Does What Happens in the ED Stay in the ED? The Effects of Emergency Department Physician Workload on Post-ED Care Use

Abstract

Problem definition:

Emergency department (ED) crowding has been a pressing concern in healthcare systems in the U.S. and other developed countries. As such, many researchers have studied its effects on outcomes within the ED. In contrast, we study the effects of ED crowding on system performance outside the ED–specifically, on post-ED care utilization. Further, we explore the mediating effects of care intensity in the ED on post-ED care use.

Methodology/results:

We utilize a dataset assembled from more than four years of microdata from a large U.S. hospital and exhaustive billing data in an integrated health system. By using count models and instrumental variable analyses to answer the proposed research questions, we find that there is an increasing concave relationship between ED physician workload and post-ED care use. When ED workload increases from its 5th percentile to the median, the number of post-discharge care events (i.e., medical services) for patients who are discharged home from the ED increases by 5% and it is stable afterwards. Further, we identify physician test-ordering behavior as a mechanism for this effect: when the physician is busier, she responds by ordering more tests for less severe patients. We document that this “extra” testing generates “extra” post-ED care utilization for these patients.

Managerial implications:

This paper contributes new insights on how physician and patient behaviors under ED crowding impact a previously unstudied system performance measure: post-ED care utilization. Our findings suggest that prior studies estimating the cost of ED crowding underestimate the true effect, as they do not consider the “extra” post-ED care utilization.

1. Introduction

The extent of emergency department (ED) crowding has risen considerably in the past two decades: the number of visits increased by 50% over this period, while the number of EDs decreased by 10% (American Hospital Association 2018). Such crowding has posed a challenge for ED physicians in how they should behave in response to rising queues. While past research has empirically studied the effects of crowding on care within the ED itself, this paper is the first to document the impacts of ED physician responses to this challenge as they extend outside the confines of the ED. We find that higher ED physician workload leads to greater post-ED care utilization. Further, we identify that increased testing focused on less severe patients who are ultimately discharged home from the ED is a causal mechanism underlying this relationship. These findings reveal novel insights regarding the behavior of ED physicians and introduce a new mechanism linking ED crowding to broader healthcare use that contributes to further overburdening of an already overtaxed medical system.

Prior medical and operations management literature on crowding and physician workload in the ED suggests that these phenomena adversely affect quality of care and productivity in the ED (e.g., Pines et al. 2018, KC et al. 2020). One feature common to these studies is that their focus is limited to the effects of ED crowding and workload on the care delivered and the patient experience during an ED visit. We argue that since an ED is part of a larger healthcare system, a comprehensive analysis of the effects of crowding in the ED requires studying its impacts on the healthcare system performance measures. To this end, we explore whether the care delivered and the patient experience in the ED impact the care that the patient receives after the ED visit. The answer to this question establishes the impact of the ED on the utilization of other channels of care in the healthcare system (e.g., primary care, specialist, imaging service facility, inpatient clinic).

Leveraging detailed visit-level data in the ED combined with exhaustive billing records of more than four years of all care events in an integrated health system, we examine whether physician workload during the patient visit in the ED impacts the care that the patient receives in the healthcare system after he leaves the ED (i.e., post-ED care). We measure post-ED care by the number of care events (rather than a simple count of the number of visits) to capture intensity of care; each care event is a medical claim, and thus one clinical visit may generate more than one care event. We use count models and an instrumental variable approach to estimate the effects of ED physician workload on the number of post-discharge care events across all channels of care. We also explore whether ED physician test ordering behavior under ED crowding mediates the effects of physician workload on post-ED care use. This research design enables us to provide an empirically-grounded understanding of how server (physician) and customer (patient) behavior in response to crowding in an upstream stage (ED) impacts utilization in downstream stages (various channels of care) in a queueing system. As detailed in the contributions of the paper, we establish that when ED physician workload increases, resource utilization increases almost everywhere in the healthcare system. More specifically, our contributions are as follows:

1. We show that the number of post-discharge care events for patients discharged home from the ED, without being admitted to the hospital inpatient unit, (hereafter discharged patients) is an increasing concave function of ED physician workload. We find no evidence of any such relationship between ED physician workload and the number of post-discharge care events for patients admitted to the inpatient unit (hereafter admitted patients). Note that post-discharge care events are distinct from the ED revisit performance measure used in prior crowding (KC 2013) and non-crowding studies (Song et al. 2017a) in the ED setting. The ED revisit performance measure ignores several frequently used channels of post-ED care. For example, in the ED that we studied for the purpose of this research, only 17% of ED visits are followed by a 30-day ED revisit, whereas 81% of ED visits have a 30-day post-discharge care event.

2. With a more granular analysis of the destination for post-discharge care events, we find that when ED physician workload increases, the increase in healthcare system utilization is not limited to a single downstream stage. Rather, we show that the number of post-ED care events for discharged patients increases in both ED and non-ED channels of care. This finding is distinct from prior work that is solely focused on the negative impact of crowding on revisits to the ED.

3. We find that care intensity in the ED mediates the effects of ED physician workload on post-ED care use. In particular, we identify an increasing concave effect of workload on the number of diagnostic tests only for discharged (i.e., less severe) patients, indicating heterogeneous effects on discharged and admitted patients. We also find that post-ED care use increases with the increased care intensity in the ED. Thus, this contribution is twofold. First, we show that ED physicians are strategic when they adjust their test-ordering behavior, and their response depends on whether a patient will be admitted to the inpatient unit or discharged home. Although the effect of crowding on test-ordering behavior has been explored before collectively (i.e., regardless of patient types), the heterogeneous component is a novel finding of this paper. Second, our analysis is the first to show that diagnostic tests in the ED have an impact on the utilization of services in other channels of care.

Together, these findings show that the effects of physician workload in the ED are more far reaching than previously documented and offer insights for ED physicians, hospital managers, and policy-makers. The results inform ED physicians that providing higher care intensity during the ED visit does not benefit the healthcare system by reducing future care needs. Instead, it leads to an increase in post-ED care use. Moreover, hospital managers should explicitly consider these effects when setting physician staffing levels. In addition, the results show the importance of balancing workload across physicians, even at low workload levels, and the estimated effects should be considered in designing patient-physician assignment policies in the ED. Lastly, the findings in this paper provide new evidence in support of efforts by policy-makers to improve access to outpatient care services in order to reduce ED crowding.

This paper also provides several novel empirical findings to guide future analytical studies on queueing theory. First, the results suggest that different stages in a tandem queue are not independent and characterize how the conditions of an upstream stage and servers’ response to these conditions impact the demand in downstream stages. Second, we underscore the importance of considering system-level performance measures to make decisions about queueing system configurations. We also show that the customer type is an essential factor in discretionary behavior of servers. Considering this aspect of server behavior can improve future queueing models in terms of resource management and the optimal control policy.

2. Related Literature

2.1. Crowding in Service Operations

Prior operations management literature has empirically studied the impacts of crowding factors, such as system congestion and server workload, on several aspects of service in a variety of settings (e.g., Tan and Netessine 2014 in hospitality, Wang and Zhou 2017 in retailing, Xu et al. 2021 in banking). In particular, the effects of crowding in healthcare services have received a great deal of research attention. These studies explore the effects of various crowding measures on service time (e.g., KC and Terwiesch 2009, Berry Jaeker and Tucker 2016, Chan et al. 2016), the provision of services (e.g., KC and Terwiesch 2017), and service configuration (e.g., Freeman et al. 2016). Further, prior research documents how the change in occupancy level affects service outcome, as measured by length of stay after the focal service (e.g., Kim et al. 2016), hospitalization cost and revenue (e.g., Powell et al. 2012), hospital readmission (e.g., Anderson et al. 2012), and mortality rate (e.g., Kuntz et al. 2014).

In the context of the ED, prior literature has examined the impact of ED crowding on several behavioral aspects of patients (Batt and Terwiesch 2015), nurses (Green et al. 2013), physicians (KC 2013, Kuntz and Sülz 2013, KC et al. 2020), and their interactions (Batt and Terwiesch 2016). However, as noted earlier, although various effects of crowding have been explored in this literature, the documented effects have been limited to the operations within the ED. One exception is the work of Freeman et al. (2021), who test whether ED congestion has an effect on the accuracy of disposition decisions, which impacts the inpatient unit. Our paper is thus the first to take a healthcare system perspective and explore the impacts of workload in the ED on the utilization of care across different channels of care. Specifically, we seek to examine whether ED physician workload impacts post-discharge care events.

2.2. Discretionary Behavior of Service Providers

We explore the changes in care intensity in response to workload as a potential cause for post-ED care use. The number of diagnostic tests is a common measure of care intensity (Leep Hunderfund et al. 2017), which affects cost of care and quality of service (Abaluck et al. 2016). ED physicians order diagnostic tests to acquire more information about a patient’s clinical condition and improve accuracy of diagnosis. Because additional tests prolong ED stay and exacerbate ED congestion (Chan 2018), ED physicians use their discretion to balance the trade-off between the costs and benefits of ordering diagnostic tests.

There is growing interest in understanding the discretionary behavior of servers in response to operational factors, such as congestion (e.g., Tan and Netessine 2014), task processing time (Ibanez et al. 2017), task scheduling (e.g., Ibanez and Toffel 2020), patient waiting time (Ding et al. 2019), and patient placement (e.g., Meng et al. 2021). In particular, several papers examine contributing factors to diagnostic test-ordering behavior. Song et al. (2017a) and Berry Jaeker and Tucker (2020) find a reduction in test utilization when a physician performance is observed by her peers and when test ordering requires a justification step, respectively. Other studies examine whether different measures of crowding affect test-ordering behavior. In an outpatient clinic, Deo and Jain (2019) find that anticipated workload is negatively associated with the probability of ordering a diagnostic test. Ergün-Şahin et al. (2022) find that the number of diagnostic tests increases with an increase in unfinished tasks but decreases with an increase in finished tasks.

Our paper complements this body of work by exploring the mediating effects of physician diagnostic test-ordering behavior on the utilization of post-ED care services. We provide evidence that the effects of this discretionary behavior extend beyond the focal service encounter. In addition, this is the first study to investigate diagnostic test-ordering behavior separately for discharged and admitted patients. The results show that ED physicians differentiate between these patients in their discretionary behavior.

2.3. Utilization in a Service Episode

We contribute to the healthcare operations management literature that measures service outcome by utilization metrics beyond the focal service encounter, such as hospital readmissions and revisits to ICUs, EDs, and outpatient clinics. This stream of literature has developed predictive models to determine the risk of readmission for individual patients prior to discharge (e.g., Helm et al. 2016), investigated the implications of readmission-related policies (e.g., Soltani et al. 2021), and explored the effects of operational factors and process design on hospital readmission (e.g., Senot 2019), ICU revisit (e.g., Kim et al. 2014), and outpatient clinic revisit (e.g., Bavafa et al. 2021). A few studies have considered this type of outcome in the ED setting. KC (2013) shows that a high physician workload leads to a higher probability of ED revisit. Batt et al. (2019) find that the probability of ED revisit is higher for patients that have been handed off. Song et al. (2017a) find that after the implementation of public physicians’ performance reporting, the probability of ED revisit decreases concurrent with a reduction in the number of diagnostic tests. However, the authors do not test for any causal effect of test utilization on ED revisit.

Despite measuring the service outcome over an episode of care, these studies consider revisits only to the same channel as the focal service encounter (i.e., readmission to the hospital, revisit to the ICU or ED). In practice, however, the patient may decide (on his own or based on physician recommendation) to visit the same or a different hospital, an imaging service facility, a specialist, or a primary care provider (PCP). Thus, our study is the first to provide a thorough picture of post-ED resource utilization by including post-discharge care events in all channels of care.

3. Hypotheses Development

An ED physician is usually responsible for multiple patients simultaneously. This multitasking is an inherent feature of the ED and a challenging aspect of the ED physicians’ work ( Leppink and Hanham 2019). Prior operations management and medical literature has documented multiple effects of multitasking and workload on physicians and on performing their work in the ED: task switching (KC 2013, Skaugset et al. 2016), increased cognitive load (KC 2013, Pines 2017), increased stress (Chisholm et al. 2000, Bendoly 2011), and increased interruptions (Chisholm et al. 2000, 2001).

3.1. Total Effects of Workload on Post-ED Care Use

High workload may impact the number of post-discharge care events for both discharged and admitted patients. For discharged patients, when physician workload increases, the physician may rush the service and discharge the patient prematurely (KC and Terwiesch 2009, Batt and Terwiesch 2016). However, the ED physician may coordinate a follow-up visit with the patient’s PCP and postpone additional care to this visit as a common practice of safety (Pathirana et al. 2017); this is especially the case for patients who are in a stable condition at the time of discharge but need early re-evaluation (Carrier et al. 2011). In addition, early discharge may degrade service quality and increase the need for post-discharge care events (KC and Terwiesch 2012, Chan et al. 2014). Moreover, task switching and interruptions may lead to errors in diagnosis and treatment (Tucker and Spear 2006, Skaugset et al. 2016), causing complications and generating the need for additional care (KC and Terwiesch 2009). As an aggregate effect of these mechanisms, we expect a positive impact of physician workload on the number of post-discharge care events for discharged patients.

Hypothesis 1

As physician workload increases, the number of post-discharge care events for discharged patients will increase.

The preceding discussion about changes in ED physician behavior related to follow-up visit coordination does not apply to admitted patients. For these patients, the inpatient physician (rather than the ED physician) is in charge of coordinating follow-up visits. As stated earlier, however, increased ED physician workload may cause service quality degradation. If such an effect exists, it impacts admitted patients as well. For example, Sun et al. (2013) find that when the ED is busy, inpatient mortality, length of stay (LOS), and costs per hospitalization increase. Nevertheless, because admitted patients stay in the hospital after leaving the ED, we expect the adverse impact of physician workload on service quality in the ED to be addressed in the inpatient unit. Thus, we state this as a null hypothesis as follows:

Hypothesis 2

As physician workload increases, the number of post-discharge care events for admitted patients will not change.

Note that hospital admission is another type of post-ED care. Prior work has found that physician workload increases the probability of hospital admission (Gorski et al. 2017). Thus, to avoid redundancy, this paper only focuses on the impact of physician workload on post-discharge care events.

3.2. Mediating Effects of Care Intensity in the ED

To establish the mediating effects of care intensity in the ED, we hypothesize two separate relationships that jointly constitute these effects: (1) the effect of physician workload on care intensity in the ED and (2) the effect of care intensity in the ED on post-ED care use.

Diagnostic tests are widely used as a measure of care intensity (Leep Hunderfund et al. 2017), and thus we use the total number of laboratory and radiology tests ordered in the ED as a proxy for ED care intensity. Resource utilization in the ED (e.g., diagnostic test utilization, medication administration) is an inherent physician practice characteristic and varies across ED physicians to the extent that some ED physicians are known as “testers” (Hodgson et al. 2018). Prior studies have found multiple mechanisms that may alter a physician test-ordering behavior when workload increases. First, the physician may order more diagnostic tests as an alternative for direct patient contact when she has less time to spend with each patient (Batt and Terwiesch 2016). Second, increased stress and interruptions may hinder the physician from systematic decision-making and critical thinking (Chisholm et al. 2000). Because test ordering requires less critical thinking compared to diagnosis through direct patient contact (Pines 2009), the physician may order more tests when workload increases. Third, the physician may order more tests to temporarily reduce workload while waiting for the test results (Berry Jaeker and Tucker 2020); this may also take the form of ordering more tests in parallel rather than serial ordering (Song et al. 2017a). Fourth, increased cognitive load may cause the physician to become more risk-averse (Deck and Jahedi 2015); this may lead to an increase in the number of diagnostic tests to mitigate the concerns that the physician may have about the medical or legal consequences of mishandling a case (Rao and Levin 2012, Dai et al. 2016).

These mechanisms suggest a positive impact of crowding on the number of diagnostic tests, and prior literature has provided empirical evidence for this effect in the ED (Batt and Terwiesch 2016, Deo and Jain 2019). However, the strategic component of physician test-ordering behavior is neglected in these studies. Past studies have shown that ED physicians are able to predict a patient disposition (discharge home or admit to the hospital) at the time of triage with an accuracy level of about 80% (Zwank et al. 2021). This has led some hospitals to employ disposition prediction as a basis to improve their patient flow through patient streaming (Saghafian et al. 2012). In practice, ED physicians often make a preliminary mental decision about the patient disposition after an initial examination and before ordering diagnostic tests (Pelaccia et al. 2014). Thus, their test-ordering behavior may depend on patient disposition status.

While the above-mentioned mechanisms theorize an increase in the number of diagnostic tests for patients who will be discharged from the ED, they do not necessarily apply to patients who will be admitted to the hospital. The physician may avoid an increase in the number of diagnostic tests for patients who will be admitted to the hospital because these patients receive immediate care after leaving the ED and there is less risk associated with missing a diagnostic test in the ED. It is also possible that the physician will order fewer diagnostic tests for these patients because excessive cognitive load may increase their reliance on early information (Deck and Jahedi 2015), causing task reduction (Oliva and Sterman 2001). Therefore, the physician may decide to admit the patient with fewer diagnostic tests to reduce workload. What distinguishes our work from prior literature that explores the impact of crowding on test ordering collectively (i.e., regardless of patient types) is that we hypothesize physician strategic test-ordering behavior that depends on patient severity and disposition status. Accordingly, we propose separate hypotheses for discharged and admitted patients:

Hypothesis 3

As physician workload increases, care intensity in the ED for discharged patients will increase.

Hypothesis 4

As physician workload increases, care intensity in the ED for admitted patients will decrease.

More diagnostic tests are generally used to reach a more definite diagnosis (Whiting et al. 2007); depending on the test results, this may lead to an increase or a decrease in coordination of follow-up visits and need for follow-up treatment. There is strong agreement in the medical community, however, that a greater number of diagnostic tests is associated with an increase in the occurrence of overdiagnosis (e.g., Carpenter et al. 2015, Pathirana et al. 2017). With additional diagnostic tests, it is possible to detect a pseudodisease, that is, a disease in an asymptomatic patient which will never be harmful if not identified (Moynihan et al. 2012). Physicians believe that even for a completely healthy person, if they perform multiple diagnostic tests, they will eventually find an abnormality; Welch et al. (2011) refer to this phenomenon as an “epidemic of diagnosis.” Overdiagnosis is believed to be followed by overtreatment and a potential sequence of unnecessary follow-up visits, tests, medications, and procedures because the physician cannot simply ignore the new findings (Pathirana et al. 2017). We also note that there has recently been a growing debate in the medical community in support of more diagnostic tests that could lead to an early detection of disease (e.g., Rosenbaum 2017). The common conclusion of both sentiments, however, is that more diagnostic tests in the ED lead to more diagnoses that require further treatment or follow-up visits to control identified anomalies. Although the impact of screening and testing on the level of diagnosis and treatment has been explored in the literature in general, it has not been investigated in the context of the ED and especially in terms of how diagnostic tests may mediate the effect of physician workload on post-ED care use. We hypothesize on this impact as follows:

Hypothesis 5

As care intensity in the ED increases, the number of post-discharge care events will increase.

We propose this hypothesis regardless of patient disposition status because as McEvoy et al. (2011) show for the case of heart screening, the impact of overdiagnosis may last for a long time. This may be the case for other conditions as well, and thus the effect of diagnostic tests in the ED on admitted patients may go beyond the inpatient stay.

4. Empirical Setting

4.1. Clinical Context

An episode of care is defined as the set of health services provided to a patient within a specific period of time (Stedman 2005). We consider an episode of care that starts with an ED visit and continues for 30 days after the patient is discharged from the hospital. We break down each episode of care into two phases: ED care and post-ED care (Figure 1), wherein the post-ED care phase is potentially comprised of inpatient care and post-discharge care. Note that not all patients necessarily experience inpatient or post-discharge care. A closer look at Figure 1 shows that an episode of care resembles a tandem queue with multiple stages: ED, inpatient unit, and various post-discharge channels.

Figure 1. Episode of Care.

Notes. *Physician workload is measured at the time of physician assignment, as described in Section 4.2.2.

**In this study, we focus on post-discharge care events within 30 days after discharge from the hospital (ED or inpatinet unit).

The typical process flow in the study ED is similar to other EDs (e.g., Batt and Terwiesch 2015). The ED care phase starts with the patient arrival in the ED. After check-in and triage, once a treatment room becomes available, the patient is transferred to the room. Soon after, a physician meets with the patient, reviews his medical history and the information recorded by the triage nurse, asks him routine questions about his current condition, and examines him. After collecting this information, the physician decides on the care plan, including a preliminary mental decision about the patient disposition (Pelaccia et al. 2014). As part of the care plan, the physician may order diagnostic tests (e.g., laboratory tests, radiology tests), and while waiting for the test results, the physician cares for other patients that she is responsible for. After the test results become available, the physician evaluates them and diagnoses the case. In more complex cases, the physician may order further tests or consult with a specialist before making a diagnosis. Finally, the physician records the disposition decision, marking the transition between the ED and post-ED care phases.

If the ED physician decides to discharge the patient, the patient is informed about the post-discharge care plan, which may include recommending follow-up visits with an outpatient care provider such as the patient’s PCP, a specialist, or an imaging service facility. If the patient is to be admitted to the hospital (the second stage in the tandem queue), a bed request is sent to the inpatient unit and the ED physician communicates the case with a hospitalist or another admitting physician. Once an inpatient bed becomes available, the patient is transferred, and the inpatient care phase begins. During the inpatient stay, the patient receives further care (e.g., surgery, medication) until there is no further need for inpatient care and he is ready to be discharged. Just prior to the discharge, similar to the discharge process for the patients that are discharged from the ED, an inpatient physician (or a nurse) provides post-discharge instructions to the patient and recommends follow-up visits.

The third stage in the tandem queue starts after the patient is discharged from the hospital (ED or inpatient unit). The patient may undergo post-discharge care in the form of one or more post-discharge care events in the ED or non-ED channels (e.g., primary care, specialist, imaging service facility, inpatient clinic).

4.2. Data Description

We combine a detailed ED visit-level dataset with exhaustive billing data from an integrated health system. The ED visit-level dataset is from an urban teaching hospital with an average of about 4,000 ED visits per month over the period of this study. These data consist of 50 consecutive months of ED visits (Jan 2013 – Feb 2017), a total of 203,213 visits. For each ED visit, the data include detailed time stamps (e.g., patient arrival, physician assignment, patient disposition), attending ED physician, diagnostic tests, patient disposition, patient demographics (e.g., age, gender), chief complaint, comorbidities, Emergency Severity Index (ESI), mode of arrival (e.g., walk-ins, ambulance), and primary insurance. The study ED uses a five-level ESI triage scale with one being the most severe and five being the least severe (Gilboy et al. 2011). The billing data are from a regional health system with six hospitals and more than 80 outpatient clinics. These data include time-stamped care events during our study period (Jan 2013 – Aug 2017). We construct our dataset by linking these two sources to identify the post-discharge care events after each ED visit.

As shown in Figure A1, we focus on the adult patients because the pediatric patients differ in their care paths and post-ED care needs (Centers for Disease Control and Prevention 2016). In addition, adult and pediatric patients are operationally different because in the study ED, patients under 18 years of age are treated in a separate pediatric area by pediatric physicians who have a different practice training and pattern than adult emergency medicine physicians. The study ED provides service to both within-network and out-of-network patients, with about 40% of ED visits made by out-of-network patients (i.e., patients whose PCPs are not affiliated with the study health system). The billing dataset, however, includes only care events within the network of the study health system. Thus, as supported by summary statistics in Table A1, for the out-of-network patients, we may not observe all post-discharge care events. Hence, to ensure that all post-discharge care events are considered in the analysis, we limit the sample to the within-network patients. In about 1% of the ED visits, the patient left the ED without being seen or against medical advice. We exclude these observations because of an incomplete ED visit. To avoid censored post-ED care, we also drop the ED visits wherein the patient died within 30 days after leaving the hospital. Finally, to avoid small sample size issues, we exclude the ED visits classified as triage level ESI 1 or 5 (0.4% of the observations) and with unknown primary payer (less than 0.1% of the observations). The final dataset includes 74,348 unique ED visits. Note that although we use this sample for the main analysis, we use all ED visits to measure physician workload.

4.2.1. Dependent Variables.

The main dependent variable in the study is the number of 30-day post-discharge care events, a benchmark measure in the industry (e.g., Sharma et al. 2010). Therefore, for each ED visit, we count the number of care events for each patient within 30 days after discharge from the ED (for discharged patients) or discharge from the inpatient unit (for admitted patients). Because our goal is to measure total resource use during the episode of care, we include all post-discharge care events rather than condition-specific post-discharge care events (Hussey et al. 2009). We also note that prior studies have found a strong correlation between all post-discharge care events and condition-specific post-discharge care events (Ellimoottil et al. 2017). Figure A2a shows the histogram of the number of post-discharge care events. As shown in Table 1, we find that a patient has, on average, 3.88 post-discharge care events with a standard deviation (SD) of 4.42 care events within 30 days after leaving the hospital. There is a substantial difference in post-discharge care use between discharged and admitted patients: an average of 3.21 and 5.54 post-discharge care events for discharged and admitted patients, respectively.

Table 1.

Summary Statistics of the Main Independent and Dependent Variables

Patients	All		Discharged		Admitted
	Mean	SD	Mean	SD	Mean	SD
Physician workload	8.03	3.98
Pr(hospital admission)	0.29	0.45
Post-discharge care events	3.88	4.42	3.21	3.79	5.54	5.35
Diagnostic tests	4.42	3.15	3.66	2.92	6.30	2.87
Observations	74,348		52,966		21,382

Notes. Table A2 provides a correlation table for these variables.

4.2.2. Independent and Mediating Variables.

The main explanatory variable in our study is physician workload during the ED care phase (Figure 1). We define physician workload following prior literature (e.g., KC 2013, Song et al. 2015): for ED visit i, to which ED physician p(i) is assigned at time t(i), we determine physician workload, Workload_i, as the number of patients that physician p(i) has been assigned to before time t(i) and are still in the ED. We observe the time when an ED physician is assigned to each patient and the time that the patient leaves the ED. Thus, we can measure the workload of each physician at any point in time. We measure physician workload at the time of physician assignment because (as described in Section 4.1) soon after the physician assignment, she meets with the patient and decides on the care plan, including the diagnostic tests and a mental decision about the patient disposition. In addition, this removes the circular logic of the focal patient affecting his own workload measurement. In the study ED, on average, a physician is simultaneously responsible for 8.03 patients (SD = 3.98 patients). Figure A2b shows the histogram of physician workload in this ED.

We measure care intensity in the ED by the number of diagnostic tests (i.e., total number of laboratory and radiology tests) as a possible mediator for the effects of physician workload on post-ED care use (Figure 1). For each ED visit, we observe the number of laboratory tests (e.g., basic or comprehensive metabolic, complete blood count, urinalysis) as well as radiology tests (e.g., CT scans, MRI, X-rays) ordered in the ED. Figure A2c shows the histogram of the number of diagnostic tests in this ED. On average, for each ED visit, an attending physician orders 4.42 diagnostic tests. Separating discharged and admitted patients, we note that, on average, physicians order more diagnostic tests for patients that will be admitted compared to patients that will be discharged.

4.2.3. Control Variables.

We control for several patient-specific, visit-specific, and time-related covariates. The patient-specific variables include the patient’s gender, age (linear and quadratic terms), and race, along with the economic variables related to the patient’s residence neighborhood: education and income level quartiles. The visit-specific covariates include the mode of arrival and primary payer. In addition, to account for heterogeneity in clinical needs, we control for patient disposition, triage level, and a binary complexity indicator. The patient disposition is a binary variable that indicates whether the patient was admitted to the hospital. As shown in Table 1, 29% of ED visits resulted in hospital admission. The ESI variable specifies the triage level. We categorize an ED visit as a complex visit if its weighted count of Elixhauser comorbidities (weights suggested by van Walraven et al. 2009) is above the median. Finally, we control for the time-related covariates including year, month, a weekend indicator, time of the day by four-hour blocks (12 a.m. to 4 a.m., 4 a.m. to 8 a.m., etc.), and the interaction term of the weekend and time of the day variables.

5. Total Effects of Workload on Post-ED Care Use

We begin the analysis of the effects of workload on post-ED care use by measuring the total effects of workload (Hypotheses 1 and 2).

5.1. Empirical Specification

5.1.1. Econometric Model.

To test Hypotheses 1 and 2, we estimate the total effect of workload on the number of post-discharge care events. Because the number of 30-day post-discharge care events is a discrete variable and an ED visit is always followed by a limited number of post-discharge care events, we estimate a negative binomial (NB) regression model (Hilbe 2011):

$$\begin{gathered} \ln (PD{E}_i)=\alpha +{\beta }_{1}Workloa{d}_i+{\beta }_{2}Workloa{d}_i^2+{\beta }_{3}Admi{t}_i \\ +{\gamma }_{1}Admi{t}_i\times Workloa{d}_i+{\gamma }_{2}Admi{t}_i\times Workloa{d}_i^2 \\ +{\text{X}}_i\theta +Physicia{n}_i+ChiefComplain{t}_i+{ϵ}_i, \end{gathered}$$ (1)

where PDE_i denotes the number of 30-day post-discharge care events after ED visit i. To allow for non-monotonic response to workload, we include both linear and quadratic terms of Workload_i. We also control for their interaction terms with Admit_i, an indicator of hospital admission for ED visit i, to allow for different effects by patient disposition. The coefficients β₁ and β₂ capture the effect of workload on the number of post-discharge care events for discharged patients (Hypothesis 1), and the summation of the coefficients β₁ and γ₁ and also β₂ and γ₂ capture the effect of workload on the number of post-discharge care events for admitted patients (Hypothesis 2). β₃ captures the potential difference in the number of post-discharge care events between discharged and admitted patients. The vector X_i includes the visit-level and time control variables associated with ED visit i, as described in Section 4.2.3. In addition, we control for waiting room census as well as nonfocal physicians’ workload to rule out the possibility that the quantities of interest are confounded by other crowding factors, which are correlated with physician workload. We also control for time-invariant attending physician and chief complaint fixed effects associated with ED visit i (we combine all chief complaints that individually account for less than 0.5% of ED visits). Finally, ϵ_i is the error term, and we assume that exp(ϵ_i) follows a gamma distribution.

5.1.2. Endogeneity and Instrumental Variables.

The estimates from Equation (1) might be biased because of two potential sources of endogeneity. First, patients may self-select receiving service in the ED, so that only more severe cases are served when the ED is busy. Table A2 suggests a moderate correlation between observed determinants of severity (age, triage level, complexity indicator) and physician workload, lending evidence to support this concern. Second, there are factors that are observable by the ED physician but unobservable in the data (e.g., aspects of patient condition such as sweating and pallor). These factors may affect the physician workload, the admission decision by her, and the number of post-discharge care events. Thus, Workload_i and Admit_i are potentially correlated with the error term ϵ_i in Equation (1), which results in biased estimation through the maximum likelihood method (Heckman 1977). To address this concern, we employ the control function (CF) method. CF is a full information maximum likelihood approach that has been used for count models with endogenous explanatory variables (e.g., Kim et al. 2014, Akkas et al. 2018). Similar to the two-stage least squares (2SLS) in linear models, CF is a two-stage approach. In the first stage of CF, we include two equations: one for each of the endogenous variables (Workload_i and Admit_i) regressed against the exogenous covariates in Equation (1) and a vector of instrumental variables (IVs). We estimate a linear regression model and a probit model for Workload_i and Admit_i, respectively:

$$Workloa{d}_i=\alpha +{\text{X}}_i\theta +Physicia{n}_i+ChiefComplain{t}_i+I{V}_i+{ϵ}_i,$$ (2)

$$\begin{gathered} Admi{t}_i^{*}=\alpha +{\text{X}}_i\theta +Physicia{n}_i+ChiefComplain{t}_i+I{V}_i+{ϵ}_i, \\ Admi{t}_i=1\{Admi{t}_i^{*}>0\}. \end{gathered}$$ (3)

In the second stage, the residuals from the first stage are included in the model in Equation (1) to adjust for endogeneity (we refer the reader to Wooldridge 2015 for details about the CF method). Note that it is sufficient to estimate the first stage of CF only for Workload_i and Admit_i because the residuals from the first stage also adjust for endogeneity of the quadratic and interaction terms (Wooldridge 2015).

For each endogenous variable, we need at least one IV that satisfies two conditions: (1) it should have an impact on the endogenous variable (relevance condition) and (2) it should not have an impact on the outcome variable (PDE_i) other than through the endogenous variable (exclusion restriction).

For Workload_i, we define a lagged average workload as an IV, following Tan and Netessine (2014). For ED visit i with physician assignment time a(i), denoted by the day and time of the day (by four-hour blocks), we compute average physician workload for the ED visits with physician assignment time at the same time of the day but one week before a(i). The lagged average workload should be correlated with Workload because of time-dependent ED arrival and physician staffing (Armony et al. 2015), satisfying the relevance condition. However, we do not expect the lagged workload to have a direct impact on post-discharge care events, satisfying the exclusion restriction.

For Admit_i, similar to the approach implemented in Phillips et al. (2015) and Cachon et al. (2019), we use two “Hausman-type” instrumental variables with matching that are constructed based on the ED visits’ similarity (Hausman 1996). We consider two ED visits to be clinically similar if the chief complaints and ESI levels are identical in these visits. The first IV is the proportion of similar ED visits, excluding the focal visit, with the same workload level in which the patient is admitted to the hospital. For ED visit i, among all other ED visits in the dataset which are similar to visit i and have a workload level of Workload_i, we compute the proportion of visits with hospital admission. Prior studies have shown that, controlling for the clinical conditions, the hospital admission decision is a function of workload (Gorski et al. 2017). Because workload and clinical conditions are the same for the focal ED visit and the matched ED visits, which are used to construct the IV, we expect the probability of admission for the focal visit to be correlated with the IV, satisfying the relevance condition. However, there is no reason to expect the proportion of nonfocal ED visits with hospital admission to have a direct effect on the number of post-discharge care events for the focal ED visit, satisfying the exclusion restriction. The second IV is the proportion of similar ED visits, excluding the focal ED visit, with overlapped treatment phase in which the patient is admitted to the hospital. For ED visit i, among similar ED visits that took place concurrently with that visit, we compute the proportion of visits with hospital admission. We consider two visits to be concurrent if their treatment phases overlap with each other. The admission decision for the concurrent, similar ED visits is expected to be relevant to the probability of hospital admission for the focal ED visit because the overall environment in the ED and hospital at the time of visit i may impact the admission decision, Admit_i. Again, there is no reason to expect the proportion of nonfocal ED visits with hospital admission to have a direct effect on the number of post-discharge care events for the focal ED visit. Following standard testing procedures in the literature (e.g., Freeman et al. 2016), we also verify the relevance condition and exclusion restriction of the proposed IVs using Sanderson-Windmeijer (SW) statistics to test for under-identification and weak identification and the Sargan-Hansen (SH) test for over-identification.

5.2. Results

5.2.1. Aggregate Effects in All Channels of Care.

To explore the changes in the number of post-discharge care events in response to physician workload (Hypotheses 1 and 2), we use Equation (1), implementing the CF approach with bootstrapped standard errors (Petrin and Train 2010). Similar to the approach implemented in Arikan et al. (2018) and Batt et al. (2019), in the first stage of the CF approach, we first include one equation for each of the potential endogenous variables. The estimation results in column (1) of Table A3 indicate that the coefficient of the residuals corresponding to the equation of Workload is not statistically significant. One possible explanation for this result could be that controlling for waiting room census and nonfocal physicians’ workload addresses the patient self-selection concern because these are the factors that may directly impact a patient’s decision to receive service in the ED. Thus, we repeat this analysis with including a first stage equation only for Admit (probit model in Equation (3) that also includes workload terms). The estimation results are shown in column (1) of Table 2. We find that there is an increasing concave relationship between the number of post-discharge care events for discharged patients and physician workload, but that the number of post-discharge care events for admitted patients does not change significantly with workload.

Table 2.

Total Effects of Workload on Post-ED Care Use

	(1)		(2)		(3)		(4)
	Post-discharge care events
	in all channels				in the ED		in non-ED channels
	CF		CF		CF		CF
Count process
Workload	0.0119**	(0.0045)	0.0120**	(0.0046)	0.0017	(0.0211)	0.0109*	(0.0044)
Workload 2	−0.0006*	(0.0003)	−0.0006*	(0.0003)	0.0000	(0.0012)	−0.0006*	(0.0003)
Admit×Workload	−0.0052	(0.0066)	−0.0060	(0.0067)	0.0119	(0.0321)	−0.0043	(0.0066)
Admit×Workload2	0.0001	(0.0004)	0.0001	(0.0004)	−0.0004	(0.0018)	0.0000	(0.0004)
Inpatient LOS			0.0330***	(0.0019)
Inflation process
Workload					−0.0369	(0.0296)
Workload 2					0.0021	(0.0017)
Admit×Workload					0.0430	(0.0447)
Admit×Workload2					−0.0018	(0.0024)
Observations	74,337		74,337		74,337		74,337

Notes. All models include all controls in Equation (1), including attending physician and chief complaint fixed effects. Robust standard errors clustered by attending physician are shown in parentheses. Table A4 shows the results for the first stage of CF for column (1), and Table A5 provides the estimation results without adjusting for endogeneity.

^*p < 0.05;

^**p < 0.01;

^***p < 0.001.

The estimation results indicate that the number of post-discharge care events for discharged patients initially increases with workload (β₁ = 0.0119, p < 0.01). The significant negative coefficient for the quadratic term of workload (β₂ = −0.0006, p < 0.05), however, indicates that the number of post-discharge care events increases only up to a stationary point (the point at which the first derivative of Equation (1) with respect to Workload_i is equal to zero, computed as −β₁/2β₂ when Admit_i = 0). Because we estimate the effects separately for discharged and admitted patients, for ease of interpretation, we show the predicted number of post-discharge care events for the 5th percentile to 95th percentile values of physician workload (1 to 14 patients) in Figure 2. Figure 2a shows that the stationary point is at the workload level of 10 patients (0.0119 ÷ (2 × 0.0006) = 10), which lies well within the range of physician workload in the data (70th percentile). To distinguish an inverted U-shaped relationship from an increasing concave relationship, we investigate the sign and statistical significance of the slope of the curve at each individual workload level in Figure 2a (Lind and Mehlum 2010): the slope of the curve is positive and statistically significant when workload changes between one and seven patients but is not significantly different from zero afterwards. These results indicate an increasing concave relationship between the number of post-discharge care events for discharged patients and physician workload, providing support for Hypothesis 1. Stated as a relative percentage change, increasing physician workload from one to seven patients corresponds to a 4.5% increase ((3.23 – 3.09) ÷ 3.09 = 4.5%) in the number of post-discharge care events for discharged patients. Note that although the increasing trend in the number of post-discharge care events is persistent only up to the stationary point, there is no significant change (negative or positive) in the number of post-discharge care events after physician workload reaches seven patients, which suggests a saturation effect. That is, post-ED care use increases with physician workload at a diminishing rate and it does not change after workload reaches its maximum impact.

Figure 2. Expected Number of 30-day Post-discharge Care Events.

Notes. Shading indicates statistical significance (at the 5% level) of the marginal effect (slope of the curve) at each point. Figure A3a shows the estimated slopes of the curves.

Turning to admitted patients, we find that the slope of the curve in Figure 2b is not significantly different from zero as physician workload ranges from its 5th percentile to 95th percentile values (1 to 14 patients). Thus, we cannot reject the null hypothesis that ED physician workload does not affect the number of post-discharge care events for admitted patients (Hypothesis 2). One possible explanation for this null result could be that because admitted patients receive further care in the inpatient unit, the effects of physician workload in the ED, if any, do not show up after the patient is discharged from the hospital. To mitigate this potential confounding effect, we re-estimate the model in column (1) of Table 2 after controlling for inpatient LOS, a common measure of inpatient care intensity (Wennberg et al. 2009). The estimation results are shown in column (2) of Table 2, indicating that our earlier results are stable and not driven by confounding effects of inpatient care intensity. This result indicates that the observed difference between the effects of ED physician workload on the number of post-discharge care events for discharged versus admitted patients is not attributed to their different care paths and is potentially induced by heterogeneous effects of ED physician workload on care provided in the ED for these patients. We explore this possibility further in Section 6.

In sum, we show that higher physician workload increases post-ED care use. Specifically, for discharged patients, as workload increases up to about its mean value, the number of post-discharge care events increases and the effect is stable afterwards. This observation is noteworthy because it shows that healthcare services utilization is not solely a function of clinical factors. Rather, the ED environment is also a driver of post-ED care use.

5.2.2. Post-discharge Care Events across Channels of Care.

Having shown that the number of post-discharge care events, specifically for discharged patients, increases with the increased physician workload in the ED, we now repeat this analysis for different channels of care to gain a richer understanding of the destination for the increased visits. Specifically, we examine whether the increased post-discharge care events occur as return visits to the ED or as visits to non-ED channels, such as PCPs, specialists, imaging service facilities, and inpatient clinics.

We estimate Equation (1) with the number of post-discharge care events in the ED and non-ED channels, separately, as the dependent variable. The only difference between these two models is that for the post-discharge care events in the ED, because of an excess of zero count (only 17% of ED visits have one or more 30-day post-discharge care events in the ED), we estimate a zero-inflated Poisson (ZIP) model, which combines a binary logit (i.e., inflation) process and a Poisson count process (Lambert 1992) and takes the following form:

$$E[PD{E}_i^{ED}]=\frac{1}{1+\exp (W_i{\eta }_{inf})}\times \exp (W_i{\eta }_{count}),$$ (4)

in which $PD{E}_i^{ED}$ is the number of 30-day post-discharge care events in the ED for ED visit i and W_iη_inf and W_iη_count are predicted for the inflation and count processes, respectively, using the same set of explanatory variables in Equation (1). Note that Equation (1) with W_iη_inf and W_iη_count as the dependent variable is estimated jointly for the inflation and count processes by maximizing a joint likelihood function (Hilbe 2011).

The estimation results of these models are shown in columns (3) and (4) of Table 2. For ease of interpretation, we focus on the predicted values shown in Figure 3, indicating that for discharged patients, the number of post-discharge care events in both ED and non-ED channels has an increasing concave relationship with physician workload. Specifically, the number of post-discharge care events in the ED increases by 6.8% ((0.220 – 0.206) ÷ 0.206 = 6.8%) when workload increases from one to five patients and it is stable afterwards. The number of post-discharge care events in non-ED channels increases by 3.5% ((2.99 – 2.89) ÷ 2.89 = 3.5%) when workload increases from one to six patients and it is stable afterwards. Although the absolute increase is smaller, the relative change is larger for ED visits compared to non-ED visits. Given that the number of post-discharge care events changes with the increased workload only for discharged patients, here, we discuss the changes in the number of post-discharge care events across different channels only for this group of patients.

Figure 3. Expected Number of 30-day Post-discharge Care Events in Different Channels.

Notes. Shading indicates statistical significance (at the 5% level) of the marginal effect (slope of the curve) at each point. Figures A3c and A3d show the estimated slopes of the curves.

These results suggest that physician workload in the ED impacts post-ED care use both in the ED and non-ED channels. ED revisits are perceived as a measure of lower quality of care (e.g., Rising et al. 2014, Batt et al. 2019). In contrast, post-discharge care events in non-ED channels are recommended in medical guidelines and have been recognized as an indicator of improved discharge instructions (Hernandez et al. 2010, Agency for Healthcare Research and Quality 2014). However, it is also possible that post-discharge care events in non-ED channels stem from inadequate care in the ED (Rupp and Delaney 2004). Taken together, these results indicate that an increased number of post-discharge care events is at least partly attributable to lower quality of care.

6. Mediating Effects of Care Intensity in the ED

6.1. Empirical Specification

To explore the mediating effects of care intensity in the ED on post-ED care use (Hypotheses 3–5), we investigate two separate relationships that jointly compose the mediating effects: first, the effect of workload on care intensity in the ED, and second, the effect of care intensity in the ED on post-ED care use. Because the number of diagnostic tests in each ED visit is a discrete variable and only a limited number of tests are ordered, we estimate a NB regression model that includes all independent variables in Equations (1). Similar to Equation (1), the estimates may be biased because of endogeneity, so we estimate the effects following the CF approach described in Section 5.1.2.

Next, we explore the second relationship, which is required to compose the mediating effects: the effects of the measure of care intensity in the ED on post-ED care use. To test Hypothesis 5, we modify Equation (1) to control for the number of diagnostic tests in the ED:

$$\begin{gathered} \ln (PD{E}_i)=\alpha +{\beta }_{1}Workloa{d}_i+{\beta }_{2}Workloa{d}_i^2+{\beta }_{3}Admi{t}_i+{\beta }_{4}DiagTes{t}_i \\ +{\gamma }_{1}Admi{t}_i\times Workloa{d}_i+{\gamma }_{2}Admi{t}_i\times Workloa{d}_i^2+{\gamma }_{3}Admi{t}_i\times DiagTes{t}_i \\ +{\text{X}}_i\theta +Physicia{n}_i+ChiefComplain{t}_i+{ϵ}_i, \end{gathered}$$ (5)

in which β₄ captures the effect of the number of diagnostic tests ordered during the ED visit on the number of post-discharge care events for discharged patients. The summation of the coefficients β₄ and γ₃ captures the same effect for admitted patients. Our measure of care intensity may only partially explain the total effect of workload on the number of post-discharge care events. By construction, the total effect of workload on the number of post-discharge care events, estimated in Equation (1), is decomposed into the indirect effect mediated by care intensity in the ED and the direct effect of workload (any effect beyond the effects through the measure of care intensity). The coefficients β₁, β₂, γ₁, and γ₂ capture the direct effect of workload on the number of post-discharge care events.

The estimates from Equation (5) might be biased because of similar endogeneity concerns as in Equation (1). In addition, the same factors that are observable by the ED physician but unobservable in the data that possibly affect the admission decision and the number of post-discharge care events may also have an impact on the number of diagnostic tests. To address this issue, we employ the CF approach described in Section 5.1.2. For Admit, we use the IVs that we developed in Section 5.1.2. For diagnostic tests, we use similar IVs to the ones used for Admit but computed for the number of diagnostic tests: (1) the average number of diagnostic tests for similar ED visits, excluding the focal ED visit, with the same workload level, and (2) the average number of diagnostic tests for similar ED visits, excluding the focal ED visit, with overlapped treatment phases. The discussion regarding the relevance and validity of these IVs follows the same logic as the discussion in Section 5.1.2.

6.2. Results

6.2.1. The Effect of Workload on Care Intensity in the ED.

We begin the analysis of mediating effects of care intensity in the ED by exploring the changes in the number of diagnostic tests in response to the variation in physician workload (Hypotheses 3 and 4). We estimate the NB regression model in Equation (1) with ln(DiagTest) as the dependent variable by implementing the CF approach. The estimation results are shown in column (1) of Table 3. For discharged patients, we observe a significant effect of workload on the number of diagnostic tests (β₁ = 0.0216, p < 0.001). Figure 4a, however, illustrates that the number of diagnostic tests increases significantly only up to the workload level of about 10 patients and is stable afterwards. We conclude that for discharged patients, there is an increasing concave relationship between the number of diagnostic tests and physician workload, and thus we find support for Hypothesis 3. One possible explanation for the stability of the number of diagnostic tests after a certain point is the limited capacity at the laboratory and radiology departments that may cause excessive delay in getting the results for additional tests. Thus, in order to avoid exacerbating congestion in the ED, the laboratory department, and the radiology department, the ED physician may avoid ordering more tests. Another possible explanation is that for each chief complaint, there is a finite number of related diagnostic tests, which puts a limit on the number of tests that the physician may order for an ED visit.

Table 3.

Mediating Effects of Care Intensity in the ED

	(1)		(2)
	Diagnostic tests		Post-discharge care events
	CF		CF
Workload	0.0216***	(0.0033)	0.0102*	(0.0044)
Workload 2	−0.0009***	(0.0002)	−0.0006*	(0.0003)
DiagTest			0.0438***	(0.0030)
Admit×Workload	−0.0211***	(0.0049)	−0.0034	(0.0066)
Admit×Workload2	0.0007*	(0.0003)	0.0000	(0.0004)
Admit×DiagTest			−0.0091**	(0.0034)
Observations	74,337		74,337

Notes. All models include all controls in Equation (1), including attending physician and chief complaint fixed effects. Robust standard errors clustered by attending physician are shown in parentheses. Table A6 provides the estimation results without adjusting for endogeneity.

^*p < 0.05;

^**p < 0.01;

^***p < 0.001.

Figure 4. Expected Number of Diagnostic Tests in the ED.

Notes. Shading indicates statistical significance (at the 5% level) of the marginal effect (slope of the curve) at each point. Figure A4 shows the estimated slopes of the curves.

For admitted patients, Figure 4b shows that the number of diagnostic tests does not change significantly when physician workload increases. Hence, we do not find support for Hypothesis 4. We note that the admitting physician may request an additional test for an admitted patient while the patient is still in the ED, and this may explain why there is no significant change in the number of diagnostic tests for admitted patients. Interestingly, the results show different patterns for the impacts of workload on the number of diagnostic tests for discharged and admitted patients, indicating that physicians’ response to workload is different for the patients that will be admitted (i.e., more severe patients) than it is for those that will be discharged (i.e., less severe patients).

In sum, we show that, all else equal, care intensity in the ED varies with physician workload. An interesting observation is that physicians respond quite differently to workload depending on whether a patient will be admitted or discharged, which is highly correlated with the physician’s preliminary mental decision about the patient disposition. One possible explanation for this difference is that for the patients that will be admitted, the service encounter continues after the patient leaves the ED, and thus the ED physician may rely on downstream services because she knows a test will be ordered in the inpatient unit if needed. In contrast, for the patients that will be discharged, the service encounter is terminated when the patient leaves the ED.

6.2.2. The Effect of Care Intensity in the ED on Post-ED Care Use.

Having shown that care intensity in the ED, especially for discharged patients, changes in response to increased workload, we now explore whether these changes mediate the effects of workload on post-ED care use. To estimate the mediating effects of care intensity in the ED on the number of post-discharge care events, we use Equation (5), implementing the CF approach. Following the approach described in Section 5.2.1, we first include one equation for each of the potential endogenous variables (the estimation results are shown in column (2) of Table A3). We note that the coefficient of the residuals is not significant for the equation corresponding to DiagTest, and thus we repeat the analysis with including a first stage equation only for Admit. The estimation results of the CF approach are shown in column (2) of Table 3, indicating that the number of diagnostic tests mediates the effect of workload on the number of post-discharge care events for discharged patients (β₄ = 0.0438, p < 0.001), and thus providing support for Hypothesis 5. In addition, the significant coefficients of the linear (β₁ = 0.0102, p < 0.05) and quadratic (β₂ = −0.0006, p < 0.05) terms of workload indicate that workload has a direct effect on the number of post-discharge care events for discharged patients beyond the mediating effects captured by the measure of care intensity in our analysis. As shown in Figure 5, the relationship between the direct effect of workload and the number of post-discharge care events is similar to the increasing concave relationship for the total effect shown in Figure 2a. Given that the number of post-discharge care events changes with the increased workload only for discharged patients, here, we discuss the mediating effects of care intensity only for these patients.

Figure 5. Expected Post-ED Care Use for Discharged Patients – Workload Direct Effect.

Notes. Shading indicates statistical significance (at the 5% level) of the marginal effect (slope of the curve) at each point. Figure A3b shows the estimated slopes of the curve.

In summary, these results suggest that care intensity in the ED mediates the effects of workload on post-ED care use. Specifically, as workload increases, physicians order more diagnostic tests, especially for discharged patients. These additional tests lead to an increased number of post-discharge care events for these patients. This observation indicates that the need to follow up on the results of additional diagnostic tests dominates the other possible effects derived from more tests (e.g., increased patient satisfaction). It should be recognized that we control for observed clinical factors and adjust for endogeneity of the measure of care intensity, and thus these results are not derived by reverse causality.

7. Robustness Checks

When we re-estimate the models in Tables 2 and 3 without adjusting for endogeneity, the estimation results are quantitatively similar and qualitatively identical in terms of direction and statistical significance. The results of these models are in Tables A5 and A6. We conduct further robustness checks to ensure that the results are robust to alternate analysis assumptions and model specifications.

In the main analysis, to allow for non-monotonic response to workload, we include both linear and quadratic terms of workload. We also investigate the sign and statistical significance of the slope of the curve to distinguish an inverted U-shaped from an increasing concave relationship. To provide a test of robustness, following prior literature (e.g., Kesavan et al. 2014, Tan and Netessine 2019), we conduct spline regressions. We use one and two knots to split Workload into equally sized intervals and estimate the effects of workload on post-ED care use in each interval. The results are shown in Table 4. The slope estimates for the number of post-discharge care events for discharged patients are consistent with an increasing concave relationship, as found earlier. For the case with one knot, the coefficient of the first spline is positive and significant but the coefficient of the second spline is not significantly different from zero. We observe similar relationships for the case with two knots.

Table 4.

Robustness: Total Effects of Workload on Post-ED Care Use (spline regressions)

	(1)		(2)
	Post-discharge care events
	One knot		Two knots
Workload1	0.0075**	(0.0026)	0.0147***	(0.0042)
Workload2	−0.0039	(0.0029)	−0.0047	(0.0032)
Workload3			0.0007	(0.0048)
Admit×Workload1	−0.0062	(0.0044)	−0.0078	(0.0081)
Admit×Workload2	−0.0014	(0.0042)	−0.0011	(0.0047)
Admit×Workload3			−0.0016	(0.0060)
Observations	74,337		74,337

Notes. All models include all controls in Equation (1), including attending physician and chief complaint fixed effects. Robust standard errors clustered by attending physician are shown in parentheses. In column (1), Workload1 and Workload2 are indicator variables for Workload less than or equal to 8 patients (50th percentile) and greater than 8 patients, respectively. In column (2), Workload1, Workload2, and Workload3 are indicator variables for Workload less than or equal to 6 patients (33rd percentile), greater than 6 patients and less than or equal to 10 patients (67th percentile), and greater than 10 patients, respectively.

^*p < 0.05;

^**p < 0.01;

^***p < 0.001.

To quantify post-ED care use, we count the number of care events within 30 days after discharge from the hospital. One care event (i.e., medical claim), however, may include several clinical procedures. To ensure that our results are not driven by this specific measure of care utilization, we re-estimate our main model with the number of clinical procedures performed within 30 days after the patient leaves the hospital as the dependent variable. The results are shown in Table 5. As with our earlier results, we observe an increasing concave relationship between post-ED care use and ED physician workload for discharged patients and no significant impact for admitted patients.

Table 5.

Robustness: Total Effects of Workload on Post-ED Care Use (alternative measure)

	(1)
	Post-discharge procedures
	CF
Count process
Workload	0.0189*	(0.0091)
Workload 2	−0.0008	(0.0005)
Admit×Workload	−0.0236	(0.0121)
Admit×Workload2	0.0008	(0.0007)
Inflation process
Workload	−0.0303	(0.0161)
Workload 2	0.0014	(0.0009)
Admit×Workload	0.0611	(0.0605)
Admit×Workload2	−0.0031	(0.0035)
Observations	74,337

Notes. The model includes all controls in Equation (1), including attending physician and chief complaint fixed effects. Robust standard errors clustered by attending physician are shown in parentheses.

^*p < 0.05;

^**p < 0.01;

^***p < 0.001.

In our main analysis, we estimate the average impact of physician workload on post-discharge care events. A patient’s chief complaint, however, is a determinant of care needs. Thus, depending on the specific chief complaint, patients may be affected differently by the variations in physician workload. To account for this potential heterogeneity, we conduct a subsample analysis on chief complaints for which the average number of post-discharge care events is above (e.g., dyspnea, stroke symptoms) or below (e.g., laceration, allergic reaction) the average number for all chief complaints. Columns (1) and (2) of Table 6 show the result of this analysis. We find that our main results are stable for chief complaints with below average number of post-discharge care events, but workload in the ED has no statistically significant impact on post-ED care use for chief complaints that on average have a high number of post-discharge care events. This result indicates that when the ED physician is busier, the changes in operations within the ED do not have a significant impact on the patients that typically need follow-up care. In contrast, these changes lead to more post-ED care use for the patients that need less follow-up care based on their clinical condition.

Table 6.

Robustness: Total Effects of Workload on Post-ED Care Use and Care Intensity in the ED (potential heterogeneity)

	(1)		(2)		(3)		(4)
	Post-discharge care events				Diagnostic tests (for chest pain)
	Below-average PDE		Above-average PDE		Troponin		D-dimer
	CF		CF		Probit		Probit
Workload	0.0142**	(0.0055)	0.0086	(0.0083)	0.0037	(0.0416)	0.0542*	(0.0249)
Workload 2	−0.0008*	(0.0003)	−0.0004	(0.0005)	−0.0004	(0.0024)	−0.0032*	(0.0014)
Admit×Workload	−0.0047	(0.0096)	−0.0082	(0.0123)	0.1445	(0.0806)	−0.0188	(0.0471)
Admit×Workload2	0.0001	(0.0005)	0.0003	(0.0007)	−0.0073	(0.0043)	−0.0002	(0.0025)
Observations	51,425		22,908		5,799		5,799

Notes. All models include all controls in Equation (1), including attending physician and chief complaint fixed effects, except for models in columns (3) and (4) that do not include chief complaint fixed effects. Robust standard errors clustered by attending physician are shown in parentheses.

^*p < 0.05;

^**p < 0.01;

^***p < 0.001.

Another possible heterogeneity is the impact of workload on care intensity in the ED across diagnostic tests. Specifically, for some chief complaints, there are tests that are commonly ordered and other tests for which the physician may use her discretion. For example, in our data, 92% of patients with chest pain received a troponin test, whereas only 30% received a D-dimer test. We separately estimate the impact of ED physician workload on the probability of ordering these two tests and present the results in columns (3) and (4) of Table 6. These results corroborate our discussion in Section 3.2 that workload has an impact on care intensity in the ED when the provision of service is discretionary (e.g., ordering a D-dimer test).

8. Discussion and Conclusion

For more than a decade, the growing use of hospital EDs has been recognized as a major source of rising healthcare spending; therefore, managing ED crowding has become a key target of healthcare reform initiatives in the U.S. and other developed countries (Schuur and Venkatesh 2012, Krämer et al. 2019). Prior operations management literature has contributed to addressing this concern by exploring the effects of crowding on ED resource utilization and various aspects of service in the ED. We extend these studies by showing that crowding in the ED also affects utilization of healthcare services outside the ED.

We quantify post-ED care use through the number of care events within 30 days after discharge from the hospital (ED or inpatient unit), and find that the ED environment is a driver of post-ED care use. Specifically, increased workload leads to more post-discharge care events for patients that are discharged home from the ED. Our analysis also reveals that there is an increasing concave relationship between workload and the number of ED revisits as well as the number of post-discharge care events in non-ED channels of care. Together, our findings show that higher ED physician workload results in an increase in healthcare system utilization and that at least part of this effect is driven by reduced quality of care. While the results of this paper underline the impact of non-clinical factors in the ED on healthcare system utilization, the relationship between utilization and health outcomes requires further investigation. On the one hand, an increase in unnecessary post-discharge care use may impose additional burden on the healthcare system without any noticeable impact on health outcomes. On the other hand, if the care is necessary, it may prevent adverse health outcomes for the patient. Future research could shed light on these potential outcomes.

Further, our empirical results show that care intensity in the ED, measured by the number of diagnostic tests, explains a causal mechanism for the effects of ED physician workload on post-ED care utilization. We find that when workload is high, a busy physician orders more tests for discharged (i.e., less severe) patients; these additional tests lead to an increase in post-ED care use. These novel results are consistent with prior empirical results, indicating that clinical factors are not the only determinants of test ordering in the ED. In addition, these findings reveal that server behavior in an upstream stage affects demand for service in downstream stages. While in this study we characterize physician diagnostic test-ordering behavior as a mediator that partly explains the total effect of workload on post-ED care use, a fruitful avenue for future research would be to unravel other aspects of physician (e.g., coordinating follow-up visits) and patient behavior (e.g., seeking care in other channels because of dissatisfaction) that contribute to this relationship.

In addition to several directions for empirical research outlined above, our findings open up interesting avenues for future analytical research on queueing theory. First, current models of tandem queues assume independent interarrival and service times (e.g., Baron et al. 2014, Song et al. 2017b). Our empirical results, however, reveal that service in one stage may impact interarrival and service times in downstream stages. Future queueing studies should account for this relationship within tandem queue networks that allow for at least a partially controllable arrival process. Second, prior studies develop models to propose optimal queueing system configurations with respect to performance measures in the focal service facility, such as the expected work-in-process and the expected wait time in queue (e.g., Do et al. 2018, Armony et al. 2021). Our results, however, demonstrate that the influence of system configurations (e.g., staffing) goes beyond the focal service system. Thus, future research may use our estimates to develop queueing models that incorporate system-level objective functions in decision- making. Third, prior literature that models queueing systems with discretionary service components considers single customer types (e.g., Hopp et al. 2007, Alizamir et al. 2013), whereas our finding of physician adaptive test-ordering behavior shows that servers strategically adjust their performance according to the type of customer. Future research may therefore benefit from allowing for multiple customer types in these systems, including in systems where customer types may be known at the time of arrival (e.g., call centers) and after an initial evaluation phase (e.g., emergency departments).

From a practical perspective, our findings provide insights for ED physicians about the impact of their behavior on the healthcare system and underscores several implications for hospital and ED administrators to better manage resources in the ED. While ED physicians might assume that diagnostic tests replace the direct time that they should spend with the patient without significant adverse effect, our results show that additional diagnostic tests cause an increase in post-ED care use. To the extent that this increase potentially contributes to an overutilized healthcare system, ED physicians should adjust their test-ordering practice in the ED, which has been an ongoing concern in the healthcare community (Carpenter et al. 2015). ED managers may also alleviate this concern by providing incentives for physicians to be consistent in their practice. Moreover, our empirical results highlight the potential conflict between what is perceived to be the best for ED efficiency and what is optimal for the healthcare system. Hospital and ED administrators should note this conflict, especially if the ED is part of an integrated healthcare system. For example, current physician staffing models only consider the impact of staffing on service outcomes within the ED (Saghafian et al. 2015). We show that these models should also consider the impact of ED staffing decisions outside the ED. Until such models are available, ED managers should explicitly account for the effects of workload on system utilization when deciding the number of physicians to staff. The system-level effects of workload should also be considered in patient-physician assignment policy. In contrast to prior research that shows that an increase in workload is initially beneficial for ED throughput (KC 2013), we find that even at low workload levels, increased workload intensifies the healthcare system utilization. Thus, from the healthcare system perspective, ED managers should employ assignment policies that lead to a balanced workload across physicians even at low workload levels. That is, when there is a new patient in the ED, the physician with the lowest workload (rather than the physician with the most recent discharge) should be assigned to him.

Our findings also provide empirical evidence in support of ongoing initiatives by policy-makers to improve timely access to outlets such as urgent care centers and primary care clinics. PCPs increasingly refer patients to the ED because of scarce same-day appointments in the primary care setting and advanced diagnostic technologies in the ED (Institute of Medicine 2006, Pitts 2012). In addition, the ED has been increasingly used as a gateway to inpatient treatment (Dong et al. 2018). Although inpatient hospital congestion does not generate additional demand in the ED, it exacerbates ED congestion by causing prolonged ED stays for admitted patients (Shi et al. 2015). Thus, various channels within the healthcare system contribute to crowding in the ED (Lurie et al. 2013). Our analysis demonstrates that there is indeed a reciprocal relationship between the ED and the other channels of care in the healthcare system, i.e., a busy ED generates increased utilization elsewhere. Altogether, this creates a vicious cycle of overutilization in the healthcare system. Given that more than 30% of ED visits in the U.S. are semi-urgent or non-urgent and about 20% of ED visits have been reported to be due to the lack of access to primary care services (Centers for Disease Control and Prevention 2016, 2017), initiatives such as walk-in retail clinics and PCP adoption of virtual appointment, which has accelerated since the onset of COVID-19 pandemic, may decrease ED physician workload and healthcare system utilization.

Finally, this study has some limitations that could be explored in future research. First, in general, it is subjective to draw a direct connection between a follow-up treatment and a prior test. Our results that diagnostic test-ordering in the ED mediates the effects of ED physician workload on post-ED care use, however, indicate that at least some of the increased post-ED care events are driven by the additional diagnostic tests ordered in the ED. Future research that has access to clinical notes surrounding follow-up utilization could investigate this relationship further. Second, our results are based on the analysis of a single teaching hospital in which the physicians’ salaries are independent of their performance. Therefore, the estimates may be different in non-teaching hospitals that serve different population and hospitals in which physicians are financially incentivized to provide more care. Future studies could examine the research questions in this paper in hospitals with different characteristics. Third, due to lack of data, we limit our analysis to within-network patients. However, the observed effects may be different for out-of-network patients, especially those who are uninsured and have limited access to care. On the one hand, we expect the impact of ED physician workload on post-ED care utilization to be more pronounced when access to care is easier; this is because, if needed, patients with easy access to care can make a follow-up visit more easily. On the other hand, an additional diagnostic test, caused by ED congestion, may have a greater impact on required follow-up care for uninsured patients; this is because the ED is the primary source of care for these patients, and thus a diagnostic test in the ED may identify several anomalies. Future research is needed to investigate this potential source of heterogeneity.