The Effect of Length of Stay in Hospital on Patients’ Health Outcomes

Abstract

The causal effect of hospital length of stay on crucial patient outcomes such as readmissions or mortality is under-investigated and therefore unknown for the vast majority of the US population. Existing evidence stems from association studies that are unable to draw causal conclusions. This study leverages Medicare’s two-midnight (2MN) and three-day (3D) rules as two natural experiments to establish causal relationships between hospital length of stay (LOS) and patient outcomes. Using a quasi-experimental regression discontinuity design with data from a large US hospital, we find that the 2MN rule increases LOS by 0.10 days and the 3D rule by 0.21 days, confirming the validity of these rules as instruments for causal inference. However, despite these increases in LOS, there are no significant effects on 90-day mortality or 30-day readmission rates. These findings suggest that while the 2MN and 3D rules effectively extend hospital stays, they do not improve patient-related outcomes, indicating an inefficient use of hospital resources.

In 2022, the United States (US) national health expenditures exceeded USD 4.4 trillion, accounting for approximately 17.4 % of the gross domestic product. Of this, hospital expenses accounted for roughly 1.3 trillion, or about 30 % [1]. By 2028, health expenditures are expected to account for over 19.7 % of GDP, with hospital care among the sectors with the highest growth rates, raising the urgent need to control hospital costs [2].

One way to reduce costs would be to prevent unnecessarily long hospital length of stay (LOS). Although hospitalization is often medically necessary, hospitalizations that are longer than they need to be place patients at risk for hospital-acquired complications such as infections, blood clots, falls, depression, reduced mobility, or even death [3, 4, 5]. With each additional day in the hospital carrying both the risk of complications and leading to increased expenses, determining a LOS that maximizes clinical benefit to the patient in the fewest possible days remains a challenge for both clinicians and payors such as Medicare [3].

Unfortunately, examining simple associations between LOS and patient outcomes does little to inform understanding of the causal relationship between the two, as there are many confounding factors that lead to both increased LOS and worse clinical outcomes (e.g., age or comorbidities [6, 7]). While adjustment for measurable factors can be done using standard multivariate regression analysis, unmeasured factors will nevertheless bias results in ways that do not permit causal interpretation [8, 9, 10].

However, ”natural experiments” created by policies that impact patients in a clinically arbitrary manner offer an opportunity to study causal relationships without the necessity of a randomized controlled trial. One such regulation is Medicare’s two-midnight rule (2MN rule) that requires beneficiaries to be hospitalized for at least two midnights for hospitals to be paid at the higher level of an inpatient stay (instead of a lower paying observation stay) [11]. From a practical standpoint, this rule impacts the actual LOS of patients depending on whether they were admitted to the hospital before or after midnight: for two otherwise-similar patients to meet criteria for an inpatient stay, the one who was admitted just after midnight would have to remain in the hospital almost an entire day longer than the one who was admitted just before midnight. Similar considerations exist for Medicare’s three-day rule (3D rule) that requires patients be hospitalized for at least three midnights to qualify for post-acute care at a skilled nursing facility (SNF).

Leveraging data from a large tertiary US hospital, we use a quasi-experimental regression discontinuity design (RDD) model to examine whether extending hospital LOS impacts mortality and readmissions by exploiting differences created arbitrarily by the 2MN and 3D rule. We hypothesized that an extra day spent in the hospital, as estimated by our RDD model, does not affect mortality or readmissions, suggesting an inefficient use of hospital resources.

Leveraging Hospital Routine Data

The study used the Medical Information Mart for Intensive Care IV (MIMIC-IV) dataset [12], which contains detailed electronic health record (EHR) data on all patient stays of patients aged 18 or older at Beth Israel Deaconess Medical Center (BIDMC) between 2008 and 2019 that were treated in an intensive care unit (ICU) or were admitted to the hospital through the emergency department (ED). BIDMC is a major academic teaching hospital for Harvard Medical School located in Boston, Massachusetts with 743 licensed beds [13]. MIMIC-IV includes data on approximately 300,000 patients and their 425,000 emergency department (ED) visits, 430,000 hospital admissions, and 73,000 ICU stays [14]. Death data in the dataset are derived from the Massachusetts State Registry of Vital Records and Statistics [14].

Sample Restriction for Medicare Rules

We included all patients age 18 and older in the MIMIC-IV databases who were admitted to BIDMC following an ED visit. We excluded patients that were admitted ± 6 minutes around midnight to avoid (non-visually detectable) bias arising from data manipulation around midnight [15].

For the 2MN rule analysis cohort, we narrowed our sample to patients with LOS between 0.5 days (12 hours) and 2.5 days (60 hours) to focus on patients whose LOS could have been plausibly impacted by the 2MN rule. Similarly, for the analysis of the 3D rule cohort, we restricted our analysis to patients with an LOS between 60 hours and 108 hours (i.e., between 2.5 and 4.5 days).

Outcomes and Covariates

Our exposure of interest was the hospital LOS based on admission and discharge timestamps. Our primary outcome measures were 90-day mortality and 30-day readmission. 90-day mortality was defined as death within 90 days of hospital admission to account for the possibility that the rules may be associated with in-hospital death. Among patients who survived their initial hospitalization, 30-day readmission was defined as a hospitalization at BIDMC post-discharge with an admission date that was between 1 and 30 days after previously being discharged. Same-day readmissions were excluded since it could not be reliably determined whether it was an inpatient transfer or a true readmission. Covariates included age, gender, race, marital status, Clinical Classification Software [16] predicted 90-day mortality, and Charlson weighted index [17, 18], admission year group (2008–2010; 2011–2013; 2014–2016; 2017–2019).

Deriving Causal Inference from Routine Data

A simple assessment of the causal relationship between hospital LOS and patient outcomes using observational data will be biased by the numerous clinical factors, observed and unobserved, that influence length of stay in a non-random fashion. For example, a patient with a preexisting diagnosis of heart failure who is admitted after a fall at home is at higher risk for both a longer hospital stay and death or readmission. Multivariate adjustment can account for bias introduced by measurable characteristics, but it cannot account for unmeasured characteristics, such as the degree of a patient’s family support at home following hospital discharge. However, the risk of unmeasured confounding can be overcome by taking advantage of situations where a patient’s hospital length of stay is impacted for reasons that are arbitrary with respect to their clinical situation. In the case of the 2MN or the 3D rule, whether a patient is admitted just before or just after midnight is clinically arbitrary, creating a natural experiment by which some patients’ hospitalization is extended in a random fashion.

Regression discontinuity (RDD) design is an established quasi experimental method to draw causal inference from real-world observational data wherein patients’ exposure vary due to a clinically arbitrary cutoff. In a ”fuzzy” RDD analysis, where the exposure can be influenced by factors other than the cutoff (e.g., the 2MN or 3D rule is not the sole determinant of LOS), the cutoff functions as an instrumental variable that randomly impacts the probability of an additional day in the hospital.

Such an analysis relies on several key assumptions: that the rule impacts the length of stay for otherwise-similar patients admitted just around midnight (i.e. the ‘first stage’ effect, which can be empirically tested); that the rule impacts patient outcomes solely through its impact on LOS (the exclusion restriction); that there is no outside factor that affects the application of the rule and patient outcomes (the independence assumption); and finally that the rule serves to either increase or decrease LOS, but not both (the monotonicity assumption) [19, 20].

Medicare Rules may Trigger Discontinuities in Length of Stay

The 2MN rule [21] was introduced in 2013 by the Centers for Medicare and Medicaid Services (CMS) with the intention of removing ambiguity surrounding which hospital-based services could be reimbursed as ”inpatient” versus ”outpatient” care. Under the rule, ”observation” hospitalizations that span less than two midnights are reimbursed as outpatient care through Medicare Part B. Meanwhile, hospitalizations that span two midnights or more are reimbursed as inpatient stays through Medicare Part A at substantially higher rates [11], creating a financial incentive for hospitals to provide care over a longer time period that is clinically disconnected from the Medicare beneficiary’s care needs.

The 3D rule [22] operates similarly, requiring that patients be hospitalized for at least three consecutive days, not including the day of discharge, in order to qualify for discharge to a SNF for rehabilitative care. In effect, a patient’s inpatient hospitalization must therefore span four midnights for the patient to qualify for Medicare to cover SNF services [23], which are often necessary for patients who cannot safely return directly home following an acute illness. Under this rule, Medicare beneficiaries who may be clinically ready for discharge to SNF after, for example, two days of hospitalization must remain in the hospital longer because of the 3D rule, extending their LOS for a clinically-arbitrary reason.

The practical implications of 2MN and 3D rule are most apparent for Medicare beneficiaries who are admitted to the hospital around midnight. For example, consider two similar patients who present to an emergency department with a hip fracture on a Monday night. One happens to be admitted just before midnight, while the other is admitted a few minutes later, just after midnight, on Tuesday. The first patient will qualify for inpatient reimbursement on Wednesday and for SNF services on Thursday. Meanwhile, the second patient qualifies for inpatient care on Thursday and SNF services on Friday–an additional day of hospitalization despite arriving at, essentially, the same time as the first patient.

Although not all patients are covered by Medicare, we hypothesized that hospital policies and practices may lead to spill-over effects for patients covered by the broad variety of payors [24] [25].

Comparison of Patients Admitted Before and After Midnight

Characteristics of patients admitted just before compared to just after midnight were compared using standardized mean-differences (SMD) [26], with an SMD below 0.1 indicating balance with respect to the tested variable [27], as well as for the 2MN and 3D cohorts. We also tested for differences in patient characteristics by estimating the effect of being admitted to the hospital after midnight on patient characteristics using our described RDD estimation strategy [23]. Statistically significant RDD estimates would indicate a discontinuity of the respective covariate around midnight and may be a sign of manipulation.

Association and Causal Analysis

We began by estimating the non-causal associations between LOS and outcomes using multivariable regression, adjusting for measured clinical characteristics.

We then applied our RDD estimation strategy to derive estimates of the local average treatment effect (LATE), which is the effect of an additional day of hospitalization for patients who would have been discharged sooner were it not for the Medicare rule; these patients are known as ”compliers” (LATE may also be referred to as the complier average causal effect, or CACE [28]). We also estimated the effect of being admitted after midnight on health outcomes. This effect, which is often referred to as the ”reduced form” [29], can be interpreted as the ”intention-to-treat” effect [30], i.e., the effect of the policy on health outcomes. In our main analysis, we run the estimations using local polynomial regression, a standard approach for fuzzy RDD [31]. We derived the bandwidth left and right of the midnight cut-off using the optimal bandwidth selection method as described in Calonico et al [32] (see Appendix C for details). We also conducted complier analysis to identify which patients are actually affected by the policies (see Appendix C for details).

Analyzing Heterogeneity in Treatment Effects

In addition to the overall population in the respective samples affected by the 2MN and the 3D rule, we tested the effect of LOS on health outcomes in several subgroups in order to identify treatment effect heterogeneity.

First, we focused on the subgroups that should be most affected by the two-midnight and the 3D rule, namely Medicare beneficiaries and, for the 2MN rule which was implemented in 2013, for Medicare patients before and after 2013. Next, we analyzed whether heterogeneity exists regarding subgroups that may be subject to discrimination. Here, we focused on heterogeneity by gender (self-reported male vs. female) and race (self-reported white vs. non-white) - two variables known to affect outcomes in healthcare settings [33, 34, 35, 36]. Finally, we report subgroup analysis by chronic comorbidity severity (Charlson weighted index of 0 vs. ≥ 1 [17] and acute illness severity (defined by the Clinical Classification software, CCSR-2023–1 [16]. Here, we assumed that more vulnerable patient groups may less severely be affected by the respective rules because higher medical necessity allows for less arbitrary variation in discharge timing.

Analyses were conducted using R version 4.2.2 and the rdrobust package for RDD [37]. Alpha levels were set at 0.05 (0.025 for each tail). The Institutional Review Boards (IRBs) at both Massachusetts Institute of Technology and the Beth Israel Deaconess Medical Center approved the use of the data for research. The MIMIC-IV (https://mimic-iv.mit.edu) database can be accessed by certified researchers, so no additional informed consent of the patient and ethic approval are required [14].

Study Population Characteristics

We identified a total of 298,502 hospital admissions that met inclusion criteria from 2008–2019. A histogram of the time of these hospital admissions to an inpatient ward or intensive care unit is displayed in Fig. A1, and the distribution of hospital LOS is displayed in Fig. A2.

Characteristics of patients admitted just before compared to just after midnight for all admitted patients and those in the 2MN and 3D rule cohorts are displayed in Table 1. Apart from marital status, year group and ICU stay for the 3D rule, all SMDs were below 0.1, indicating well-balanced groups and supporting the assumption that midnight divides admitted patients in a clinically arbitrary fashion. Using the RDD approach to measure covariate values around the midnight threshold, we found no statistically significant discontinuity around midnight for either the 2MN or the 3D rule groups, further supporting the assumption of balanced groups on each side of the midnight discontinuity (Table A2; A3).

Table 1:

Standardized mean differences ± 30 minutes around midnight

	Overall			2MN rule			3D rule
	Before midnight	After midnight	SMD	Before midnight	After midnight	SMD	Before midnight	After midnight	SMD
n	8518	6853		3190	2438		219	186
Sociodemographics
Age (mean (SD))	58.29 (19.81)	58.93 (19.46)	0.033	56.65 (20.07)	56.19 (20.15)	0.022	78.72 (12.29)	77.68 (11.60)	0.087
Gender = M (%)	4151 (48.7)	3354 (48.9)	0.004	1490 (46.7)	1126 (46.2)	0.010	84 (38.4)	78 (41.9)	0.073
Race: white (%)	0.65 (0.48)	0.67 (0.47)	0.044	0.64 (0.48)	0.66 (0.48)	0.036	0.79 (0.41)	0.78 (0.42)	0.025
Main language=English (%)	7663 (90.0)	6161 (89.9)	0.002	2877 (90.2)	2208 (90.6)	0.013	188 (85.8)	163 (87.6)	0.053
Marital status (%)			0.050			0.055			0.151
Divorced	658 ( 7.7)	497 ( 7.3)		243 ( 7.6)	162 ( 6.6)		16 ( 7.3)	17 ( 9.1)
Married	2946 (34.6)	2521 (36.8)		1123 (35.2)	904 (37.1)		73 (33.3)	51 (27.4)
NA	170 ( 2.0)	149 ( 2.2)		40 ( 1.3)	34 ( 1.4)		8 ( 3.7)	8 ( 4.3)
Single	3814 (44.8)	2948 (43.0)		1456 (45.6)	1106 (45.4)		65 (29.7)	54 (29.0)
Widowed	930 (10.9)	738 (10.8)		328 (10.3)	232 ( 9.5)		57 (26.0)	56 (30.1)
Insurance (%)			0.041			0.066			0.032
Medicaid	974 (11.4)	709 (10.3)		368 (11.5)	262 (10.7)		7 ( 3.2)	5 ( 2.7)
Medicare	3272 (38.4)	2598 (37.9)		1147 (36.0)	816 (33.5)		165 (75.3)	140 (75.3)
Other	4272 (50.2)	3546 (51.7)		1675 (52.5)	1360 (55.8)		47 (21.5)	41 (22.0)
Year group (%)			0.015			0.043			0.168
2008 – 2010	3952 (46.4)	3179 (46.4)		1548 (48.5)	1179 (48.4)		104 (47.5)	103 (55.4)
2011 – 2013	1924 (22.6)	1515 (22.1)		705 (22.1)	552 (22.6)		53 (24.2)	35 (18.8)
2014 – 2016	1590 (18.7)	1312 (19.1)		555 (17.4)	445 (18.3)		36 (16.4)	28 (15.1)
2017 – 2019	1052 (12.4)	847 (12.4)		382 (12.0)	262 (10.7)		26 (11.9)	20 (10.8)
Clinical variables
Charlson wscore (mean (SD))	1.78 (2.24)	1.83 (2.23)	0.023	1.33 (1.88)	1.28 (1.82)	0.025	2.54 (2.14)	2.55 (2.04)	0.005
Died in hospital (mean (SD))	0.02 (0.13)	0.02 (0.12)	0.011	0.01 (0.10)	0.01 (0.09)	0.013	0.00 (0.00)	0.00 (0.00)	<0.001
ICU stay (mean (SD))	0.14 (0.34)	0.15 (0.35)	0.026	0.04 (0.20)	0.05 (0.21)	0.030	0.11 (0.31)	0.14 (0.35)	0.106
Treatment and Outcomes
LoS (mean (SD))	3.74 (5.50)	4.25 (6.92)	0.082	1.11 (0.53)	1.20 (0.53)	0.167	3.22 (0.51)	3.42 (0.47)	0.409
90-day mortality (%)	591 ( 6.9)	510 ( 7.4)	0.020	122 ( 3.8)	88 ( 3.6)	0.011	27 (12.3)	19 (10.2)	0.067
30-day readmission (%)	1711 (20.3)	1390 (20.5)	0.006	576 (18.2)	444 (18.3)	0.003	35 (16.0)	35 (18.8)	0.075

Non-causal Association between LOS and Health Outcomes

Non-causal multivariable regression, adjusting for measured covariates, estimated no association between LOS and 90-day mortality in either the 2MN rule or 3D rule cohorts. One additional day of LOS was associated with increased odds of 30-day readmission among patients in the 2MN rule group (adjusted odds ratio 1.062, 95 % CI: 1.031–1.093), but there was no association with readmission among patients included in the 3D rule group (Table A1).

Causal Effect of Length of Stay on Health Outcomes Triggered by the Two Midnight Rule

The discontinuity in LOS for patients subject to the 2MN rule that were admitted near midnight is displayed in Fig. 1. Patients admitted just before midnight had significantly lower LOS than those admitted just after midnight, with an estimated average increase in LOS of 0.10 days (95 % CI: 0.07–0.13), corresponding to a relative increase of 8.7 % (95 % CI: 6.1 %–11.3 %). Among subgroups, there was a significant increase in LOS observed in each group except Medicare beneficiaries admitted prior to 2013 when the 2MN rule was implemented (Fig. A3).

Figure 1:

Discontinuity for the two-midnight rule sample

Note: Discontinuity for the sample that is affected by the 2MN rule (0.5 days to 2.5 days of LOS).

Despite a significant increase in LOS attributable to the 2MN rule, the RDD model estimated no difference in 90-day mortality or 30-day readmission, either overall or among subgroups (Fig. 2; see Fig. for OLS results¹). As for LOS, we could not detect any statistically significant effect for the ITT analysis for the effect of being admitted after midnight on health outcomes A5.

Figure 2:

Effect of Length of Stay on Mortality and Readmission for the 2MN rule sample

Note: Estimated using the local polynomial regression.

Causal Effect of Length of Stay on Health Outcomes Triggered by the Three Day Rule

The regression discontinuity adjusted LOS for patients subject to the 3D rule that were admitted near midnight are displayed in Fig. 1. Patients admitted just before midnight had significantly lower LOS than those admitted just after midnight, with an estimated average increase in LOS of 0.21 days (95% CI 0.12–0.30), a 6.3% relative increase (95% CI: 3.6 %–9.0 %), attributable to the 3D rule (Fig. A8). Among subgroups, we observed a significant increase in LOS except among non-white patients (Fig. A10).

As before, despite the observed discontinuous increase in LOS, there was no discontinuous difference in 90-day mortality or 30-day readmission either overall or among subgroups. The same holds for the ITT effect, where we could not detect any statistically significant effect of being admitted after midnight A10.

Differences in LOS by Gender, but not by Race, Were Explained by Mediating Variables

As a result of the heterogeneity by subgroup as seen in Fig. A3, A8, we ran analysis using interaction terms to identify where the heterogeneity for the effect of the two rules on LOS arises for race and gender.

We find that these analyses were not able to explain the subgroup heterogeneity by race, but we were able to identify that the heterogeneity by gender was explained by other factors. For the 3D rule, we also found heterogeneity by race and gender, and additional analysis revealed that these effects were mediated by observable variables (see C for details).

Discussion

In this study of patients admitted to a large, tertiary academic medical center, we observed that despite a clinically arbitrary increase in hospital length of stay attributable to Medicare’s 2-midnight and 3-day rules, there was no difference in 90-day mortality or 30-day readmission rates. These results raise questions about current Medicare regulations that affect healthcare resource utilization without improving outcomes for patients.

Prior observational studies have found both positive and negative non-causal associations of LOS with readmission or mortality [10, 38, 39, 40], leading to speculation about potential causal effects. While one prior study leveraged another midnight rule impacting newborns [15], to our knowledge, this is the first study describing the impact of the 2MN and 3D rules on general adult patient outcomes using quasi-experimental methods that address unmeasured confounding and permit causal inference. Both the newborn study and our study found that additional LOS brought on by arbitrary rules did not impact meaningful patient-centered outcomes. Our findings of an average additional 0.10 days of LOS attributable to the 2MN rule and an additional 0.21 days translate to approximately one in ten patients in the 2MN rule short hospitalization cohort (37.2 % of all hospital patients), as well as one in five patients in the 3D rule longer-hospitalization cohort (2.9 % of all hospital patients) admitted near midnight spending an entire additional day in the hospital for no benefit in mortality or readmission.

Unnecessarily prolonged hospitalizations can lead to myriad costs and problems for patients, hospitals, and payors. Patients do not return home as soon as they could, leaving them away from family and other supports that may be better able to assist in their recovery at home. Financial costs of an additional day of hospitalization are incurred by payors and patients alike. Patients remaining in the hospital unnecessarily also effectively reduce inpatient capacity, which, when strained, can have wide-ranging externalities that negatively impact the care of other hospitalized patients [41]. Although the 2MN and 3D rules are Medicare regulations, the effects of the rules on LOS were similar in magnitude among Medicare beneficiaries as for the entire cohorts which included other payors. This suggests that global hospital practices surrounding the determination of LOS are influenced by Medicare regulations, that other payors have adopted similar regulations, or both.

We found somewhat stronger effects for the 2MN rule for the subgroups female, non-white and low chronic/acute disease patients, compared to their counterparts (Fig.A3). Heterogeneity by race and gender raised the need for further investigation, especially since discrimination based on gender or race is known from other contexts in healthcare [33, 34, 35, 36]. As a result, we identified only unexplained heterogeneity by race for the 2MN rule, which warrants further investigation.

This study comes with some limitations. First, we included patients from all types of insurance and we were limited in distinguishing private insurance/self-payers from Medicare advantage. However, the advantage of this approach was that we were able to determine the policy effects on the overall hospital population in contrast to insurance-type dependent subpopulations. Further, we aimed to disentangle at least the effect for classic Medicare in the subgroup analysis. Second, confidence intervals for the analysis of LOS on health outcomes were broad, reflecting limited sample size around the midnight discontinuity. Third, while we were able to provide real-world evidence with generally good external validity as compared to randomized controlled trials [42], the main limitation here is that we only measure the effects for patients close to an admission time at midnight. We can therefore not necessarily say that these results hold for patients with an admission time further away from midnight as well. Especially for the 3D rule, where we restricted our sample also to patients that were discharged to an SNF, only a small percentage of hospital patients is affected (i.e., the ones that are discharged to an SNF). Fourth, using the RDD approach only allows us to infer the impact of the 2MN and 3D rule around midnight, not necessarily how it affects patients admitted at other times (e.g., admitted at 6pm). It may be plausible to assume that even patients admitted in the late afternoon or early morning are affected by the respective rules, yet it was not possible to test this using our study design. Fifth, we found that the effect of the 2MN rule prior to 2013 was statistically insignificant, although not far from being significant (Fig. A3). Including patients with a weaker effect may have potentially biased our estimates downwards. However, we found a strong overall effect for the full sample, limiting this limitation. Finally, in 2013, a lawsuit against BIDMC was settled due to irregularities in the hospital’s approach to bill Medicare patients regarding inpatient/outpatient stay between 2004 and 2008 [43]. It may be that this lawsuit yields consequences for the effect of the midnight discontinuity before and after 2013. For example, the hospital may have acted more stringently than other hospitals in complying with the 2MN rule following 2013.

Conclusion

Our study demonstrates that patients affected by the 2MN and the 3D rule experience longer LOS, on average. Per intention-to-treat analysis, we do not find that the policies lead to different health outcomes. Further, the increase in LOS does not have a causal effect on health outcomes. However, heterogeneity regarding the effect of the midnight discontinuity on LOS exists, with non-white patients being disproportionately affected by the rule. Overall, we suggest redesigning the 2MN and the 3D rule as the current state leads to a waste of limited resources that could be more efficiently allocated.

Figure 3:

Discontinuity for the three-day rule sample

Note: Discontinuity for the sample that is affected by the 3D rule. Bandwidth was set to 3 hours.

Figure 4:

Effect of Length of stay on Mortalit and Readmissions for the three-day rule sample

Note: Estimated using the local polynomial regression. OLS estimates are presented in the appendix.