact of the SDU size on patient outcomes, we will assume in our analyses that the ICU is

generally uncongested.2 In particular, we assume that the arrival rate of new patients to the ICU

is such that at least 95% of patients have less than T hours blocked waiting for ICU admission,

i.e.,

P(Waiting time≤ T )≥ 95%. (5)

Here T is a patient’s tolerance for waiting. For example, Chalfin et al. (2007) demonstrates that

waits greater than 6 hours leads to worse outcomes, so we set T = 6 hours. To explicitly calibrate the

arrival rate of new ICU patients, we approximate the waiting time distribution by an M/M/c queue

(see Gross et al. 2008). In particular, we assume that all semi-critical patients are routed to the

SDU, which will provide a lower bound of the true ICU readmission rate and subsequently, a lower

bound on the total time a patient is critical, thereby the total required ICU LOS, TOTAL LOSICU .

Note that this does not include time a patient is reverse access blocked since these patients are

semi-critical and could be treated in an SDU if space were available. The average total ICU service

time (TOTAL LOSICU) for each patient, defined as the total time a patient spends in the critical

state, including the first ICU admission and all sequential ICU admissions, is given by

TOTAL LOSICU = Average Total LOS in the ICU

= LOS0ICU︸︷︷︸

LOS for 1st ICU admission

+∞∑k=1

(pSCpRSDU)kLOSRICU︸︷︷︸LOS for readmitted ICU admissions

= LOS0ICU +

pSCpRSDU1− pSCpRSDU

LOSRICU .

Let µICU = 1TOTAL LOSICU

be the service rate of the ICU, r= λICUµICU

and ρ= λICUBICUµICU

be the traffic

intensity in the ICU, one has

P(Waiting time> 6hours) =rBICU

BICU !(1− ρ) ·(

rBICU

BICU !(1−ρ) +∑BICU−1

n=0rn

n!

) · e−6·(BICU ·µICU−λICU ).

We choose the arrival rate λICU such that the above P(Waiting time> 6hours) equals to 5%.

In order to focus on the role of the SDU, we assume that there is ample capacity in the general

ward. We vary the capacity of the SDU in order to understand the impact of these capacity limits

(or lack thereof) on the patient outcomes.

2 To be more precise, the ICU has limited capacity in our settings, but we assume that the ICU is not congested byselecting a sufficiently low arrival rate such that the utilization in the ICU is small.


While this model does not capture every possible patient flow into and out of the ICU and SDU,

it describes the most common patient care pathways. In particular, the SDU is used as a true Step-

Down Unit in the sense that patients treated in the SDU come from the ICU as an intermediate

step down before being sent to the ward.

5. Simulation

We now examine how the SDU size affects patient outcomes and utilize these insights to explore

capacity management of the SDU via simulation for our general patient flow model described in

Section 4.

5.1. Parameter Calibration and Selection

We start by using our patient data to determine the parameters for patient LOS. Recall that the

LOS in the ICU, SDU, and ward are assumed to follow log-normal distributions. We estimate the

mean and standard deviation of LOS in an impatient unit using all patients who are discharged

from that unit when it is not congested. The reason that we use data when the hospital unit is

not congested is due to adaptive mechanisms physicians use when congestion is high, which may

censor our estimates (e.g. Kc and Terwiesch 2012 and Chan et al. 2012). For instance, we find ICU

LOS tends to be longer for patients who are discharged when the SDU is congested. Therefore, in

estimating the average ICU LOS, we consider patients who are discharged from the ICU when both

the ICU and the SDU are not-busy; this should mitigate the effects of demand-driven discharges

and reverse access blocks.

We use results of our econometric model from Section 3.2 to calibrate the patient outcomes for

different ICU to SDU routing decisions. In particular, we set the probability of in-hospital death

as 3.96% for patients who are routed to the SDU following their ICU discharge and 10.26% for

patients who are rerouted to the ward (see Table 4). As 73% of readmitted patients return to the

ICU within 5 days of ICU discharge, we consider the ICU readmission rate within five days to

estimate the ICU readmission probabilities of 3.93% and 10.10% for patients who are routed from

the ICU to the SDU and wards, respectively (see Table 4).

We also estimated the likelihood of a patient entering the semi-critical state following ICU

discharge by examining the percentage of patients who are discharged from the ICU and routed

to the SDU when both the ICU and the SDU are not-busy. In the baseline model, we set this

percentage to be 60%, i.e., pSC = 0.6, which is the average in our data. However, this percentage

varies across the 10 hospitals in our dataset, so we test the sensitivity of our results by considering

pSC ∈ {0.5,0.6,0.7,0.8}.

Finally, to address the question of what SDU size is appropriate, we varied the SDU size from

10% to 100% of the ICU size, i.e., BSDUBICU

∈ {0.1,0.2,0.3, . . . ,1}. Our baseline model considers 20 ICU


Table 5 The Value of Parameters

Parameter ValueNumber of beds BICU = 20, BSDU = {0.1,0.2,0.3, . . . ,1}×BICU

LOS for 1st ICU admission (hours) LOS0ICU = 56, σ0

ICU = 60LOS for Readmitted ICU admission (hours) LOSRICU = 66, σRICU = 74

LOS for SDU (hours) LOSSCSDU = 67, σSCSDU = 77LOS for ward (hours) LOSSCWard = 74, σSCWard = 108

Percentage of SDU requests pSC = 0.6ICU Readmission rate pRSDU = 3.93%, pRWard = 10.10%

Mortality rate pMSDU = 3.96%, pMWard = 10.26%Sensitivity test BICU ∈ {10,20,30,40}, pSC ∈ {0.5,0.6,0.7,0.8}

beds, which is the average ICU size in the 10 hospitals. However, Table 1 shows substantial variation

in ICU size across different hospitals. We test the sensitivity of simulation results by considering

four different ICU sizes, BICU ∈ {10,20,30,40}. The value of these parameters is summarized in

Table 5. We run the simulation for 100,000 iterations over 14 months, where the first 2 months are

used as a warm-up period.

Validating the M/M/c approximation. Recall that the length-of-stay in the ICU is a log-normal

distributed random variable in our simulation model, while the arrival rate is chosen to meet a

desired performance benchmark (the probability a critical patient needs to wait more than 6 hours

for ICU admission is less than 5%) by using an approximation based on the M/M/c queueing

model. We verify in our simulation that choosing the arrival rate in this manner is reasonably

accurate. Indeed, we find that on average 94.5% patients spend less than 6 hours waiting for an

ICU bed.

5.2. Simulation Results

The baseline model considers 20 ICU beds and 60% of patients enter the semi-critical state after

ICU discharge. The simulated ICU utilization (excluding RAB patients) is close to 70% with

slight fluctuations for different SDU sizes. (The ICU utilization calculated according to M/M/c

approximation is 69.99%.) Table 6 reports the simulation results for ICU readmission rate, mortality

rate, average queue length and waiting time for new and readmitted ICU patients, and average

number of RAB patients who are blocked in the ICU after completing ICU service as well as their

blocked time.

• ICU readmission and mortality: It is intuitive that a large SDU size reduces the likelihood

of ICU readmission and in-hospital death since adding SDU capacity reduces the need for rerouting

patients to the ward. The marginal improvement of adding one SDU bed is significant when the

SDU is small, for example a 21.5% reduction in the ICU readmission rate is achieved when the

SDU size is increased from 2 beds to 4 beds and another 20% reduction from 4 SDU beds to 6

SDU beds. This marginal improvement decreases with the SDU size. In particular, 14 SDU beds

results in practically the same outcomes as a large SDU (20 beds).


Table 6 Simulation Results (BICU = 20, pSC = 0.6)

Avg Queue length Avg Waiting time (hrs)BSDU New Readmitted RAB New Readmitted RAB ICUReadm Mortality

2 0.22 0.0036 4.01 0.91 0.43 36.46 8.23% 8.25%4 0.19 0.0024 2.81 0.79 0.39 32.09 6.46% 6.41%6 0.18 0.0018 1.42 0.75 0.35 21.85 5.17% 5.18%8 0.18 0.0016 0.63 0.74 0.31 14.10 4.57% 4.57%10 0.18 0.0016 0.29 0.72 0.30 10.38 4.29% 4.26%12 0.18 0.0016 0.12 0.75 0.28 7.91 4.09% 4.15%14 0.18 0.0017 0.04 0.74 0.29 6.16 4.03% 4.03%16 0.18 0.0016 0.01 0.75 0.27 4.73 3.98% 4.01%18 0.18 0.0017 0.00 0.75 0.29 3.45 3.98% 3.98%20 0.18 0.0017 0.00 0.74 0.28 1.04 4.00% 3.98%

• Queue length and waiting time: For readmitted patients, the queue length is negligible

due to the operating regime we’ve selected and the fact that priority is given to readmitted patients.

We also observe that the queue length of new arrivals is insensitive to the SDU size. At first glance,

one may expect that a large SDU will reduce the ICU readmission rate due to fewer reroutings,

which, in turn, will result in a smaller queue length. However, the change in readmission rate is

very small and so does little in affecting the overall arrival rate of new and readmitted critical

patients. As such, the system load, and subsequently queue length, does not change significantly.

By Little’s Law, the same insights carry over to explain the negligible impact of SDU size on the

waiting time for new and readmitted patients.

• RAB Patients: Adding SDU capacity reduces the number of RAB patients and their time

in the ICU. With more SDU beds, fewer semi-critical patients will find the SDU full, so will not

be blocked. Additionally, if they are blocked, the time until an SDU bed becomes available is

decreased, thereby reducing the total time spent blocked in the ICU.

Our key observation from the baseline simulation is that the SDU size is a major factor associated

with patient outcomes. In particular, we find that adding SDU capacity improves patient outcomes,

but the marginal improvement decreases with the SDU size. An SDU which is 70% of the ICU size

(14 SDU beds in this case) results in patient outcomes that are very similar to those associated

with a much larger SDU.

5.2.1. Sensitivity Analysis We now test the sensitivity of our baseline simulation results by

changing the number of ICU beds and the percentage of patients who become semi-critical and

need SDU care. In the first scenario, we test the sensitivity to ICU beds by varying the ICU size. In

the second scenario, we test the sensitivity to pSC . Similar to the baseline model, we find that the

SDU size has very little impact on the average queue length and waiting time for new patients and

readmitted patients in the ICU. As such, we report only mortality, ICU readmission, the number

of reverse access blocked patients and their blocked time.


Sensitivity to ICU size. We vary the ICU size from {10,20,30,40} and fix the percentage of

SDU requests to be pSC = 60%. Figure 4 reports the mean and 95% confidence intervals of our

Figure 4 Sensitivity Analysis of ICU Size (p= 0.6)

3%

4%

5%

6%

7%

8%

9%

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1The SDU size / the ICU size

Readmission

10 ICU Beds 20 ICU Beds 30 ICU Beds 40 ICU Beds

(a) ICU Readmission Rate

3%

4%

5%

6%

7%

8%

9%


Mortality


(b) Mortality Rate

0

1

2

3

4

5

6

7


Avg Number of RAB Patients


(c) Number of RAB patients

0

510

15

2025

3035

40

4550


Avg Blocked Time for RAB Patients


(d) RAB blocked time (hours)

simulation. Similar to what we saw with the baseline simulation, we find that adding SDU beds

improves patient outcomes, but the marginal benefits are diminishing.

An artifact of our simulation model is that increasing ICU capacity results in worse outcomes.

If demand were held constant, an increase in ICU capacity would certainly result in improved

outcomes. However, in the simulation, ICU capacity and demand are tightly intertwined, so that

an increase in capacity also results in an increase in demand. Recall that the ICU arrival rate is

endogenously chosen so that 95% of patients wait less than 6 hours. By the economies of scale

in queueing systems, a bigger ICU allows for a higher ICU utilization by Critical patients. In

particular, the ICU utilization is ∼57% for 10 ICU beds, ∼70% for 20 ICU beds, ∼76% for 30 ICU

beds, and ∼80% for 40 ICU beds. Because of the higher utilization, more semi-critical patients are

rerouted, which, in turn, increases readmission and mortality rates. Thus, we see that an increased

ICU size results in higher ICU workload and, subsequently, higher mortality and ICU readmission

rates.

We also find that a large ICU increases the number of RAB patients but reduces their average

blocked time in the ICU. The former is intuitive as more ICU beds implies more capacity for RAB


patients. However, it is somewhat surprising that the time spent blocked decreases with ICU size.

The reason is because, as discussed before, with an endogenously selected arrival rate, a large ICU

means higher ICU utilization. As such, there are more demand-driven discharges of RAB patients

to accommodate new ICU arrivals, thereby reducing the average blocked time of RAB patient in

the ICU. These demand-driven discharged patients are rerouted to the ward, which results in a

higher likelihood of death and/or ICU readmission.

Sensitivity to the probability of semi-critical state. We now perform sensitivity analysis to another

important parameter–the percentage of ICU patients that become semi-critical and request SDU

care (pSC)–by changing pSC in {0.5,0.6,0.7,0.8}. The simulation results are reported in Figure 5,

which also displays the 95% confidence intervals.

Figure 5 Sensitivity Analysis of Percentage of SDU Request (BICU = 20)

3%

4%

5%

6%

7%

8%

9%

2 4 6 8 10 12 14 16 18 20The SDU size

Readmission

P(ICU2TCU) = 0.5 P(ICU2TCU) = 0.6 P(ICU2TCU) = 0.7 P(ICU2TCU) = 0.8

(a) ICU Readmission Rate

3%

4%

5%

6%

7%

8%

9%

2 4 6 8 10 12 14 16 18 20The SDU size

Mortality


(b) Mortality Rate

0

1

2

3

4

5

6

2 4 6 8 10 12 14 16 18 20The SDU size

Avg Number of RAB Patients


(c) Number of RAB patients

0

5

10

15

20

25

30

35

40

45

2 4 6 8 10 12 14 16 18 20The SDU size

Avg Blocked Time for RAB Patients


(d) RAB blocked time

We note that changing pSC does not substantially alter the qualitative insight of how SDU size

impacts patient outcomes, but does introduce slight changes in the exact magnitude of the effects.

An increase in pSC increases the demand for SDU beds and so, as a result, more patients are

rerouted to the ward. This, in turn, increases the likelihood of ICU readmission, in-hospital death,

and the number of RAB patients. As for the blocked time of RAB patients, a high pSC has two

opposing effects for a given SDU size. First, it increases the ICU readmission rate since a higher pSC

increases the rerouting percentage and rerouted patients are more likely to be readmitted to the


ICU. The increased ICU readmission rate increases the frequency of the demand-driven discharge

of RAB patients to accommodate readmitted patients and thus reduces the average RAB blocked

time. On the other hand, the arrival rate of new patients decreases with a higher pSC , as the total

ICU LOS (TOTAL LOSICU =LOS0ICU +

pSCpRSDU

1−pSCpRSDU

LOSRICU) increases. Recall that the arrival rate

of new patients is endogenously chosen to satisfy the waiting time constraint (e.g. the arrival rate

of new patients is 0.2442 when pSC = 0.5 compared to 0.2407 when pSC = 0.8). The reduced arrival

rate reduces the frequency of transferring out RAB patients and increases the blocked time. The

dominance of the above two forces of pSC on blocked time depends on various model parameters

including the SDU size.

5.3. Managerial Insights

The simulation results provide important insights about how to allocate resources between ICUs

and SDUs. We summarize these insights in the follows:

• Adding SDU capacity helps: Our simulation shows that adding SDU capacity could

improve patient outcomes, even when the ICU has ample capacity.

• Marginal improvement diminishes: The marginal benefit of adding one SDU bed decreases

with the SDU size. In all scenarios we tested, we observed that an SDU with 70% of ICU size could

achieve outcomes that are as good as those associated with a much larger SDU. Applying basic

economic principles, hospitals could leverage this insight to determine the ideal SDU capacity via

a cost-benefit analysis. Of course, this is for the case where the SDU is used only for ICU patients;

further analysis is necessary for SDUs which include non-ICU demand.

• Blocked time indicates capacity mismatch: The measure of reverse access blocked

patients provides useful insights on how resources might be reallocated across the ICU and SDU.

The regular presence of many RAB patients with long blocked times indicates ample ICU capacity

but scarce SDU capacity. Thus, hospitals could potentially improve efficiency by allocating more

resources to the SDU and reducing ICU capacity. On the other hand, when there are many RAB

patients with negligible blocked time, there are two possible scenarios: (1) when the rerouting per-

centage is large, this implies a shortage of capacity in both the SDU and the ICU; (2) when the

rerouting percentage is small, this suggests a scarcity of ICU capacity and an abundance of SDU

capacity. Thus, one can consider investments in new beds or reallocation of current beds depending

on which scenario exists.

Our simulation and econometric models provide a way for physicians to estimate the marginal

benefit, in terms of better patient outcomes, of adding SDU capacity. Our findings provide hospital

decision makers very useful insights in determining the size of the SDU and resource reallocation

between the ICU and the SDU, to achieve good patient outcomes while considering the economic

costs of adding beds. Most importantly, our study lends weight to support the use of SDUs in

critical care–an issue which continues to be debated by the medical community.


6. Conclusions and Future Research

This paper studies the role of a hospital step-down unit (SDU) in the care of critical patients.

To that end, we consider two fundamental questions regarding the SDU: (1) Does admitting a

patient to the SDU following ICU discharge improve patient outcomes and, if so, what is the

magnitude of these improvements? (2) How does the size of the SDU affect patient outcomes, and,

more importantly, how many SDU beds should hospitals operate and what is the best allocation

of resources between the SDU and the ICU? Our work represents an important first step towards

answering these questions.

Using patient data from 10 hospitals, we use econometric models to estimate the benefit of SDU

care. Our empirical results suggest that routing an ICU discharge to the SDU is associated with

substantial improvements in patient outcomes: reduced in-hospital mortality rate of 70%, ICU

readmission rate of 67.7%, hospital readmission rate of 52%, and decreased hospital length-of-stay

of 34%. As such, we find compelling evidence that there are measurable benefits to having an SDU.

Using our empirical results to calibrate a simulation model, we find that increasing SDU capacity

is associated with better patient outcomes, but the marginal improvement is decreasing. We also

find that the number of reverse access block patients who are in the ICU, but do not medically

need to be there, provides a useful indicator about potential capacity mismatches between the ICU

and SDU.

It is important to note that our findings provide guidelines and demonstrate the potential for

using SDUs in a way that not only results in better clinical outcomes, but also can result in

significant cost savings for hospitals. Because SDUs are significantly less expensive to operate

than ICUs, and have the potential to significantly decrease ICU and hospital readmissions as well

as remaining hospital LOS, properly used they can result in decreased hospital bed utilization

and staffing costs. In the current healthcare environment in which hospitals are under increasing

pressure to be more cost-effective, findings like the ones in this paper can be very valuable in

achieving that goal.

Our work complements the results of Armony et al. (2013). When ICU and SDU capacity is

limited, Armony et al. (2013) provides insights into how to allocate resources between the two

units depending on the relative costs of abandonment of critical patients and bumping of semi-

critical patients. This work is a first step towards estimating the impact of bumping semi-critical

patient on patient outcomes, thereby providing insights into the bumping cost component which

drives the capacity allocation decision. In contrast to Armony et al. (2013), this work examines

how much SDU capacity is required when a hospital has the ability to invest in more capacity and

the ICU is relatively uncongested. These two studies can be used by hospital administrators when


determining the SDU size and resource reallocation between the ICU and the SDU. Depending on

the availability of critical care resources, Armony et al. (2013) or this work will be more pertinent.

There are a lot of opportunities for future work. Our empirical analysis relies on the variation in

patient routings following ICU discharge due to capacity constraints. As such, it is not possible to

make any statements about the impact of SDU care for patients whose care pathway is invariant

to SDU bed availability. Because SDUs go in and out of favor at individual hospitals, there may be

opportunities for natural experiments to make such inferences without requiring an instrumental

variable analysis. Alternatively, at a hospital system such as Kaiser Permanente, it might be possible

to conduct a controlled randomized trial by randomizing which hospitals have SDUs. Of course,

such a study would require substantial buy-in from hospital administrators and staff. The purpose

of our work is to measure the relationship between SDU care and patient outcomes rather than to

build a predictive model to determine the role of SDU care for each individual patient. In such a

setting, a split-validation approach would be useful to verify the out of sample predictive power of

such a model.

From an analysis point of view, it would be interesting to study the optimal control policies

regarding where to transfer patients following ICU discharge in the presence of an SDU. This would

provide a system-level view of the SDU admission decision, rather than focusing on the medical

needs of an individual patient at each decision epoch as we do in our simulation model by assuming

a semi-critical patient will be admitted to the SDU as long as there is an available bed. Also, in this

paper, we have considered an SDU as serving only as a step-down unit; patients are only admitted

to the SDU following ICU discharge. In a number of hospitals, patients may be directly admitted

to the SDU or may be transferred from the ward or operating rooms. It would be interesting to

extend our work to include non-ICU demand for the SDU and examine the tradeoff between ICU

demand and non-ICU demand. Unfortunately, due to data limitations, we are unable to estimate

the benefits of SDU care for non-ICU demand. However, as more data becomes available, e.g. that

which includes requests and denials for SDU care for non-ICU patients, such estimates will become

possible. Our work demonstrates that SDUs play an important role in patient outcomes in critical

care; however, more work needs to be done to fully grasp the potential benefits these units may

provide.

Acknowledgments

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Appendix A: Supporting Table

Table 7 Control variables for patient characteristics and hospital care

Variable DescriptionGender Dummy variable: Males were coded 1 and females 0Age Continuous variable: Coded as piecewise linear spline variables with knots at

its 50th and 80th percentiles (65 and 81)LAPS2 Laboratory-based Acute Physiology Score; measures physiologic derangement

at admission and is mapped from 14 laboratory test results, such as arterial pHand white blood cell count, obtained 72 hours preceding hospitalization to aninteger value that ranges from 0 to 262 in our data set(higher scores indicatepoorer condition); coded as piecewise linear spline variables with knot at its50th and 80th percentiles (94 and 134)

COPS2 Comorbidity Point Score; measures the chronic illness burden and is basedon 41 comorbidities, such as diabetes, to which patients are categorized usingoutpatient and inpatient data from the 12 months preceding hospitalization. Itranges from 0 to 267 in our data set, a higher score indicates a higher comorbidillness burden, it was coded as piecewise linear spline variables with knot at its50th and 80th percentiles (33 and 87)

SAPS3 Simplified Acute Physiology Score; measures the severity of illness and predictvital status at hospital discharge based on ICU admission data. SAPS3 score isassociated with each ICU admission and is calculated based on data obtainedwithin on hour of ICU admission. SAPS3 ranges from 14 to 100 in our dataset; coded as piecewise linear spline variables with knot at its 50th and 80th

percentiles (52 and 61)Admitting diagnosis A way of classifying ICD9 codes. This clinical classification system was devel-

oped by HCUP and buckets ICD9’s into about 200 groups. A further groupingof the variable HCUP developed by Gabriel Escobar to condense the HCUPgrouping into 38 groups so it could be used in a similar fashion as PRIM-COND3.

Seasonality Month/day-of-week/time-of-day; Category variable for each month and day-of-week. For time-of-day, we use category variables for nurse shifts happeningthree times a day at 7am, 15pm, and 23pm.

Previous unit Category variable to track impatient unit a patient is admitted to immediatelybefore ICU admission.

LOS before ICU Continuous variable that is the total lengh-of-stay (hrs) prior to the ICU admis-sion. It measures how long a patient has been in hospital before being admittedto the ICU, coded as piecewise linear spline variables with knot at its 50th and80th percentiles (2 and 31).

ICU LOS Continuous variable that is the lengh-of-stay (hrs) at the first ICU. It measureshow long a patient has been taking care of at ICU, coded as piecewise linearspline variables with knot at its 50th and 80th percentiles (38 and 83).


Appendix B: Detailed Estimation Results for the ICU to SDU Routing Decision

This section briefly summarizes the estimation results for the ICU to SDU routing decision given in Equation

(2). Recall that the ICU to SDU decision and the patient outcomes are jointly estimated using full MLE.

As such the coefficients for the ICU to SDU decision may vary slightly for different outcomes. That said, we

observe that differences are very minor. For the sake of brevity, we present estimation results associated with

Mortality. We report estimates for a subset of patient and operational controls in Table 8; the complete set

of estimation results are provided in Table EC.7 in the online Appendix.

Table 8 Estimation Results for the ICU to SDU Routing Decision

Covariate Estimationb/se

SDUBusy -0.5110*** (0.0503)SAPS3 [0, 52] 0.0016 (0.0030)SAPS3 [52,61] 0.0025 (0.0060)SAPS3 [61, ] -0.0182** (0.0055)LOSB4ICU [0, 2] (hrs) -0.0119 (0.0340)LOSB4ICU [2,31] 0.0114*** (0.0021)LOSB4ICU [31, ] 0.0005** (0.0002)ICULOS [0, 38] -0.0108*** (0.0016)ICULOS [38,83] 0.0046*** (0.0010)ICULOS [83, ] 0.0004+ (0.0002)NightShift[11pm,7am] baseMorningShift[7am,3pm] -0.6186*** (0.0506)AfternoonShift[3pm,11pm] -0.5018*** (0.0490)Pseudo R2 0.1396Number of obs 11057Note. +(p < 10%),∗(p < 5%),∗ ∗ (p < 1%),∗ ∗ ∗(p < 0.1%)

The empirical results for the ICU to SDU routing provide some interesting managerial insights. We sum-

marize these insights in the follows:

• SDU congestion: The coefficient for SDUBusyi is negative and highly statistically significant, sug-

gesting that the SDU congestion reduces the likelihood of routing an ICU patient to the SDU. We also predict

the percentage of patients routed to SDU under two scenario: (a) the percentage is 35.91% when the SDU

is not congested and (b) the percentage is 21.14% if SDU is congested. Thus, a congested SDU results in a

46% relative reduction in the likelihood of transferring an ICU patient to the SDU.

• Severity: The impact of severity scores (LAPS2, COPS2, and SAPS3) is very marginal on the ICU

discharge decision. The coefficients are very small and most of them are not significant. This is likely because

these severity scores are not updated at time of ICU discharge. LAPS2 and COPS2 are assigned at hospital

admission and SAPS3 is assigned at ICU admission. The time the patient spends in the ICU (ICULOS)

seems to more accurately measure patient severity and has a significant effect on where a patient is transferred

after ICU discharge.


• LOS before ICU: We find that an increase in hospital length-of-stay (hours) before a patient is

admitted to the ICU, denoted by LOSB4ICUi, increases the likelihood of going to the SDU. One possible

explanation is that a longer LOSB4ICUi indicates a longer ‘delay’ for the ICU bed. As a result, the patient’s

health condition may be worse and is therefore more likely to be routed to the SDU.

• Nurse shift: Our results also show that the ICU to SDU routing decision is highly related to the time

of ICU discharge. In particular, a patient is less likely to be transferred to the SDU when the patient is

discharged in the morning shift [7am, 3pm] or afternoon shift [3pm, 11pm], compared to the night shift

[11pm, 7am]. This time-of-day effect is likely due to the fact that more patients are discharged from ICU in

the morning and afternoon, i.e., the demand for SDU beds is high in the morning and afternoon; therefore,

a high percentage of patients will need to be rerouted.

Overall, we find that operational factors, especially congestion in the SDU, have a significant impact on the

ICU to SDU routing decision.

Appendix C: Robustness Checks

We now describe a number of robustness checks for our main results described in Section 3.3. First, we

tried different specifications of control variables. Recall that, some of our control variables – severity scores

(LAPS2, COPS2, SAPS3), length-of-stay at ICU, and length-of-stay before ICU admission – are modeled as

spline variables to account their possible non-linear effects on the ICU to SDU routings and patient outcomes.

We repeated the analysis with different specifications, including changing the number of cutoffs and values

of these cutoffs. Our results are qualitatively similar to these changes.

The second robustness check we did is with respect to the length of time window for readmission. For

ICU readmission, we varied the time window of the ICU readmission from time of ICU discharge from 2 to

7 days and also during any time frame during the same hospital stay. For hospital readmission, we consider

hospital readmission within 1 week, 2 weeks, 3 weeks, and 30 days after a patient is discharged from the

hospital. We found that our main results are similar to those in Table 4 with slight quantitative changes.

For example, the effect of the ICU to SDU routing is weaker when the elapsed time between two consecutive

hospital stays is longer. We provide the detailed estimation results in Table EC.3 in the online Appendix.

For ICU readmission, we also checked alternative specifications of AvgOccV isited. In the paper, we define

AvgOccV isited for ICU readmission as the average occupancy for all units a patients is admitted to between

two consecutive ICU admissions. We considered three alternatives: 1) the average occupancy for all units a

patient is admitted to in the remaining hospital stay before leaving hospital ; 2) the average occupancy for

all units a patient is admitted to within 3 days after the ICU discharge and before the next ICU admission;

and 3) excluding a control for AvgOccV isited. While these three specifications yield similar results, there

are slight differences in the significance level – the first is the strongest and the last is the weakest, see Table

EC.1.

We also vary the definition of a busy SDU, considering different cutoffs for the number of available beds,

ranging from one bed to four. On average, the percentage of patients, who are discharged from ICU when

SDU is congested, varies from 34% to 3% when the cutoff is decreased from four beds to one (Table EC.2).

While the quantitative effect of a busy SDU varies for these different specifications, the main results do not


change–being admitted to the SDU is associated with better patient outcomes. See Table EC.3. We also

considered alternative measures of SDU congestion based on percentiles of the SDU occupancy level. First,

we use a dummy variable that equals one when the occupancy level in the SDU exceeds its 95th percentile.

Next, we use is a piece-wise linear spline variable for the SDU occupancy level with a knot at the 95th

percentile. The estimation results are similar to our results obtained in the other specifications. We also

repeated the analysis with different cutoff values replacing the 95th percentile by the 80th, 85th, and 90th

percentile, and the results were qualitatively similar. See Table EC.4 and Table EC.5.

Finally, we also ran our econometric model for other admission categories: ED-Surgical, Non-ED Medical,

Non-ED Surgical. These three categories contain much fewer observations than ED-Medical; as such, the

joint estimation does not converge for most of patient outcome models due to the small sample size. Thus,

we could not examine the impact of the ICU to SDU transfer decision on patient outcomes. We were able

to estimate the first-stage of these models, which captures the decision to admit (or not admit) patients

to the SDU following ICU discharge. We present these results in Table EC.7. The results for all admitting

categories are similar to those for ED-Medical. Namely, the operational factors (particularly SDU congestion

and nurse-shift) have a significant impact on the ICU to SDU routing decision. Potentially, with a larger

patient cohort, one may be able to use a similar estimation strategy used in this work to examine the impact

of SDU care for the remaining admission categories.

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Online Appendix: Full Estimation Results and RobustnessAnalysis

Table EC.1 Robustness Test on ICU Readmissions: Alternative Specifications for AvgOccV isited

With IV Without IVOutcome Estimate (SE) AME ARC ρ(SE) Test ρ= 0 Estimate (SE)

AvgOccV isited : for all units before next ICU admission (Baseline)

ICUReadm2d -0.51** (0.20) -0.04 -68% 0.32* (0.12) 0.02 0.01 (0.05)ICUReadm -0.24 (0.20) -0.04 -36% 0.25* (0.12) 0.05 0.17*** (0.04)

AvgOccV isited : for all units before hospital discharge

ICUReadm2d -0.62*** (0.19) -0.05 -74% 0.38** (0.11) 0.00 -0.00 (0.05)ICUReadm -0.40* (0.18) -0.06 -53% 0.34** (0.11) 0.00 0.16*** (0.04)

AvgOccV isited : for all units within 3 days before next ICU admission

ICUReadm2d -0.50** (0.20) -0.04 -67% 0.31* (0.12) 0.02 -0.00 (0.05)ICUReadm -0.23 (0.20) -0.04 -35% 0.24+ (0.12) 0.06 0.16*** (0.04)

AvgOccV isited : not included

ICUReadm2d -0.40* (0.20) -0.03 -58% 0.25* (0.12) 0.05 0.00 (0.05)ICUReadm -0.15 (0.20) -0.02 -24% 0.19 (0.12) 0.11 0.17*** (0.04)Note. Standard error in parentheses. +(p < 10%),∗(p < 5%),∗ ∗ (p < 1%),∗ ∗ ∗(p < 0.1%).

AME - Average Marginal Effect; ARC - Average Relative Change.

Table EC.2 Percentage of patients who are discharged from ICU when SDU is busy

% when number of available SDU bedsHosp SDU Size ≤ 1 ≤ 2 ≤ 3 ≤ 4

1 24 0.93 3.57 7.80 12.172 25 0.66 2.95 7.54 12.463 14 0.56 7.94 24.29 45.634 19 3.17 12.68 27.07 41.595 24 0.28 1.54 3.93 7.876 19 0.82 3.34 6.76 15.377 20 0.00 2.84 16.74 36.778 27 2.81 9.34 18.80 31.749 11 9.76 37.72 63.94 80.3410 32 0.34 2.66 6.19 12.71

All hosp 2.52 10.64 21.70 34.00


Table EC.3 Robustness Test on Patient Outcomes: Binary SDUBusy Based on Number of Available Beds


IV: SDUBusy= 1{SDUFreeBeds <= 4}, P (SDUFreeBeds <= 4) = 34.00%

Mortality -0.56* (0.27) -0.06 -70% 0.23 (0.17) 0.17 -0.18*** (0.05)log(HospRemLOS) -0.42*** (0.03) -0.42 -37% 0.47*** (0.05) 0.00 0.38*** (0.02)

ICUReadm2d -0.70*** (0.20) -0.06 -78% 0.43*** (0.12) 0.00 0.01 (0.05)ICUReadm3d -0.30 (0.31) -0.03 -47% 0.21 (0.19) 0.28 0.04 (0.04)ICUReadm5d -0.41 (0.27) -0.05 -56% 0.30+ (0.16) 0.08 0.09+ (0.04)ICUReadm -0.28 (0.25) -0.04 -41% 0.27+ (0.15) 0.08 0.17*** (0.04)HospReadm1w -0.49* (0.25) -0.07 -62% 0.24 (0.15) 0.12 0.08+ (0.04)HospReadm2w -0.26 (0.22) -0.05 -36% 0.10 (0.13) 0.46 0.05 (0.04)HospReadm3w -0.22 (0.20) -0.05 -29% 0.11 (0.12) 0.35 0.06+ (0.03)HospReadm30d -0.18 (0.20) -0.05 -23% 0.08 (0.12) 0.49 0.05+ (0.03)


Mortality -0.47* (0.23) -0.05 -64% 0.17 (0.14) 0.22 -0.18*** (0.05)log(HospRemLOS) -0.38*** (0.10) -0.38 -36% 0.46*** (0.05) 0.00 0.38*** (0.02)

ICUReadm2d -0.76*** (0.17) -0.07 -81% 0.47*** (0.10) 0.00 0.01 (0.05)ICUReadm3d -0.52* (0.22) -0.05 -67% 0.35* (0.13) 0.02 0.04 (0.04)ICUReadm5d -0.55** (0.20) -0.07 -67% 0.39*** (0.12) 0.00 0.09+ (0.04)ICUReadm -0.35+ (0.20) -0.05 -48% 0.32** (0.12) 0.01 0.17*** (0.04)HospReadm1w -0.27 (0.25) -0.04 -41% 0.10 (0.15) 0.49 0.08+ (0.04)HospReadm2w -0.32 (0.22) -0.06 -42% 0.14 (0.13) 0.30 0.05 (0.04)HospReadm3w -0.18 (0.20) -0.04 -24% 0.09 (0.12) 0.45 0.06+ (0.03)HospReadm30d -0.20 (0.21) -0.05 -24% 0.09 (0.12) 0.45 0.05+ (0.03)


Mortality -0.60** (0.22) -0.06 -72% 0.26+ (0.14) 0.07 -0.18*** (0.05)log(HospRemLOS) -0.35*** (0.10) -0.35 -34% 0.44*** (0.05) 0.00 0.38*** (0.02)

ICUReadm2d -0.51** (0.20) -0.04 -68% 0.32* (0.12) 0.02 0.01 (0.05)ICUReadm3d -0.45* (0.20) -0.05 -61% 0.31* (0.12) 0.02 0.04 (0.04)ICUReadm5d -0.51** (0.18) -0.06 -64% 0.37*** (0.10) 0.00 0.09+ (0.04)ICUReadm -0.24 (0.20) -0.04 -36% 0.25* (0.12) 0.05 0.17*** (0.04)HospReadm1w -0.22 (0.23) -0.03 -34% 0.07 (0.13) 0.60 0.08+ (0.04)HospReadm2w -0.43* (0.21) -0.08 -52% 0.21+ (0.12) 0.09 0.05 (0.04)HospReadm3w -0.39* (0.19) -0.09 -45% 0.22+ (0.11) 0.06 0.06+ (0.03)HospReadm30d -0.44* (0.20) -0.11 -47% 0.24+ (0.12) 0.05 0.05+ (0.03)


Mortality -0.69*** (0.25) -0.07 -77% 0.31+ (0.16) 0.06 -0.18*** (0.05)log(HospRemLOS) -0.36*** (0.12) -0.36 -34% 0.44*** (0.06) 0.00 0.38*** (0.02)

ICUReadm2d -0.39 (0.27) -0.03 -58% 0.24 (0.17) 0.16 0.01 (0.05)ICUReadm3d -0.18 (0.35) -0.02 -32% 0.14 (0.21) 0.53 0.04 (0.04)ICUReadm5d -0.15 (0.29) -0.02 -26% 0.14 (0.18) 0.42 0.09+ (0.04)ICUReadm -0.02 (0.27) -0.002 -3% 0.11 (0.16) 0.49 0.17*** (0.04)HospReadm1w -0.34 (0.31) -0.05 -49% 0.15 (0.18) 0.43 0.08+ (0.04)HospReadm2w -0.79*** (0.21) -0.15 -74% 0.43*** (0.13) 0.00 0.05 (0.04)HospReadm3w -0.70*** (0.20) -0.16 -66% 0.41*** (0.12) 0.00 0.06+ (0.03)HospReadm30d -0.71*** (0.23) -0.18 -64% 0.41** (0.14) 0.01 0.05+ (0.03)




Table EC.4 Robustness Test on Patient Outcomes: Binary SDUBusy Based on Occupancy


IV: SDUBusy= 1{SDUOcc >= 80thpercentile}Mortality -0.55* (0.27) -0.06 -70% 0.23 (0.17) 0.19 -0.18*** (0.05)

log(HospRemLOS) -0.50*** (0.08) -0.50 -43% 0.51*** (0.04) 0.00 0.38*** (0.02)ICUReadm2d -0.63*** (0.20) -0.05 -75% 0.39*** (0.11) 0.00 0.01 (0.05)ICUReadm3d -0.44 (0.27) -0.04 -61% 0.30+ (0.17) 0.09 0.04 (0.04)ICUReadm5d -0.54*** (0.22) -0.07 -66% 0.38*** (0.13) 0.01 0.09+ (0.04)ICUReadm -0.54*** (0.18) -0.08 -64% 0.43*** (0.11) 0.00 0.17*** (0.04)HospReadm1w -0.37 (0.23) -0.05 -51% 0.27+ (0.14) 0.06 0.08+ (0.04)HospReadm2w -0.23 (0.23) -0.05 -32% 0.17 (0.14) 0.24 0.05 (0.04)HospReadm3w -0.14 (0.22) -0.03 -19% 0.12 (0.13) 0.37 0.06+ (0.03)HospReadm30d -0.06 (0.23) -0.02 -8% 0.07 (0.14) 0.63 0.05+ (0.03)

IV: SDUBusy= 1{SDUOcc >= 85thpercentile}Mortality -0.72** (0.29) -0.08 -78% 0.33+ (0.18) 0.09 -0.18*** (0.05)

log(HospRemLOS) -0.47*** (0.09) -0.47 -42% 0.50*** (0.04) 0.00 0.38*** (0.02)ICUReadm2d -0.55* (0.23) -0.05 -71% 0.34* (0.14) 0.02 0.01 (0.05)ICUReadm3d -0.19 (0.32) -0.02 -34% 0.14 (0.20) 0.47 0.04 (0.04)ICUReadm5d -0.40 (0.26) -0.05 -55% 0.30+ (0.16) 0.08 0.09+ (0.04)ICUReadm -0.49** (0.19) -0.07 -60% 0.40*** (0.12) 0.00 0.17*** (0.04)HospReadm1w -0.55** (0.22) -0.08 -65% 0.38** (0.13) 0.01 0.08+ (0.04)HospReadm2w -0.37+ (0.23) -0.07 -47% 0.26+ (0.14) 0.00 0.05 (0.04)HospReadm3w -0.22 (0.22) -0.05 -29% 0.17 (0.13) 0.20 0.06+ (0.03)HospReadm30d -0.08 (0.22) -0.02 -11% 0.08 (0.13) 0.53 0.05+ (0.03)

IV: SDUBusy= 1{SDUOcc >= 90thpercentile}Mortality -0.72** (0.27) -0.08 -78% 0.33+ (0.17) 0.07 -0.18*** (0.05)

log(HospRemLOS) -0.42*** (0.09) -0.43 -39% 0.48*** (0.05) 0.00 0.38*** (0.02)ICUReadm2d -0.38 (0.30) -0.03 -58% 0.24 (0.18) 0.20 0.01 (0.05)ICUReadm3d -0.05 (0.38) -0.01 -11% 0.06 (0.23) 0.80 0.04 (0.04)ICUReadm5d -0.19 (0.32) -0.02 -31% 0.16 (0.19) 0.41 0.09+ (0.04)ICUReadm -0.12 (0.26) -0.02 -21% 0.18 (0.16) 0.28 0.17*** (0.04)HospReadm1w -0.06 (0.25) -0.01 -11% 0.08 (0.15) 0.58 0.08+ (0.04)HospReadm2w -0.18 (0.22) -0.04 -26% 0.14 (0.14) 0.33 0.05 (0.04)HospReadm3w -0.20 (0.22) -0.05 -26% 0.16 (0.13) 0.25 0.06+ (0.03)HospReadm30d -0.13 (0.24) -0.03 -17% 0.11 (0.14) 0.45 0.05+ (0.03)

IV: SDUBusy= 1{SDUOcc >= 95thpercentile}Mortality -0.81*** (0.27) -0.09 -82% 0.39* (0.17) 0.04 -0.18*** (0.05)

log(HospRemLOS) -0.42*** (0.10) -0.42 -37% 0.47*** (0.05) 0.00 0.38*** (0.02)ICUReadm2d -0.54* (0.24) -0.05 -70% 0.33* (0.14) 0.03 0.01 (0.05)ICUReadm3d -0.24 (0.33) -0.02 -39% 0.17 (0.20) 0.40 0.04 (0.04)ICUReadm5d -0.36 (0.26) -0.04 -52% 0.27 (0.15) 0.10 0.09+ (0.04)ICUReadm -0.29 (0.23) -0.04 -42% 0.27+ (0.14) 0.06 0.17*** (0.04)HospReadm1w -0.54* (0.23) -0.08 -65% 0.38** (0.14) 0.01 0.08+ (0.04)HospReadm2w -0.71*** (0.21) -0.14 -70% 0.47*** (0.13) 0.00 0.05 (0.04)HospReadm3w -0.67*** (0.20) -0.16 -65% 0.45*** (0.12) 0.00 0.06+ (0.03)HospReadm30d -0.69*** (0.23) -0.18 -63% 0.45** (0.14) 0.01 0.05+ (0.03)




Table EC.5 Robustness Test on Patient Outcomes: Continuous SDUBusy Modeled as a Spline Variable


IV: SDUOcc. modeled as a piece-wise linear spline with knot at 80th pct

Mortality -0.79*** (0.25) -0.08 -81% 0.38* (0.16) 0.03 -0.18*** (0.05)log(HospRemLOS) -0.44*** (0.09) -0.44 -44% 0.49*** (0.04) 0.00 0.38*** (0.02)

ICUReadm2d -0.43+ (0.24) -0.04 -61% 0.26+ (0.15) 0.09 0.01 (0.05)ICUReadm3d -0.06 (0.31) -0.01 -12% 0.06 (0.19) 0.74 0.04 (0.04)ICUReadm5d -0.23 (0.27) -0.03 -37% 0.19 (0.16) 0.25 0.09+ (0.04)ICUReadm -0.24 (0.21) -0.04 -36% 0.25+ (0.13) 0.07 0.17*** (0.04)HospReadm1w -0.37+ (0.22) -0.05 -51% 0.27+ (0.14) 0.05 0.08+ (0.04)HospReadm2w -0.38+ (0.21) -0.07 -47% 0.26+ (0.13) 0.06 0.05 (0.04)HospReadm3w -0.30 (0.20) -0.07 -37% 0.22+ (0.12) 0.09 0.06+ (0.03)HospReadm30d -0.24 (0.22) -0.06 -29% 0.17 (0.13) 0.19 0.05+ (0.03)



ICUReadm2d -0.40 (0.26) -0.03 -59% 0.25 (0.16) 0.14 0.01 (0.05)ICUReadm3d -0.02 (0.33) -0.002 -3% 0.04 (0.20) 0.85 0.04 (0.04)ICUReadm5d -0.18 (0.28) -0.02 -31% 0.16 (0.17) 0.35 0.09+ (0.04)ICUReadm -0.15 (0.23) -0.02 -24% 0.19 (0.14) 0.18 0.17*** (0.04)HospReadm1w -0.33 (0.23) -0.05 -47% 0.25+ (0.14) 0.09 0.08+ (0.04)HospReadm2w -0.39+ (0.21) -0.08 -49% 0.27+ (0.13) 0.05 0.05 (0.04)HospReadm3w -0.34+ (0.21) -0.08 -41% 0.25+ (0.12) 0.06 0.06+ (0.03)HospReadm30d -0.29 (0.22) -0.08 -34% 0.21 (0.13) 0.13 0.05+ (0.03)



ICUReadm2d -0.42 (0.26) -0.04 -61% 0.26 (0.16) 0.11 0.01 (0.05)ICUReadm3d -0.05 (0.34) -0.005 -10% 0.06 (0.20) 0.78 0.04 (0.04)ICUReadm5d -0.20 (0.28) -0.02 -32% 0.17 (0.17) 0.33 0.09+ (0.04)ICUReadm -0.07 (0.25) -0.01 -12% 0.14 (0.15) 0.34 0.17*** (0.04)HospReadm1w -0.29 (0.25) -0.04 -43% 0.23 (0.15) 0.14 0.08+ (0.04)HospReadm2w -0.42+ (0.23) -0.08 -51% 0.29+ (0.14) 0.05 0.05 (0.04)HospReadm3w -0.40+ (0.21) -0.09 -46% 0.28* (0.13) 0.04 0.06+ (0.03)HospReadm30d -0.39+ (0.23) -0.10 -43% 0.27+ (0.14) 0.07 0.05+ (0.03)



ICUReadm2d -0.50* (0.24) -0.04 -67% 0.31* (0.15) 0.05 0.01 (0.05)ICUReadm3d -0.12 (0.34) -0.01 -23% 0.10 (0.20) 0.62 0.04 (0.04)ICUReadm5d -0.31 (0.26) -0.04 -46% 0.24 (0.15) 0.14 0.09+ (0.04)ICUReadm -0.12 (0.25) -0.02 -20% 0.17 (0.15) 0.26 0.17*** (0.04)HospReadm1w -0.45+ (0.23) -0.06 -58% 0.33* (0.14) 0.03 0.08+ (0.04)HospReadm2w -0.63*** (0.21) -0.12 -65% 0.42*** (0.13) 0.00 0.05 (0.04)HospReadm3w -0.55** (0.20) -0.13 -57% 0.37** (0.12) 0.01 0.06+ (0.03)HospReadm30d -0.60** (0.22) -0.16 -58% 0.40** (0.14) 0.01 0.05+ (0.03)




Table EC.6 Full Estimation Results for the ICU to SDU Routing Decision – Supplementing Table 8

Covariate Estimationb (se)

SDUBusy -0.51*** (0.05)Male 0.06* (0.03)LAPS2 [0, 94] -0.00 (0.00)LAPS2 [94, 134] 0.00+ (0.00)LAPS2 [134, ] -0.00 (0.00)COPS2 [0, 33] -0.00+ (0.00)COPS2 [33, 87] 0.00* (0.00)COPS2 [87, ] 0.00 (0.00)SAPS3 [0, 52] 0.00 (0.00)SAPS3 [52,61] 0.00 (0.01)SAPS3 [61, ] -0.02*** (0.01)Age [,65] 0.01*** (0.00)Age [65,81] 0.00 (0.00)Age [81, ] -0.01 (0.01)LOSB4ICU [0, 2] -0.02 (0.03)LOSB4ICU [2,31] 0.01*** (0.00)LOSB4ICU [31, ] 0.00** (0.00)ICULOS [0, 38] -0.01*** (0.00)ICULOS [38,83] 0.00*** (0.00)ICULOS [83, ] 0.00+ (0.00)

[Hospital]8 (base case)9 -0.74*** (0.06)1 0.85*** (0.06)6 -0.31*** (0.05)2 0.28*** (0.08)3 -0.21*** (0.05)7 0.46*** (0.06)4 -0.37*** (0.06)5 0.49*** (0.06)10 -0.01 (0.05)

[Admitting Diagnosis: HCUP]Sepsis (base case)Fluid and electrolyte disorders -0.04 (0.12)Coma stupor and brain damage 0.02 (0.09)AMI 0.42*** (0.09)Atherosclerosis 0.61*** (0.11)Chest pain 0.44*** (0.07)Dysrhythmia 0.30** (0.10)Cardiac arrest 0.43* (0.17)CHF 0.30** (0.09)Acute CVD 0.11 (0.08)CAP 0.22** (0.08)Asp pneumonia 0.18 (0.23)GI bleed -0.13+ (0.07)UTI 0.14 (0.15)Hip fracture -0.05 (0.19)Residual codes -0.17 (0.12)ALLRF -0.14 (0.13)CANCER -0.02 (0.27)CATAS 0.16+ (0.08)COPD 0.11 (0.10)ENDOC -0.23** (0.08)GIMISC -0.38** (0.14)HART 0.10 (0.08)

Covariate Estimationb (se)

HEMAT -0.18 (0.18)ILLDEF -0.07 (0.07)LIVPAN 0.03 (0.15)MISC -0.44+ (0.26)MLG -0.33 (0.29)NEURO 0.01 (0.08)NUTRT -0.07 (0.28)OBSDIV -0.31* (0.15)OTHGI -0.13 (0.16)OTHGU -0.31 (0.19)OTHINF -0.10 (0.08)OTHRSP 0.25*** (0.06)PSYCH -0.33** (0.12)SURGCX 0.10 (0.12)TRAUMA 0.09 (0.10)

[Impatient unit before ICU admission]Out-of-hospital (base case)ED -0.12 (0.10)Ward -0.39** (0.12)OR -0.21+ (0.13)OTH -0.38 (0.27)PAR -0.18 (0.13)SDU 0.03 (0.13)

[Nurse Shift]night [23pm,7am] (base case)morning [7am,15pm] -0.62*** (0.05)afternoon [15pm,23pm] -0.50*** (0.05)

[Day of week]Sun (base case)Mon -0.07 (0.05)Tue -0.03 (0.05)Wed -0.04 (0.05)Thu -0.15** (0.05)Fri -0.10* (0.05)Sat 0.01 (0.05)

[Month]Jan (base case)Feb -0.08 (0.08)Mar -0.04 (0.07)Apr 0.02 (0.07)May -0.01 (0.07)Jun -0.01 (0.07)Jul 0.04 (0.07)Aug -0.00 (0.07)Sep -0.03 (0.07)Oct 0.09 (0.07)Nov -0.19* (0.08)Dec -0.22** (0.07)Constant 0.10 (0.19)

Observations 11057Pseudo R2 0.1396

+p < 10%,∗p < 5%,∗ ∗ p < 1%,∗ ∗ ∗p < 0.1%


Table EC.7 Estimation for the ICU to SDU Routing Decision for All Admitting Categories

Covariate ED,Medical ED,Surgical Non-ED, Surgical Non-ED, Medicalb (se) b (se) b (se) b (se)

SDUBusy -0.5110*** (0.0503) -0.7018*** (0.1831) -0.4234*** (0.1013) -0.5364*** (0.1591)LAPS2 [0, 94] -0.0013 (0.0008) 0.0010 (0.0022) -0.0019 (0.0018) -0.0002 (0.0018)LAPS2 [94, 134] 0.0022+ (0.0012) 0.0024 (0.0042) 0.0041 (0.0118) -0.0014 (0.0083)LAPS2 [134, ] -0.0001 (0.0012) -0.0009 (0.0046) -0.0070 (0.0264) -0.0104 (0.0117)COPS2 [0, 33] -0.0033+ (0.0018) -0.0045 (0.0055) -0.0034 (0.0034) -0.0027 (0.0053)COPS2 [33, 87] 0.0022* (0.0010) 0.0019 (0.0033) -0.0011 (0.0022) 0.0016 (0.0029)COPS2 [87, ] 0.0006 (0.0007) 0.0032 (0.0026) -0.0050+ (0.0027) -0.0018 (0.0023)SAPS3 [0, 52] 0.0016 (0.0030) 0.0053 (0.0077) 0.0307*** (0.0041) -0.0043 (0.0077)SAPS3 [52,61] 0.0025 (0.0060) 0.0104 (0.0198) 0.0264 (0.0168) 0.0188 (0.0162)SAPS3 [61, ] -0.0182** (0.0055) -0.0105 (0.0171) -0.0087 (0.0176) -0.0131 (0.0151)LOSB4ICU [0, 2] -0.0119 (0.0340) -0.3239* (0.1424) 0.8090+ (0.4730) -0.1903 (0.2407)LOSB4ICU [2,31] 0.0114*** (0.0021) 0.0106* (0.0043) -0.0026 (0.0038) 0.0173** (0.0056)LOSB4ICU [31, ] 0.0005** (0.0002) 0.0004 (0.0003) 0.0011* (0.0004) 0.0005* (0.0002)ICULOS [0, 38] -0.0108*** (0.0016) -0.0092+ (0.0054) -0.0039 (0.0043) -0.0099* (0.0048)ICULOS [38,83] 0.0046*** (0.0010) 0.0029 (0.0030) 0.0020 (0.0023) 0.0106*** (0.0030)ICULOS [83, ] 0.0004+ (0.0002) 0.0006 (0.0004) 0.0003 (0.0004) -0.0003 (0.0007)

NightShift[11pm,7am] (base case)MorningShift[7am,15pm] -0.6186*** (0.0506) -0.6301*** (0.1651) -0.9586*** (0.1329) -0.6202*** (0.1521)AfternoonShift[15pm,23pm] -0.5018*** (0.0490) -0.4462** (0.1487) -0.7886*** (0.1242) -0.6323*** (0.1437)Hospital-fixed effect

√ √ √ √

Admitting Diagnosis√ √ √ √

Impatient unit before ICU√ √ √ √

Day of week√ √ √ √

Month√ √ √ √

Pseudo R2 0.1396 0.2298 0.4505 0.2301Number of obs 11057 1348 3836 1545

Note. +(p < 10%),∗(p < 5%),∗ ∗ (p < 1%),∗ ∗ ∗(p < 0.1%)

the role of a step-down unit in improving patient outcomes

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