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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
Med Care. Author manuscript; available in PMC 2014 January 1.
Published in final edited form as:
PMCID: PMC3518633

Impact of length of stay after coronary bypass surgery on short-term readmission rate: An instrumental variable analysis

Yue Li, PhD,1 Xueya Cai, PhD,2 Dana B. Mukamel, PhD,3 and Peter Cram, MD, MBA4,5



To determine the effect of postoperative length of stay on 30-day readmission after coronary artery bypass surgery.

Data Sources/Study Setting

We analyzed a final database consisting of Medicare claims of a cohort (N=157,070) of all fee-for-service beneficiaries undergoing bypass surgery during 2007-2008, the American Hospital Association annual survey file, and the rural urban commuting area file.

Study Design

We regressed the probability of 30-day readmission on postoperative length of stay using (1) a (naïve) logit model that controlled for observed patient and hospital covariates only; and (2) a residual inclusion instrumental variable (IV) logit model that further controlled for unobserved confounding. The IV was defined using a measure of the hospital’s risk-adjusted length of stay for patients admitted for gastrointestinal hemorrhage.

Principal Findings

The naïve logit model predicted that a one-day reduction in median post-operative length of stay (i.e. from a median of 6 days to 5 days) lowered the 30-day readmission rate by 2 percentage points. The IV model predicted that a one-day reduction in median post-operative length of stay increased 30-day readmission rate by 3 percentage points.


The findings indicate that a reduction in postoperative length of stay is associated with an increased risk for 30-day readmission among Medicare patients undergoing bypass surgery, after both observed and unobserved confounding effects are corrected.

Keywords: bypass surgery, length of stay, 30-day readmission, instrumental variables, Medicare, quality of care


Coronary heart disease (CHD) is a leading cause of morbidity and mortality in the United States which accounted for 1 of every 6 deaths in 2007.1 Invasive cardiac procedures such as coronary artery bypass graft (CABG) surgery are a common treatment option for patients with CHD.2 In 2007, 408,000 CABG operations were performed in the US, with mean charges for in-hospital care over $10,000; over half of these procedures were performed on people 65 years or older.1

During the past several decades, many efforts to contain healthcare costs have focused on reducing the number of hospital admissions and for those who are admitted, lowering hospital resource use through the reduction in hospital length of stay (LOS). For patients undergoing CABG surgery, efforts to reduce hospital LOS through the introduction of protocols and guidelines3-6 have been highly successful. From 1988 to 2005, the median length of stay for bypass surgery declined from 11 to 8 days nationally,6 resulting in apparent cost savings in perioperative care associated with the primary procedure.

One concern among clinicians and researchers alike is that, by focusing cost-control efforts largely on the inpatient setting, payers such as Medicare have pushed hospitals to reduce LOS at the expense of increasing premature hospital discharge and putting patients at a higher risk for post-discharge adverse outcomes, such as major complications, short-term readmissions, and mortality. Broad evidence exists that reduced postoperative length of stay for revascularization is associated with more discharges to post-acute care settings (rather than to home) such as skilled nursing facilities or rehabilitation centers.5-8 This suggests the increased disease management requirements after “fast-track” discharge and a cost shift from perioperative acute care to post-acute care.

Reducing readmissions after initial hospitalization has been an important component of recent federal initiatives, including public reporting, payment incentives, and the Patient Protection and Affordable Care Act,9-11 to simultaneously improve quality of care and reduce costs. However, the evidence about the relationship between early discharge and short-term readmissions for bypass surgery is mixed, with previous studies reporting either negative, positive, or no association between length of stay of CABG surgery and readmission rate.3-5,7,12,13

We conducted this study with an aim to improve the causal inferences about the relationship between postoperative length of stay of CABG surgery and 30-day readmission rate. Specifically, we used the instrumental variable technique to analyze data on a national cohort of Medicare patients receiving bypass surgery. Instrumental variable (IV) analyses are a potential powerful tool to address unobserved confounding in observational studies.14-16 In the present study we chose as an instrumental variable the average risk-adjusted length of stay of patients admitted for a medical condition (gastrointestinal hemorrhage) in the same hospital. We assumed and to the extent possible, empirically confirmed, that the IV induced exogenous variations of post-operative length of stay (the “treatment” variable) but did not directly affect the outcome (30-day readmission), thereby allowing for consistent estimates of the hypothesized “treatment” effect.


Data sources

We analyzed the 2007 and 2008 Medicare Provider Analysis and Review (MedPAR) inpatient files obtained from the Centers for Medicare and Medicaid Services. The MedPAR data contains uniform administrative and clinical elements obtained from discharge abstracts for acute care hospital stays of all fee-for-service beneficiaries. Patient-level records include demographics (age, gender, race/ethnicity), principal and up to 9 secondary diagnoses classified by the International Classification of Diseases, Ninth Revision, Clinical Modification (ICD-9-CM) codes, principal and up to 5 secondary ICD-9-CM procedure codes, length of stay, discharge date and disposition, date of surgery (for surgical patients), date of death up to 3 years after discharge, an encrypted patient identifier that allows for identification of patient admissions and readmissions longitudinally, and each hospital’s unique identifier allowing for linkage of the MedPAR to external hospital databases.

The MedPAR was merged with (1) the 2007 American Hospital Association (AHA) annual hospital survey file to obtain variables for hospital characteristics; and (2) the University of Washington rural urban commuting area (RUCA) file to define rural vs. urban location of the hospital.17


We identified the cohort of beneficiaries who underwent coronary artery bypass graft (CABG) surgery between January 1, 2007 and September 30, 2008 using ICD-9-CM procedure codes 36.10–36.19. Patients were excluded from the sample if they (1) had a concomitant open-heart procedure such as valve replacement, (2) were younger than 65 years old at admission, (3) were transferred to another acute care hospital, (4) died in hospital, or (5) had a postoperative length of stay (PLOS) less than 1 day or greater than 35 days (the 99 percentile for all patients). The PLOS was defined as the number of days between the principal procedure date and the discharge date.


Our dependent variable was a binary variable taking the value of 1 if the patient had one or more readmissions within 30 days of discharge after CABG surgery (excluding readmissions for rehabilitation, DRG 462), and zero otherwise. The primary independent variable was the PLOS during the index hospitalization for CABG surgery. Other patient-level independent variables included age (in years), female gender (yes/no), race/ethnicity (non-Hispanic White, Black, and other); admission type (elective, emergent, urgent, or other); acute myocardial infarction (principal ICD-9-CM code 410) at admission, cardiogenic shock (principal ICD-9-CM code 785.51) at admission, number of comorbidities (coded as 0, 1, 2, 3, and ≥4 comorbidities) with each comorbidity defined using the AHRQ comorbidity algorithm described by Elixhauser and her colleagues.18,19 The comorbidity algorithm defines each of 30 individual comorbidities based on administrative data and is widely used as a tool for estimating hospital outcomes and resource uses. Hospital level covariates included major teaching hospital (yes/no), ownership status (for-profit, non-for-profit, or government-owned), and rural versus urban location.


Naïve logit analysis

The analyses started with a simple logit model in which the probability of 30-day readmission of patient i receiving CABG in hospital j ( Pij ) is modeled as a function of the natural-log transformation of postoperative length of stay ((PLOSijcabg)), the vector of patient covariates ( Xij ), and the vector of hospital covariates ( Hj ) which are described above and listed in Table 1:


In this model the natural-log transformation of PLOS was used to account for the potential nonlinear effect of PLOS on the dependent variable. The logit model given in equation (1) does not address the issue that the key independent variable – (PLOSijcabg) – is endogenous due to unobserved confounders, such as severity of disease, that tend to be correlated with the outcome and the key independent variable. Therefore, the model was labeled naïve logit analysis.

Table 1
Characteristics of Medicare patients undergoing bypass surgery (n=157070)

Instrumental variable analysis

We employed the instrumental variable approach recently described by Terza, Basu, and Rathouz15 to address the issue of endogeneity. Terza and his colleagues15 indicated that correcting for endogeneity with the conventional two-stage least square method would be biased due to the nonlinearity of the logit model. The authors recommended a two-stage residual inclusion (2SRI) approach which represents a consistent nonlinear extension of conventional instrumental variable analyses.

The IV we used for (PLOSijcabg) is hospital j’s risk-adjusted length of stay (natural-log transformed) for its Medicare patients admitted for gastrointestinal (GI) hemorrhage. We used the risk-adjusted, rather than crude, average ln(LOS) of hospital j to define the IV because hospitals tend to vary in case mix and the crude log-transformed LOS may reflect largely such case mix variation for GI hemorrhage patients rather than the variations of hospital clinical practices and discharge policies.20

The choice of the instrument was also based on the assumption that a hospital’s clinical practice and discharge polices are a contextual factor that determines the length of stay of all patients in the hospital, above and beyond diagnostic groups (e.g. GI hemorrhage vs. coronary heart disease), procedures received during hospitalization (e.g. endoscopy for GI hemorrhage versus CABG for CHD), and severity of disease. Previous studies supported this presumption by showing that variations in discharge policies across hospitals tended to affect the lengths of stay of multiple common conditions and surgical procedures in a similar way.21-23 Given this assumed across-the-board impact of hospital practice patterns, the average risk-adjusted, natural-log transformed LOS of patients admitted for GI hemorrhage is likely associated with the postoperative length of stay for patients undergoing CABG in the same hospital j.

Moreover, there is no plausible reason to believe that the instrumental variable (the risk-adjusted ln(LOS) for GI hemorrhage) is directly associated with the 30-day readmission for patients undergoing CABG surgery (i.e., other than through the intermediation of post-CABG length of stay). In other words, the IV can be appropriately excluded from the outcome equation described in equation (4) below.15

Lastly, we considered alternative candidate IVs in our preliminary analyses. A previous study used the average LOS for all psychiatric admissions of other hospitals in the same zip code as an IV to predict the psychiatric length of stay of a particular patient in the hospital.24 In this study, however, we could not construct the IV in a similar way (e.g. as the average PLOS for all CABG procedures performed in other hospitals of the same zip code area) because in the majority cases there is only 1 or no hospital in a zip code that can perform the open heart surgery. We have also considered as potential IVs the risk adjusted LOS of other conditions/procedures reported in the two previous studies,21,22 such as congestive heart failure, stroke, pneumonia, or peripheral vascular surgery. However, we were concerned that these thoracic or vascular conditions/procedures may require similar lines of post-discharge community services to coronary heart disease, thus making the hospital LOS of these conditions likely correlated with the 30-day readmission rate after CABG surgery directly. In other words, these conditions/procedures may not meet the exclusion criterion for appropriate IV.15 For example, the discharge decisions for patients undergoing CABG and patients admitted for congestive heart failure may be determined by common community factors such as accessibility of cardiologists for follow-up care or rehabilitation services.

Thus, we chose to use the hospital’s risk-adjusted LOS for patients admitted for GI hemorrhage21,22 – a condition unrelated to coronary heart disease – as the instrumental variable. To construct this IV, we identified all admissions of GI hemorrhage (principal ICD-9-CM diagnostic codes 456.0, 530.7, 530.82, 531-535, 537.83, 562.02, 562.03, 562.12, 562.13, 569.3, 569.85, 578) during 2007 and 2008 and excluded them from the following risk adjustment analyses if the patient (1) was younger than 65 years; (2) was transferred to another acute care hospital; or (3) died in the hospital. We then estimated a patient-level OLS model of the natural-log transformed length of stay after admission for GI hemorrhage ((LOSijgi)), as a function of patient covariates including age, female gender, race, admission type, and number of comorbidities, as follows:


See the Appendix for the characteristics of this cohort of patients admitted for GI hemorrhage, and the estimation of the risk adjustment model. From this model we obtained the estimated error term ε^ijgi for each patient. We then calculated each hospital’s risk-adjusted length of stay (natural-log transformed) as the average value of ε^ijgi for all GI hemorrhage patients in hospital j plus the grand mean of the natural-log transformed LOS for all GI hemorrhage patients in the sample.20 This variable was used as the instrumental variable ((IVjgi)) for the 2SRI analyses on patients receiving CABG surgery described below.

The IV analysis was based on the 2-stage residual inclusion approach and had two components:



where in equation (3), the first stage equation, the natural-log transformed postoperative length of stay for patients undergoing CABG surgery ((PLOSijcabg)) was regressed on the IV and exogenous patient and hospital covariates for patients undergoing CABG surgery. Equation (4), the second stage equation, is identical to the naïve logit model of equation (1) except that the estimated residuals from equation (3),ε^ijcabg, are also included in equation (4) to control for endogeneity due to the unobserved confounders. In other words, the 2SRI model partitioned the residual obtained from the naïve model (described in the previous subsection) into two parts: the residual obtained from the first stage model which controls for the endogeneity effect, and the residual unique to the 2nd stage equation. The inclusion of ε^ijcabg in the outcome equation offers an opportunity to statistically test for the endogeneity of (PLOSijcabg).15 If the coefficient β2 of ε^ijcabg is statistically significant then (PLOSijcabg) is indeed endogenous; otherwise we cannot reject the null hypothesis of the exogeneity of (PLOSijcabg).


Table 1 describes the characteristics of the sample of patients undergoing bypass surgery. Approximately 17 percent of patients were readmitted to an acute care hospital within 30 days of discharge. The post-operative length of stay was 7.4 days on average and varied substantially (with skewed distribution, Figure 1) over individual patients.

Figure 1
Distribution of postoperative length of stay among Medicare patients undergoing coronary bypass surgery.

Table 2 summarizes the results of the naïve logit model and the instrumental variable analyses, respectively. In the naïve logit model where endogeneity was not controlled for, the natural-log transformed PLOS showed a positive effect on the likelihood of 30-day readmission (β=0.69, odds ratio [OR] =1.99, 95% confidence interval [CI] of OR 1.93 – 2.05, p<.001).

Table 2
Effect of postoperative length of stay on 30-day readmission for Medicare patients undergoing bypass surgery

In the two-stage residual inclusion model we used the risk-adjusted ln(LOS) for all GI hemorrhage patients in the hospital as the IV (see Appendix for the risk-adjusted model). In the first stage of the 2SRI estimates, this IV strongly predicted the ln(PLOS) for individual patients receiving bypass surgery; it was indeed the strongest predictor of the dependent variable compared to other patient and hospital predictors in this equation. The F-statistic of the IV was 350.72, rejecting the null hypothesis of no association at a highly significant level (P<.001). Therefore, weak correlation of the instrument with the endogenous key independent variable is unlikely to be a source of bias.25

We could not test empirically the exclusion criterion because the system equations were exactly identified. As we mentioned before, there is no theoretical reason that the IV constructed based on the LOS for GI hemorrhage patients in the hospital would directly affect the 30-day readmission rate for patients receiving bypass surgery. In addition, if residual confounding exists, it is plausible that the error would be toward the null, i.e. an estimate of positive, rather than negative, association of postoperative length of stay and 30-day readmission.

The 2nd stage equation of the 2SRI model shows a negative association between the natural-log transformed post-CABG length of stay and 30-day readmission (β=-0.75, OR=0.47, 95% CI of OR 0.25 – 0.90, p=0.02). In addition, the β-coefficient of the residual derived from the 1st stage equation is positive and statistically significant (β=1.44, OR=4.21, 95% CI of OR 2.22 – 7.99, p<.001), indicating a strong endogeneity bias in the estimates of the naïve logit model; the bias due to unobserved confounding was strong enough to reverse the direction of the estimate toward a positive association between post-operative LOS and 30-day readmission in the naïve logit model.

To help better interpret the results, we calculated the predicted probability of 30-day readmission for patients undergoing bypass surgery with 6 days post-operative stays (the median PLOS of the sample) and compared it to the predicted probability of 30-day readmission for patients with 5 days post-operative stays (Table 3). In the predictions we kept patient and hospital covariates at their mean values. The result of the 2SRI model indicates that a one-day decrease in median post-operative length of stay would increase 30-day readmission rate by 3 percentage points. By comparison, the prediction from the naïve logit model was that a one-day decrease in median PLOS would reduce 30-day readmission rate by 2 percentage points.

Table 3
Predicted effect of a one-day reduction in median postoperative length of stay (from 6 to 5 days) on 30-day readmission rate after bypass surgery

Finally, we checked the robustness of our findings by repeating the above analyses for a redefined outcome of readmission and/or death within 30 days of discharge. The results remained similar, with the naïve logit model showing a positive relationship between the post-operative length of stay and 30-day readmission/death (β=0.79, OR= 2.19, 95% CI of OR 2.13 – 2.26, p<.001), and the 2SRI model showing a negative relationship (β=-0.54, OR= 0.58, 95% CI of OR 0.31 – 1.11, p=0.09). The predicted changes of 30-day readmission/death rate based on the two models are also presented in Table 3.


In this study, we performed an instrumental variable analysis to obtain consistent estimates of the effect of post-operative length of stay on 30-day readmission rate for Medicare patients undergoing CABG surgery. We demonstrated that the IV we used – the average risk-adjusted LOS for a hospital’s patients with GI hemorrhage – strongly and exogenously predicted the post-operative length of stay for each patient with bypass surgery. Assuming that by construction the IV affects the 30-day readmission after bypass surgery only through its impact on post-operative length of stay, our consistent estimate indicated that a one-day shortened median post-operative length of stay (from 6 days to 5 days) would increase the risk for 30-day readmission by 3 percentage points.

There is growing concern that cost containment efforts in hospital care (such as Medicare’s prospective reimbursement system) have reduced hospital length of stay to the extent that may harm patient outcomes. In particular, after the widespread adoption of “fast-track” protocols, the length of hospital stays for CABG surgery has been substantially reduced during the past 2 decades.3-6 The shortened length of stay may increase downstream adverse outcomes such as short-term readmissions.

While the concern is widespread, prior studies attempting to address this issue reported mixed results. For example, Lazar and colleges5 found that after the adoption of clinical pathways, reduced length of stay of CABG surgery was associated with substantially increased readmission rate; other studies found that the 30-day readmission rate did not change after the length of hospital stay for bypass surgery declined;3,7 and still other studies reported in their bivariate and multivariate analyses positive association between postoperative length of stay and short-term readmission for patients undergoing CABG surgery.4,12,13

These prior studies were based on observational designs that involved analyses of existing patient records, and may have suffered from methodological challenges. In particular, the conventional statistical techniques employed by these studies could have been considerably confounded when failing to control for unmeasured severities of disease that tend to be correlated with both length of hospital stays and the risk for readmission.

Observational studies using readily available data play a pivotal role in understanding contemporary healthcare issues and providing real-world comparative effectiveness evidence to inform policy development. This is especially true when randomized trials are not feasible or show limited external validity.26 However, determining the causal effect of shortened length of stay on important outcomes such as readmissions is difficult in observational studies. A selection bias exists in observational studies because patients are not randomly assigned to groups with shorter or longer hospital stays. In this case, unmeasured severity of disease is not balanced across “intervention” groups within which patients have the same length of stay. Because the unmeasured and unbalanced severity of disease is positively correlated with both postoperative length of stay and risk for short-term readmission, it will confound the negative effect of PLOS on readmission (i.e., the effect that shortened PLOS increases 30-day readmission rate after bypass surgery) in a positive way. Because of the positive confounding, the (true) negative effect of PLOS on readmission rate could be underestimated, or when the positive confounding is larger than the true effect, the estimated association could be inverted resulting in a false interpretation of positive relationship between PLOS and readmission rate.

Our results provide empirical evidence supporting the concern of the negative impact of reduced hospital LOS on post-discharge outcomes. While previous studies controlled for observed confounders to various degrees, our study, to the best of our knowledge, is the first that further tried to control for self-selection due to unobserved severity of disease by using instrumental variable regression technique. Our improved estimates underscore the need to closely monitor post-discharge clinical outcomes after the initial hospitalization has been the subject of continued cost containment efforts for bypass surgery.

There could be multiple reasons why reduced post-CABG length of stay increases 30-day readmission rate. For example, when patients are discharged earlier, their conditions may be less stable at the time of discharge; major complications are more likely to occur after discharge rather than during initial hospital stay; and increased difficulties in arranging appropriate ambulatory follow-up care are more likely to occur as well. All these factors may disrupt the transitioning of patients and underlie the inverse association of post-operative length of stay and 30-day readmission for bypass surgery. Similar effects of shortened length of hospital stays have been found in other areas of inpatient care including inpatient psychiatric care,24,27 hospital care for newborns,28 and hospital care for children and adolescents.29

For many conditions and procedures including bypass surgery, short-term readmissions are common and costly.30 The findings of our study suggest that optimal cost containment and quality improvement initiatives for bypass surgery should not focus solely on the care during initial hospitalization. Rather, broader attention should be paid to the whole episode of care: there seems to be a tradeoff between care provided at the initial admission and care required later on. Cutting costs and care initially seems to lead to higher costs and worst outcomes downstream. Future research should evaluate the total cost over the full episode to determine if overall costs increase. Among current federal initiatives aimed at reducing hospital readmissions, the Medicare bundled payment established by the Affordable Care Act of 2010 proposes to test a single reimbursement for multiple services incurred before, during, and after an initial hospitalization.11 The single episode-based payment is expected to provide incentives for improved coordination of care and to lower overall Medicare costs.

This study has several limitations. First, our analyses were based on data of Medicare fee-for-service patients undergoing CABG surgery. Thus, our results may or may not be generalizable to patients of other insurance types. Second, although our instrumental variable analyses addressed the issue of self-selection due to unobserved confounders and should be able to mitigate against its resultant biases, the validity of the estimated impact of post-operative length of stay on 30-day readmission was dependent on the assumptions required for such analyses. In general, the results in instrumental variable analyses using observational data would not be interpreted with the same degree of confidence as those in well-conducted randomized trials. Third, although the Medicare administrative data have been widely used in observational studies and have proved to be of high quality in recording patient administrative and clinical information,31,32 the data are not error free; errors of the data would lower the accuracy of our estimates in all models. Fourth, the administrative databases do not contain more detailed information necessary for fuller control of confounders, such as quality of in-hospital care (e.g. receipt of beta-blockers, appropriate use of antibiotics for individual CABG patients) and annual hospital/surgeon volume of CABG cases (since the claims only include Medicare patients). However, we believe that the unobserved confounding effect is dominated by omitted severity of disease – as our results show in table 2, its effect is strong enough to reverse the association between post-operative length of stay and 30-day readmission; our instrumental variable analyses successfully addressed the unobserved effect of disease severity. Finally, our study is limited in scope and given our focus on 30-day readmission/mortality, we did not analyze other important outcomes such as post-operative complications.

In conclusion, this study employed instrumental variable analyses to determine the impact of post-operative length of stay on 30-day readmission rate for Medicare patients undergoing coronary bypass surgery. We found that a one-day reduction in median post-operative length of stay (from 6 to 5 days) resulted in an increase in 30-day readmission rate by 3 percent points. Efforts to improve the outcomes and efficiency of care for bypass surgery should focus on care both during the initial admission and after discharge.

Table thumbnail
The risk adjustment model of natural-log transformed length of stay for Medicare patients admitted for GI hemorrhage (n=391759)


Dr. Li gratefully acknowledges funding from the National Institute on Aging (NIA) under grant R01AG033202. Dr. Cram is supported by a K24 award from NIAMS (AR062133) and by the Department of Veterans Affairs. This work is also funded in-part by R01 HL085347 from NHLBI and R01 AG033035 from NIA at the NIH. The views expressed in this article are those of the authors and do not necessarily represent the views of the Department of Veterans Affairs.



Conflicts of Interests: no conflicts of interest for any authors.

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