Melinda Beeuwkes Buntin

Partha Deb

José Escarce

Carrie Hoverman

Susan Paddock

Neeraj Sood 

RAND Health

1200 South Hayes Street

Arlington, VA 22202-5050

MedPAC

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Fax: (202) 220-3759

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•

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The views expressed in this report

are those of the authors.

No endorsement by MedPAC

is intended or should be inferred.

Comparison of

Medicare Spending

and Outcomes for

Beneficiaries with

Lower Extremity

A study conducted by RAND Health for the

Medicare Payment Advisory Commission

June 2005 • No. 05-2

Joint Replacements
WORKING 

P A P E R

Comparison of Medicare 

Spending and Outcomes 

for Beneficiaries with 

Lower Extremity Joint 

Replacements 

MELINDA BEEUWKES BUNTIN 

PARTHA DEB 

JOSÉ ESCARCE 

CARRIE HOVERMAN 

SUSAN PADDOCK 

NEERAJ SOOD 

WR-271--MedPAC

JUNE 2005 

Prepared for Medicare Payment Advisory Commission 

This product is part of the RAND

Health working paper series. 

RAND working papers are intended

to share researchers’ latest findings

and to solicit informal peer review. 

They have been approved for 

circulation by RAND Health but 

have not been formally edited 

or peer reviewed. Unless otherwise 

indicated, working papers can be

quoted and cited without permission

of the author, provided the source is

clearly referred to as a working paper. 

RAND’s publications do not necessarily 

reflect the opinions of its research 

clients and sponsors. 

 is a registered trademark. 
Comparison of Medicare Spending and Outcomes for Beneficiaries with Lower 

Extremity Joint Replacements 

I. Executive Summary 

Last year, the Centers for Medicare and Medicaid Services (CMS) released a 

regulation revising the definition of an inpatient rehabilitation facility (IRF) for payment 

purposes under the Medicare program. Specifically, the revised regulation (known as 

the “75 percent rule”) replaced polyarthritis, one of the 10 conditions that had to 

constitute 75 percent of a facility’s patients, with four arthritis-related conditions. The 

change was highly controversial. IRF industry leaders charged that the regulation would 

lead to reduced access to IRF care for lower extremity joint replacement (LEJR) patients. 

They claimed that LEJR had been implicitly included under the polyarthritis definition 

since arthritic joints are replaced. Under the revised definition, however, only LEJR 

patients with certain risk factors will be counted towards the threshold, which could lead 

to a reduction in access to IRF care for LEJR patients. CMS has pointed out that all types 

of LEJR patients can continue to receive rehabilitative care in skilled nursing facilities —

a setting some have suggested might be a more appropriate site of care for uncomplicated 

joint replacements. 

 The primary objective of this study is to conduct a set of analyses comparing 

costs and outcomes of lower extremity joint replacement patients discharged to three 

different post-acute settings: inpatient rehabilitation facilities, skilled nursing facilities, 

and patient homes. We employ multivariate techniques in order to adjust these analyses 

for observable differences in severity of illness across sites of care. In doing so, we use 

multinomial models that predict which type of institutional post-acute care a beneficiary 

accesses, and we describe these predictors. In addition, we use instrumental variables 

(IV) techniques that allow us to account for unobserved patient selection into IRFs and 

SNFs in order to learn how patient costs and outcomes are affected by the availability of 

IRF and SNF care. 

We analyzed data on elderly Medicare joint replacement patients discharged from

hospitals between January 2002 and June 2003. Approximately 30 percent of the sample 

used SNF care, 35 percent used IRF care, and the remainder returned home (either with 

home health care or without any Medicare-paid post-acute care). We assembled, and 

included as independent variables in our models, a wide array of indicators of clinical, 

individual, discharging hospital, and PAC supply factors that might affect PAC choices. 

We created indicators for the outcomes death and institutionalization within 60 and 120 

days of acute discharge. We then combined these two variables (institutionalization and 

mortality) into a composite measure since just examining the institutionalization variable 

for the population of survivors would result in a biased subsample. Using the home 

health, skilled nursing, and inpatient rehabilitation standard analytic files and hospital 

claims, we built length of stay and payment variables for each site of care for each 

beneficiary with an acute admission for lower-extremity joint replacement in 2002 or 

2003. To account for selection on the basis of unobservable patient characteristics, we 

develop an IV model that uses the variation in proximity to IRFs and SNFs as a natural 

experiment. The resulting model examines whether patients who go IRFs and SNFs 

because of their proximity to these facilities have different outcomes and costs than 

patients who go home. 

1
Our results indicate that there are differences in costs and possibly in outcomes 

across PAC sites for LEJR patients. The unadjusted data show that patients whose first 

site of care is an IRF or SNF have higher rates of mortality or care in an institutional 

setting 120 days after discharge from acute care compared to patients who receive care at 

home. However, our analysis suggests that these results are primarily driven by observed 

and unobserved differences in severity of illness and patient health at admission across 

sites of care. The apparently deleterious effects of IRFs and SNFs diminish significantly 

in our IV models that attempt to control for patient selection on both observable and 

unobservable characteristics. In particular, we find that after controlling for patient 

selection there no statistically significant differences in mortality rates across patients in 

different sites of post-acute care. However, the results from the IV models suggest that 

patients in IRFs and SNFs are more likely to be institutionalized. In particular the results 

indicate that compared to patients at home, patients in IRFs and SNFs are more likely to 

be to be dead or institutionalized at post-discharge day 120 by 0.18 percentage points and 

0.46 percentage points respectively. 

The results from the models of Medicare payments show that episodes of postacute care in an IRF or SNF are much more expensive than episodes of care for patients 

who receive care at home or in a non-institutional setting. The results from the IV model 

that accounts for selection both on observable and unobservable patient characteristics 

show that total Medicare post-acute care payments (for 120 day episodes of care 

following acute discharge) for IRF and SNF patients were $8,023 and $3,578 respectively 

higher than Medicare payments for patients in the reference group who were discharged 

home. The results are similar when one compares total Medicare payments for the acute 

stay plus post-acute care. Finally, these results also highlight the importance of 

controlling for patient selection, although controlling for selection had a smaller effect in 

the payment models compared to the outcome models. 

It is important in evaluating these findings to understand a key limitation of 

studies of health outcomes based on observational data: controlling fully for selection is 

extremely difficult. Our best estimates of the causal effect of PAC on outcomes are the 

IV models, but we cannot rule out the possibility that some selection remains in these 

estimates. Outcomes depend on many factors, including patients’ physical and cognitive 

abilities, underlying medical diseases, sensory and emotional factors, willingness to 

participate in care, and supportive environments. No risk adjustment approach can 

control for every factor affecting outcomes of care. While our choice of instrumental 

variables was carefully considered to address this problem, our estimates could be biased 

if our instruments are invalid. 

Another limitation of the study is that the outcomes we analyzed are not the ideal 

outcomes for LEJR patients. We would have preferred to examine functional status and 

changes therein, but we did not have the necessary data. Death and institutionalization at 

120 days are imperfect proxies for functional decline and are likely to be less closely 

related than functional status to the surgical procedure and the rehabilitation process. In 

addition, our outcome measures do not capture other dimensions of quality of life. The 

evidence from our unadjusted functional measures suggests that patients going to IRFs

and SNFs experience a short-term increase in functional status, with IRF patients 

beginning their stays with a lower level of functioning and achieving with a higher level 

of functioning than SNF patients over a similar period of time. 

2
Finally, we underscore that our results do not apply to all patients who use IRFs 

or SNFs. Rather, our IV models show the effects of IRF and SNF use for marginal

patients. In this context, marginal patients are those whose decision to use IRF or SNF is 

swayed by the proximity and availability of these PAC sites. Thus our results apply to 

patients for whom, in a sense, the clinical decision is gray. They do not apply to patients 

who are ideal candidates for IRF or who clearly require SNF care. Rather than being a 

limitation of our analysis, our focus on the marginal patient is an asset from a policy 

decision-making perspective since it is precisely these patients who will likely be affected 

by the reduced accessibility of IRF care as the 75 percent rule is enforced. 

Our analyses of costs have limitations as well. We have not captured the costs of 

physician, outpatient and hospice care. If patients not using institutional PAC rely more 

heavily on those types of care, then our findings overstate the degree to which IRF and 

SNF episodes of care are more expensive. If patients in IRFs and SNFs are using these 

services after their stay, our findings could understate costs for these patients. However, 

we do include costs of home health care, which is used at comparable rates by patients 

regardless of discharge destination. It seems reasonable to believe that use of outpatient 

and hospice care is likewise comparable across all categories of patients (i.e., those use 

institutional PAC and those who do not). 

Ultimately, in order to fully assess the impact of the 75 percent rule, we would 

need three additional types of information. First, we would ideally measure real resource 

use across sites of care rather than measuring only Medicare payments. Second, we 

would need a method for evaluating the trade-off between better outcomes and higher 

costs. Finally, we would need better measures of outcomes, including a measure of 

functional status that was captured consistently across all discharge settings. 

3
II. Introduction

Last year, the Centers for Medicare and Medicaid Services (CMS) released a 

regulation revising the definition of an inpatient rehabilitation facility (IRF) for payment 

purposes under the Medicare program. Specifically, the revised regulation (known as 

the “75 percent rule”) replaced polyarthritis, one of the 10 conditions that had to 

constitute 75 percent of a facility’s patients, with four arthritis-related conditions. The 

change was highly controversial. IRF industry leaders charged that the regulation would 

lead to reduced access to IRF care for lower extremity joint replacement (LEJR) patients. 

They claimed that LEJR had been implicitly included under the polyarthritis definition 

since arthritic joints are replaced. Under the revised definition, however, only LEJR 

patients with certain risk factors will be counted towards the threshold, which could lead 

to a reduction in access to IRF care for LEJR patients. CMS has pointed out that all types 

of LEJR patients can continue to receive rehabilitative care in skilled nursing facilities —

a setting some have suggested might be a more appropriate site of care for uncomplicated 

joint replacements. 

 The primary objective of this study is to compare costs and outcomes of lower 

extremity joint replacement (LEJR) patients treated in inpatient rehabilitation facilities 

(IRFs) and skilled nursing facilities (SNFs) with those returning to their homes after 

surgery. We employ multivariate techniques in order to adjust these analyses for 

observable differences in severity of illness across sites of care. In doing so, we use 

multinomial models that predict which type of institutional post-acute care a beneficiary 

accesses, and we describe these predictors. In addition, we use instrumental variables 

techniques that allow us to account for unobserved patient selection into IRFs and SNFs 

in order to learn how patient costs and outcomes are affected by the availability of IRF 

and SNF care in an area. From a policy perspective, these analyses answer questions 

similar to the ones raised by the 75 percent rule – i.e., what is the effect on costs and

outcomes of making IRF care less “accessible” to LEJR patients. 

III. Background 

Below we provide additional detail about the origins and provisions of the 75 

percent rule regulation and information about the limited amount of research conducted 

to date on the outcomes of post-acute care after lower extremity joint replacement – or 

the outcomes of post-acute care in general. 

75 Percent Rule Legislation 

The Social Security Act gives the Secretary of Health and Human Services the 

discretion to define a rehabilitation hospital and unit. Hospitals and units meeting those 

criteria are eligible to be paid on a prospective payment basis as an IRF under the IRF 

PPS. Specifically, Section §412.23(b)(2) of Medicare regulation specifies one of the 

criteria Medicare uses for classifying a hospital or unit of a hospital as an IRF, commonly 

known as the “75 percent rule.” This 75% rule was put in place more than 20 years ago 

when Medicare’s prospective payment system (PPS) for acute care hospitals was 

implemented. Its purpose was to help define those facilities that are excluded from the 

acute PPS as rehabilitation facilities. A facility may be classified as an IRF if it can show 

4
that, during its most recent 12-month cost reporting period, it served an inpatient 

population of whom at least 75 percent required intensive rehabilitation services for the 

treatment of one or more of the following ten conditions: 

 Stroke 

 Spinal cord injury 

 Congenital deformity 

 Amputation 

 Major multiple trauma

 Fracture of femur (hip fracture) 

 Brain injury

 Polyarthritis, including rheumatoid arthritis 

 Neurological disorders, including multiple sclerosis, motor neuron diseases, 

polyneuropathy, muscular dystrophy, and Parkinson's disease 

 Burns 

The August 7, 2001 final rule that implemented the IRF PPS did not change the 

survey and certification procedures for classification as an IRF. However, its 

implementation did increase attention to IRF regulations and enforcement of the existing 

75 percent rule. CMS found that the rule was being enforced unevenly, and the prospect 

of stringent and uniform enforcement quickly brought to the fore that very few IRFs 

would be in compliance with an interpretation of “polyarthritis” that did not include 

lower extremity joint replacement. Indeed, only 13 percent of IRFs would qualify under 

such a definition (CMS Final Rule, April 30, 2004). A series of discussions, 

administrative actions, and moratoria on enforcement ensued culminating in a final rule 

issued in April 2004. 

The regulation issued in April 2004 removed "polyarthritis" and added four 

arthritis-related medical conditions, resulting in 13 "qualifying" medical conditions used 

to classify a facility as an IRF. For example, Medicare will now count a patient towards 

the compliance threshold if the patient has severe or advanced osteoarthritis involving 

two or more major joints (elbows, shoulders, hips, or knees, but not counting a joint that 

has been replaced), and have met other medical criteria outlined in the regulation. Hip 

replacement patients with a preceding hip fracture count towards the compliance 

threshold. The final rule also provides for a transition to targeting payments to facilities

that treat a large share of patients with diagnoses likely to require intensive 

rehabilitation.1

 

The 2004 final rule counts toward the compliance threshold certain patients who 

undergo knee or hip joint replacement, or both, during an acute hospitalization 

immediately preceding the IRF stay, and if they meet one or more of three conditions. 

The set of categories defined by CMS excludes lower extremity joint replacement 

patients except in cases of bilateral knee or hip replacements, extremely obese patients, or 

those over age 85. Other joint replacement patients do not count towards the 75 percent 

 

1 In the first year, the final rule requires only a limited percentage of patients of an IRF's total patient population to

have one of the qualifying medical conditions in order for a facility to be classified as an IRF. For cost reporting 

periods beginning on or after July 1, 2004, and before July 1, 2005, the compliance threshold is set at 50 percent of the 

IRF's total patient population. For cost reporting periods beginning on or after July 1, 2005, and before July 1, 2006, the 

compliance threshold is set at 60 percent of the IRF's total patient population. For cost reporting periods beginning on 

or after July 1, 2006, and before July 1, 2007, the compliance threshold is set at 65 percent of the IRF's total patient 

population (CMS Final Rule, April 30, 2004).

5
rule unless they have other qualifying conditions (these other conditions include hip 

fracture as the event precipitating a hip replacement). As we discuss below, relatively 

few joint replacements are bilateral procedures and over one hundred thousand patients 

with single replacements use IRF care each year. In fact, LEJRs are now the single 

largest category of patients seen in IRFs. There is widespread concern, therefore, that far 

fewer joint replacement patients will receive rehabilitation in IRFs. 

Determinants of Outcomes of Lower Extremity Joint Replacement 

The enforcement and revision of 75 percent rule was complicated by the dearth of 

clinical or health services research that explains where patients should go to receive the 

most appropriate post-acute care. In fact, little is understood about best practices 

regarding lower extremity joint replacement and the effectiveness of various 

rehabilitation options (Kane 1997, Kramer et al. 1997, DeJong et al. 2002, Jette and 

Keysor 2002). Research in this area struggles to address the problem of patient selection: 

in order to isolate the effects of PAC treatments, researchers need to account for variance 

attributable to factors including patient, clinical, demographic, and other unobservable 

items that vary across sites (Kane 1997). 

The importance of observable predictive variables in the outcomes literature is 

mixed. Patient-related factors that have been correlated to total knee replacement 

outcomes include psychosocial variables, comorbidity, hospital volume, race, and 

preoperative functional status (Lingard et al. 2004; Heck et al. 1998; Sharma et al. 1996; 

Wasielewski et al. 1998; Fortin et al. 2002). The most frequently documented 

determinant of poor outcomes in total hip replacement is low procedural volume, either 

by individual surgeons, or by hospitals (Lavernia et al. 1995; Solomon et al. 2002; Taylor 

et al. 1997). In other cases, researchers have failed to find significant predictors (Kreder 

et al. 1998; Khuri 1999; Kane 2003). Other factors associated with LEJR outcomes 

included age, gender, race, medical comorbidity, abnormal laboratory values, 

postoperative deterioration of mental status, body mass index, low income, therapy 

intensity and rehabilitation duration (Braeken et al. 1997; Chen et al. 2002; Imamura and 

Black 1998; Jones et al. 2001; Lubitz et al. 1985; Mahomed et al. 2003; Poór et al., 1995; 

Weaver et al. 2003). 

Outcomes of Post-Acute Care

There are no studies of outcomes of lower extremity joint replacement across 

post-acute care sites. The limited number of existing studies on PAC outcomes that have 

been able to account for patient selection focus generally on hospitalized Medicare 

patients, or subsamples of stroke or hip fracture patients. Previous studies comparing 

post-acute outcomes from IRFs, SNFs, and other post-acute locations for these 

populations have mixed results. Studies of stroke and hip fracture populations are also 

informative as they note how others have controlled for unobservable selection into PAC. 

The importance of accounting for selection to different post-acute care settings is 

underscored in a study by Hadley et al. (2000). Using a Medicare Current Beneficiary 

Survey sample of hospitalized patients and instrumental variables analysis, their 

estimates suggested that home health care (HHC) users experienced greater 

improvements in functional status than nonusers. In contrast, estimation using only the 

observational data on HHC use implied that HHC users had poorer health outcomes. 

6
The evidence on stroke rehabilitation favors the use of intensive rehabilitation, 

such as that provided in IRFs, for greater functional gain (Kane et al. 1998, 2000, Kramer 

et al. 1997), more frequent return to community (Deutsch 2003, Kane et al. 1998, Kramer 

et al. 1997), and lower death rates (Kane et al. 1996). Kane et al. (1996) found that 

stroke patients fared better when treated in IRFs; there was no substantial benefit for 

rehabilitative nursing home care over regular nursing home care. In addition, the 

mortality rates among stroke patients at each follow-up point were significantly higher 

for patients discharged to the two types of nursing homes than for patients sent to IRFs. 

Using predicted values of patient hospital discharge location as independent variables to 

control for selection, Kane et al. (1998) found that among stroke patients, those 

discharged to a nursing home had consistently higher adjusted mortality rates and were 

significantly more likely to be in a nursing home at each follow-up point than those 

discharged elsewhere. Comparing six-week post-discharge functional status, Kane et al. 

(2000) found that stroke patients discharged to formal home health care or rehabilitation 

regained a significant amount of function, while those discharged home without formal 

care showed only modest functional improvement and patients discharged to nursing 

homes experienced functional decline. Ang (2003) found that a specialized stroke unit, 

which combined acute and rehabilitative services, had benefits in reducing mortality, 

institutionalization, and LOS and improved functional status. However, it is important to 

note that the evidence in favor of intensive rehabilitation for stroke patients might not 

generalize to LEJR patients due to the substantial difference in clinical conditions and 

types of rehabilitative care needed for these two patient populations. 

The evidence on hip fracture outcomes across post-acute sites is mixed. Some

studies indicate that SNF is the best post-acute site for hip fracture patients. Deutsch et 

al. (2005) found that SNF-based subacute rehabilitation was less costly and discharge to 

community and functional outcomes were in most, but not all, instances similar or better 

than IRF-based rehabilitation for Medicare fee-for-service beneficiaries who had a recent 

hip fracture. 

Other studies indicate that SNFs are not the best post-acute site for hip fracture 

patients. Kane et al. (1998) found that hip fracture patients discharged to nursing homes 

were more likely to be institutionalized than those sent to HHC, IRF or home and that hip 

fracture patients who received PAC in rehabilitation facilities or HHC had significantly 

more functional improvement compared with those discharged to nursing homes or to 

home without formal care. Without accounting for unobservable selection, Munin et al. 

(2005) found that patients in an IRF had significantly higher FIMTM motor scores than 

those in a SNF across time. A significantly higher percentage of IRF patients were 

discharged home after rehabilitation compared to SNF patients. Kane et al. (1996) found 

that for healthier hip fracture patients, the best functional outcome was associated with 

use of a rehabilitation facility and the worst was associated with rehabilitative nursing 

home. However, the same study found that for sicker hip fracture patients, the location at 

which post-hospital care was provided did not make a significant difference in terms of 

their functional recovery. In a later study, Kane et al. (1998) found that the mortality 

differences in hip fracture patients across settings were not as significant as those for 

stroke patients. Similarly, results from a study by Kramer et al. (1997) suggest that hip 

fracture patients admitted to rehabilitation hospitals do not differ from those admitted to 

7
nursing homes in their rates of return to the community or in the number of ADLs 

recovered to premorbid level. 

In conclusion, there is a dearth of research on joint replacement outcomes across 

different sites of post-acute care, and the research on PAC outcomes in general is limited. 

The available evidence does indicate that some patients receive more therapy and have 

better outcomes in more intensive settings (e.g. in IRFs than in SNFs) although often at a 

higher cost. The evidence is less strong, however, for hip fracture, an orthopedic 

condition like joint replacement, than for stroke. These studies described above indicate 

that, after controlling for selection, type of post-acute setting can make a difference in 

outcomes for hip fracture and stroke patients. Our study of Medicare joint replacement 

patients will help to clarify the implications of the 75 percent rule for outcomes of LEJR. 

IV. Data and Measures 

Sample Studied 

We have data on all elderly Medicare joint replacement patients discharged from

hospitals between January 2002 and June 2003. Joint replacement was defined using the 

DRGs for joint replacement procedures (209, 471) minus those patients with a primary 

diagnosis of hip fracture and minus those with reattachment procedures 84.26, 84.27 and 

84.28. Hip fracture patients are included in the 75% rule so their use of PAC is not 

affected by the regulation. 

We defined post-acute location as the first post-acute care site used after 

discharge from an acute care hospital. We chose to use the first site because a large 

majority of acute discharges use only one site in their post-acute care episode. Ninetythree percent of all acute discharges use only one site of care. We considered post-acute 

care use to be IRF use, SNF use, or HHC that began within 30 days of discharge from

acute care and was covered by Medicare.2

 We grouped care delivered in swing beds with 

SNF care. We also constructed files that contain data on sample patients’ use and costs 

of care in long-term care hospitals (LTCHs). Each of these types of care was defined 

using Medicare provider numbers and/or claim types. 

Patients who were readmitted to the hospital during the 30-day window were kept 

in the sample. Although Medicare rules allow SNF patients to delay entry for more than 

30 days after their acute discharge (in order to gain enough strength to undertake 

rehabilitation) this did not greatly affect our analyses: 97.3 percent of SNF patients in our 

sample began SNF care within 30 days of discharge if they used it at all. Patients who 

died in the hospital or within 30 days of discharge were dropped from the sample because 

they were unlikely to be considered good candidates for rehabilitation. This excluded 

population was small – less than 1 percent of joint replacement patients died.3

 We

 

2 We defined acute care hospitals using Medicare provider numbers. However, we dropped acute admissions that took place outside

of the 50 states plus the District of Columbia and admissions to children’s hospitals and psychiatric hospitals and units. We counted 

critical access hospitals (rural primary care hospitals) as acute care hospitals (provider numbers 1300 to 1399). We also excluded all 

patients residing in or receiving acute care in the state of Maryland as that state has its own hospital prospective payment system that 

makes it impossible to distinguish admissions to IRF facilities from acute admissions. In addition, care delivered in long term care

hospitals (LTCHs) often qualifies as institutional PAC as well. We do not analyze LTCHs here, however, since there are relatively 

few of them. Less than 0.05 percent of Medicare patients discharged from acute care use these facilities, and the facilities do not all 

provide post-acute care. A few LTCHs, for example, serve a primarily psychiatric population (Liu et al. 2001). 3

 While this population is small, it could be argued that they are a key group of seriously ill patients. However, the data suggests that 

they are not good candidates for PAC as their rates of PAC use are considerably lower than those of the Medicare population as a 

whole over the time period examined.

8
excluded patients receiving custodial care in nursing homes because they are expected to 

return there and patients who are discharged to custodial nursing homes (defined using 

MDS data), because they are not candidates for rehabilitation. We also excluded patients 

discharged to LTCHs and those who receive rehabilitation in acute hospitals (under DRG 

462) because our data suggests very low use and Medicare beneficiaries enrolled in 

HMOs within 4 months of their discharge because we do not have complete claims data 

for them. Patients were excluded if they were missing personal information, such as their 

zip code, or discharging hospital characteristics, such as disproportionate share. If a 

patient had more than one acute admission within 90 days for joint replacement, we only 

included the first stay in our dataset, and classified the second stay as a readmission. In 

total approximately three percent of the population was excluded for one or more of the 

reasons above. 

Measures 

We assembled, and included as independent variables in our models, a wide array of 

indicators of clinical, individual, discharging hospital, and PAC supply factors that might 

affect PAC choices. 

Individual Predictors. We identified a number of patient-level characteristics 

hypothesized to affect use of PAC care and type of PAC site used. We included the age 

of the beneficiary and their age squared to capture a non-linear relationship between 

outcome and age should one exist. We also included gender, race and place of residence 

(defined as a MSA, an area adjacent to a MSA, or rural area/not adjacent to an MSA) in 

our analyses. We also include an interaction between gender and age, and this interaction 

term squared. All of these patient-level predictors were created using fields on the 

inpatient claims. In addition, we used the Medicare Denominator file to create indicators 

for whether patients were receiving Medicaid at the time of their acute admission or 

within 4 months of discharge. (Those who went on Medicaid soon after discharge were 

presumed to have been income-eligible for coverage, but not yet enrolled.) 

Clinical Predictors. To capture the complexity of patients at the time of hospital 

discharge we included a large set of comorbidities and complications tailored to our joint 

replacement patients. These were derived from diagnoses on the hospital discharge 

records. The comorbidities used in our analyses were the chronic conditions identified by 

Iezzoni et al. (1994) as conditions that are nearly always present prior to hospital 

admission and hence are extremely unlikely to represent complications arising during the 

hospitalization. These conditions included primary cancer with poor prognosis, 

metastatic cancer, chronic pulmonary disease, coronary artery disease, congestive heart 

failure, peripheral vascular disease, severe chronic liver disease, diabetes mellitus with 

and without end-organ damage, chronic renal failure, nutritional deficiencies, dementia, 

and functional impairment. 

The second type of case mix variable was complications that were likely to have 

arisen during the hospital. To develop this list, we adapted the list of complications 

developed by Iezzoni et al. (1994). From that list, we kept only those complications that 

were likely to have a continued effect after hospital discharge, and therefore to potentially 

influence the choice of site for post-acute care (e.g., we excluded transient metabolic 

derangements and side effects of medications). In addition, we augmented the list to 

include some important complications for the Medicare population that had been omitted 

9
from Iezzoni’s list. The resulting list of complications included post-operative 

pulmonary compromise, post-operative gastrointestinal hemorrhage, cellulitis or 

decubitus ulcer, septicemia, pneumonia, mechanical complications due to a device, 

implant, or graft, shock or arrest in the hospital, post-operative acute myocardial 

infarction (AMI), post-operative cardiac abnormalities other than AMI, procedure-related 

perforation or laceration, venous thrombosis and pulmonary embolism, acute renal 

failure, miscellaneous complications, delirium, dementia, and stroke. 

We created indicators of the type of replacement the patient received, such as a hip or 

knee replacement, a total replacement, a partial replacement, and/or a revision of a 

previous joint replacement, and whether a bilateral replacement took place (Beeuwkes 

Buntin et al. 2005). 

Characteristics of Discharging Hospitals. Patterns of care and approaches to 

discharge planning in the acute care hospital can influence the PAC use of patients. 

Accordingly, we included a number of covariates to capture the orientation of acute care 

hospitals. They include size (average daily census or ADC), teaching status (resident to 

ADC ratio), ownership status (government, private non-profit, or for-profit), Medicare 

patient percentage, case-mix index of the hospital, and low-income patient percentage. 

We also included a measure of the HMO penetration rate. These measures were created 

using cost report and provider of service data available from the CMS website and the 

area resource file. 

 PAC Availability. We defined availability from a patient-specific perspective 

based on how close IRFs and SNFs were to patients’ homes and how many of each type 

of facility were within reasonable distances of patients’ homes. To construct our 

measures, we used patient and provider zip code information to measure the distance 

traveled from patients’ residences to IRFs and SNFs. We used geocoding software to 

calculate distances from the midpoint of each beneficiary’s zip code to the midpoint of 

the closest provider zip code. 

We created two measures of the availability of PAC. The first captures the 

distance from the patient to the closest provider (separate measures are created for closest 

IRF and closest SNF). Both the distance to the closest and the distance squared are 

included, since the effects of distance on PAC choice are likely diminishing as distances 

become large. These variables measure how accessible the provider type is in terms of 

proximity. The second measure includes the number of PAC providers of each type 

within a given radius around the patient’s home. We calculated these radii for joint 

replacement patients by area type, and defined the radii using the 90th percentile of the 

distance traveled to that type of provider by beneficiaries living in that type of area; the 

90th percentile was chosen since it reflected a generous definition of the market area, but 

was not biased by the care patterns of patients who might be receiving care far from

home due to holidays or other reasons. We also created indicators for areas without any 

of a given type of provider as the lack of providers would have a strong negative effect 

on the use of that type of PAC.4

Outcomes. We examined descriptive statistics on five health outcomes and 

modeled two outcomes. We looked at rehospitalization within 60 days and 120 days 

 

4 We calculated the correlation between our measures of PAC supply and more typical measures of supply that take into account only 

the number of providers within patients’ counties. As expected, the measures of numbers of providers were positively correlated. 

However, they were strongly correlated only within MSAs. In addition, our radius-based measures had higher coefficients of

variation, suggesting that they are more sensitive to variations in availability.

10
descriptively using Medicare claim files. We used the Minimum Data Set for nursing 

home residents (MDS) to identify those patients residing in a custodial nursing home at 

60 and 120 days. The MDS file contains assessments of all residents in nursing homes in 

the U.S. regardless of the payer. Each record in the MDS is an assessment with a date—

assessments are performed at various times in the resident’s stay according to national 

regulation. The assessment schedule mandates that assessments will be performed for a 

nursing facility resident at admission, quarterly, and annually, whenever the resident 

experiences a significant change in status, and whenever the facility identifies a 

significant error in a prior assessment. Using these assessment records, we created an 

array for each patient with their location on each day. If there are two assessments that 

are less than 95 days apart, we assume that this patient was in the nursing home for the 

entire period between the assessments. We chose the 95-day threshold because nursing 

homes are mandated to complete an assessment quarterly at a minimum (every 90 days), 

and then allowed a 5-day tolerance. 

To examine the validity of these MDS-based outcomes measures we looked at 

whether those we found to be institutionalized at these intervals were in fact highly 

unlikely to be community residents. Of those discharged from an IRF, 30 percent of 

those still in the nursing home at day 180 went there without going home first. Only 0.38 

percent of those at home on day 180 were discharged to custodial care first. Of those 

discharged from a SNF, 60 percent of those in the nursing home at day 180 went there 

without going home first, while 3.5 percent of those at home on day 180 were discharged 

to a custodial nursing home. These figures indicate that our measures are valid indicators 

of nursing home residence. 

We created an indicator for patients who died within 60 and 120 days of their 

hospital discharge using Medpar data. We then combined these two variables 

(institutalization and mortality) into a composite measure since just using the variable for 

the populations of survivors would result in a biased subsample. We used this composite 

measure of institutalization or mortality and the mortality indicator in our models of

health outcomes. Additionally, we created a variable that indicated that the beneficiary 

was independent in the community—not in a nursing home, not dead and not using any 

post-acute care (including home health care) as an indicator for a “positive” outcome. 

(We could not, however, examine outpatient or hospice care use in creating this 

measure.) 

Payments and Length of Stay. Using the home health, skilled nursing, and 

inpatient rehabilitation standard analytic files and hospital claims, we built length of stay 

and payment variables for each site of care for each beneficiary with an acute admission 

for lower-extremity joint replacement in 2002 or 2003. We wage-adjusted the acute 

payments using the impact file for post-reclassified wage index data for PPS hospitals 

and post-acute payments using the MSAX file for the pre-reclassified wage index, which 

is a longitudinal file at the MSA level. We then created summary variables of total postacute length of stay and payments, and total length of stay and payments (including the 

initial acute stay). 

 Functional Status. We created a measure of functional status similar to the 

Barthel Index (Mahoney and Barthel 1965) and mapped it to the MDS and the IRF 

patient assessment instrument (PAI) using methods analogous to those described by 

Johnson et al. (2001). This is a particularly daunting undertaking because the assessment 

11
instruments ask differing questions and the patients are assessed at different times in their 

post-acute stay. For example, to evaluate the patient’s ability to walk, the MDS has two 

separate items for locomotion. The first is “Walk in Corridor (how resident walks in 

corridor on unit)” rated on a scale from 0-4 or did not occur. The second item is “Modes 

of Locomotion”, where one is to “check all that apply” among cane/walker/crutch, 

wheeled self, other person wheeled, wheelchair primary mode of locomotion. The IRF 

PAI has one item for locomotion—split into walk, wheelchair, or both, and is scored 

from 0-7. In addition to these differences, the patient only has to be evaluated once in the 

first 5 days in a SNF, while the IRF PAI is completed within 72 hours of admission. The 

IRF PAI is also completed at discharge, while the SNF MDS is only completed at the 14th

day if the patient has a length of stay greater than 14 days. 

Because of the differences between the instruments and the timing of assessments, 

we also looked at the individual walking and transfer items and created a dichotomous 

variable that indicates whether the beneficiary can walk or transfer on their own (or with 

supervision). We examine these variables descriptively below, but they are not included 

in our models because we felt they were too inconsistently measured across IRFs and 

SNFs to be treated formally as outcomes. 

V. Methods 

Descriptive Analysis 

We conducted descriptive analyses of LEJR patients’ characteristics, use of PAC, 

costs, and outcomes. We examined how costs and outcomes vary by the first post-acute 

setting used following acute hospital discharge as described above. 

Standard Multivariate Analysis 

After conducting the descriptive analyses we used multivariate regression to 

estimate how the site of PAC care affected outcomes measures. The multivariate analysis 

allows us to control for observable differences in the patient population in each site of 

care that might confound our estimates of the effect of site of PAC care on outcomes. In 

particular, all our models control for the individual predictors, clinical predictors and 

characteristics of discharging hospitals described in the previous section. 

For this analysis, we looked at whether the patient’s first site of post-acute care 

was an IRF or a SNF. Outcomes of these two groups of patients were compared to the 

outcomes of a reference group who did not receive PAC in a SNF or IRF within 30 days 

of discharge from acute care. A significant proportion (63%) of patients in the reference 

group received home health care. It is also likely that some patients in the reference group 

received outpatient rehabilitation care. However, since we did not have data on outpatient 

care we could not measure the use of outpatient care by these patients. 

As described in the previous section, we used two measures of health outcomes 

for this analysis – (1) a composite measure of mortality and institutionalization that 

indicated whether the patient had died or was receiving care in an institutional setting 120 

days after discharge from acute care; (2) whether the patient died within 120 days of 

discharge from acute care. Because both our outcome measures are binary we used probit 

models to model each of the outcomes. While probit models account for the binary nature 

of the outcome variables, it is difficult to directly interpret the magnitude of coefficient 

12
estimates from these models. Thus, we report the “marginal effect” of each site of PAC 

care on the outcome measures for a person with average characteristics. The marginal 

effect for a particular site of care measures the extent to which receiving care in that site 

increases (or decreases) the probability of having the outcome compared to patients in the 

reference group. 

Finally, we also model how the site of PAC affects Medicare payments for the 

episode of care. We used two measures of Medicare payments – (1) total post-acute care 

payments starting with acute care discharge and ending 120 days after discharge from

acute care; and (2) total Medicare payments for acute and post-acute care starting with

the acute care admission and ending 120 days after discharge from acute care. Since 

payments are measured on a continuous scale, we used ordinary least squares (OLS) 

regression to model payments. 

Instrumental Variables Analysis 

In addition to confounding due to selection on observables, which the probit and 

least squares models for health outcomes and payments, respectively, take into account, it 

is likely that there is confounding due to selection on unobservable characteristics of the 

patients. Instrumental variables (IV) methods can be used to purge the estimates of such

confounding due to unobservable characteristics. The linear instrumental variables 

model is a widely used and powerful tool in such contexts. Although it was developed 

for models of continuous outcomes and endogenous regressors, it has been shown to 

work well even when the outcome and/or endogenous regressor is binary (see, e.g., 

Angrist, 2001). Under appropriate conditions IV methods provide consistent estimates 

without strong distributional assumptions and are computationally simple. For nonlinear 

and limited dependent variable models in general, however, the linear IV model may 

either be inappropriate or not work well in practice. Specifically, in our case, although 

the outcomes of interest are either binary or linear, the endogenous regressors (dummy 

variables for IRF and SNF) are from a multinomial distribution. A linear IV model 

would treat the endogenous regressors as if they were unrelated, which is not true 

because a patient goes to an IRF, SNF, or neither upon acute discharge. 

Instead, we formulate a nonlinear instrumental variables model using latent 

factors to account for selection on unobservables.5

 Our model respects the multinomial 

nature of the endogenous regressors as well as the binary nature of the health outcome. 

Specifically, we assume that the endogenous regressors have a multinomial logit form, 

while the health outcome and payments have probit and normal (linear) forms 

respectively. Then, latent factors are incorporated into the equations to allow for 

unobserved influences on care choice to affect outcomes and their joint distribution 

specified. Such models have been developed in Deb and Trivedi (2004). 

The main computational problem is that the joint distribution, which involves a 

multidimensional integral, does not have a closed form solution. This difficulty can be

addressed using simulation-based estimation (Gourieroux and Monfort, 1996). Using 

normally distributed random draws for the latent variables, a simulated likelihood 

function for the data is defined and its parameters estimated using a Maximum Simulated 

Likelihood Estimator. Because of the complexity of our model and the large sample size, 

standard simulation methods are quite slow. Therefore, we adapt an acceleration 

 

5 The equations can be found in Appendix I. 

13
technique that uses quasi-random draws based on Halton sequences (Bhat, 2001; Train, 

2002). Additional details on estimation and simulation are reported in Deb and Trivedi 

(2004). 

Validity of Instruments 

We use the measures of PAC availability described in Section III as instruments. 

We anticipate that these PAC factors are uncorrelated with beneficiaries’ clinical needs 

since seniors are unlikely to choose where to live based on proximity to IRFs and SNFs. 

We use the instruments to predict use of IRFs and SNFs, and thus to infer the effect on 

outcomes of a marginal patient (i.e., a patient whose choice among IRF, SNF, or neither 

site would be affected by our instruments) going to an IRF or a SNF. We use two sets of 

instruments in the analyses. The first set of instruments captures the distance from the 

patient to the closest provider and includes distance to closest SNF, distance to closest 

IRF, distance to closest SNF squared, and distance to closest IRF squared. The second set 

of instruments measures the number of PAC providers of each type within a given radius 

around the patient’s home. Instruments in this set include number of SNFs within travel 

radius, number of IRFs within travel radius, an indicator for no SNFs in travel radius, and 

an indicator for no IRFs in travel radius 

As in all instrumental variable based models, the validity of our results rests on 

the validity of our instruments. Valid instruments must satisfy two properties. First, they 

should be strongly correlated with the endogenous variable, i.e. our measures of PAC 

availability should be strong predictors of the PAC site used. Second, the instruments 

should only affect outcomes through their effect on the choice of post-acute care and they 

should be uncorrelated with unobserved factors that affect outcomes. Our instruments 

pass the first test of instrument validity convincingly. The descriptive statistics in Table 

1 clearly show that our PAC availability measures for both SNFs and IRFs are strong 

predictors of SNF and IRF use respectively. This result is also confirmed in multivariate 

analysis that controls for patient and discharging hospital characteristics. In all our 

multinomial logit models of the choice of site of PAC care the PAC availability measures 

for both SNFs and IRFs are highly statistically significant (p value < 0.001) and are 

important predictors of the site of care. Our prior work (Beeuwkes Buntin et al., 2005) 

also provides evidence that the relative supply of and distance to IRFs and SNFs in the 

area in which a beneficiary lives are important and strong predictors of the site of postacute care. 

The second condition is trickier. As noted, instrumental variable estimates are 

unbiased if and only if the instruments only affect outcomes through their effect on the 

choice of post-acute care and they are uncorrelated with unobserved factors that affect 

outcomes. Unfortunately, this assumption cannot be tested directly. Thus, to address this 

issue we examined indirect evidence for the validity of our instruments and considered 

possible reasons why they might not be valid. 

An important concern is that our instruments might be invalid if they are 

correlated with unobserved determinants of our outcomes. If this were the case, then our 

instruments would influence outcomes independent of their effect on the choice of site of 

PAC care. As one test for this, we estimate whether our instruments are correlated with 

observable patient and clinical predictors. If our instruments are correlated with 

observable patient characteristics then they might also be correlated with unobservable 

14
patient characteristics that determine outcomes. To implement this test we estimate OLS 

models of PAC availability as a function of patient and clinical predictors. A high Rsquare from these regressions would suggest that our patient and clinical characteristics 

are correlated with our instruments and are important predictors of availability of PAC. 

However, our results show that the R-squares of the regressions for each of our 4 

measures of PAC availability (distance to closest SNF, distance to closest IRF, number of 

SNfs within 90th percentile travel radius, number of IRFs within 90th percentile travel 

radius) ranged from 0.004 to 0.008. The low R-squares from these regressions clearly 

suggest that markets that vary substantially in their availability of PAC do not vary much 

in their patient populations. 

Our instruments could also be correlated with unobserved provider attributes that 

influence outcomes, such as quality of care. This could happen, for instance, if IRFs and 

SNFs in more competitive markets provide higher quality. The problem is that our 

instruments, which essentially measure the geographical density of IRFs and SNFs, 

capture dimensions of competition. Again, we cannot test this directly, but we did 

develop two indirect tests. 

One indirect way to judge the importance of unobservable differences in patient 

characteristics or provider quality across markets is to test the extent to which variation in 

our outcomes is generated by market level heterogeneity that is independent of the 

variation in PAC availability across markets. To implement this test we estimate 2 

models for each of our health outcome measures. The first model is fully non-parametric 

model of the outcome measures with 604 dummy variables for each MSA (or market) 

with at least 100 patients in the sample and our set of patient and clinical predictors. The 

second model is a parsimonious model of outcomes that only includes our 8 instruments, 

patient and clinical predictors. If market level heterogeneity in patient populations is 

important then the fully non-parametric model will have a much higher R-square 

(predictive power) compared to the parsimonious model with only PAC availability 

measures. The results from this test also confirm that heterogeneity across markets in 

patient attributes or provider quality is not an important threat to the validity of our 

instruments. The R-squares from the fully non-parametric model were only marginally 

higher despite the inclusion of 604 MSA dummies in the model. For example, the Rsquare for the fully non-parametric model was 0.0715 for our Mortality/Institutalization 

outcome and the R-square for the parsimonious model was marginally lower at 0.0698. 

In the second indirect test of instrument validity, we checked the robustness of our 

results to the inclusion or exclusion of certain sets of instruments. This test is in the spirit 

of the Hausman over-identification test and is based on the principle that if all our 

instruments are valid then the estimates obtained by using only a subset of instruments 

should differ only as a result of sampling error (Hausman, 1978). Thus, for this test we 

estimated two different sets of models. The first set of models only used the distance 

measures as the instruments -- distance to closest IRF, distance to closest SNF, distance 

to closest IRF squared, and distance to closest SNF squared. The second set of models 

only used the radius measures as instruments -- number of IRFs in travel radius, number 

of SNFs in travel radius, no IRFs in travel radius, no SNFs in travel radius. The results 

from both these sets of models were virtually identical to the model that used both 

distance and radius measures as instruments. Thus, these results also suggest that our 

instruments are valid. 

15
We underscore that our tests for the validity of our instruments are indirect tests, 

as there are no direct and definitive tests. These tests suggest that our instruments are 

valid and, therefore, that our instrumental variable estimates are unbiased. Nonetheless, 

we cannot rule out the possibility that we have failed to detect a problem with our 

instruments. The consequence would be that our instrumental variable estimates are not 

fully purged of selection effects. We discuss this further in the conclusion section. 

VI. Results 

Table 1 shows descriptive statistics for our patient population by first post-acute 

care location. Approximately 30 percent of the sample used SNF care, 35 percent used 

IRF care, and the remainder returned home (either with home health care or without any 

Medicare-paid post-acute care). The asterisks on these tables indicate a statistically 

significant difference between the IRF and SNF population, and the asterisk is placed 

next to the higher of the means. These data highlight the differences in patient 

populations across different sites of care, and clearly demonstrate why it is crucial to 

worry about selection when we examine outcomes. In particular, the first set of 

characteristics show that SNF patients are on average older and sicker, and there is some

evidence that they have lower socioeconomic status. Specifically, patients who went to 

SNFs were on average 1.4 years older than those who went to IRFs and 3.6 years older 

than those who went home. Those who went to a SNF were also more likely to be 

Medicaid beneficiaries than those who went to an IRF or home. Those who went to an 

IRF were more likely to live in an MSA. Patients in SNFs have more complications and 

comorbidities on average than those going to IRFs or home. 

There are also important differences in procedures performed and discharging 

hospital characteristics. More hip replacement patients go to SNFs for post-acute care, 

while knee replacements tend to use IRFs or go home. On average, IRF patients come

from larger discharging hospitals with a higher case mix and they tend to use teaching 

hospitals more. 

Prior research has found that PAC availability is related to choice of post-acute 

site (Beeuwkes Buntin et al. 2005). The descriptive statistics show that those who go to 

an IRF have, on average, more IRFs within their travel radius, while those who go to 

SNFs have more SNFs within their travel radius. IRF patients have a shorter travel 

distance to both the closest IRF and the closest SNF. This is probably due to IRF patients 

living in more urban areas. 

Table 2 displays the mean values of our outcome measures. Functional status is 

only measured for our IRF and SNF populations because the patients who go home

without care are not assessed. IRF patients are assessed at admission and discharge, 

while SNF patients are assessed at 5 days and 14 days (if they are still in the SNF). On 

average, SNF patients have a higher functional status score (indicating that they are more 

able) at the beginning of their stay (at admission or 5 days), and a lower functional score 

toward the end of their stay (at discharge or 14 days) than IRF patients. Scores in both 

locations increase during the stay, but descriptively the IRF patients gain more function. 

This trend holds when we compare only the populations who have a stay 14 days or 

longer. This trend also holds when we look at individual functional items, such as ability 

to walk or transfer independently. While we cannot compare improvement in functional 

16
status directly given the different assessment instruments and timeframes, there is clearly 

a greater functional gain from admission to discharge among IRF patients than among 

SNF patients over a similar time period. 

The health outcomes we looked at descriptively include rehospitalization, 

institutionalization, mortality, and independence in community. We looked at these 

variables at 60 and 120 days and looked at independent in community out to 180 days. 

IRF patients are the most likely to be rehospitalized, by both 60 and 120 days. SNF 

patients are most likely to die or be institutionalized. Patients returning home after their 

hospital stay are, on average, more likely to be independent in the community at all 

intervals, while IRF patients are more likely than SNF patients to be independent. As 

seen from the table, the means are very low for institutalization and mortality. For 

example, only 0.8 percent of those who have IRF as their first site of PAC are dead or 

institutionalized at 120 days. Because joint replacement is an elective surgery, the 

population under examination is very healthy. Of course, these descriptive differences in 

outcomes are in large part, if not fully, due to differences in patient populations. Our 

multivariate analyses shed light on the importance of selection of different types of

patients into SNFs and IRFs in determining outcomes. 

We also looked at length of stay and payments for 60 day and 120 day “episodes” 

of care. Those who go to SNFs tend to have the largest number of post-acute and total 

(acute and post-acute) days of care during both intervals, while costing less than IRF 

patients. As Table 2 shows, patients who use IRF care do not use much SNF care, and 

vice versa. IRF and SNF patients both have a high rate of transfer to HHC. However, 

SNFs discharge patients to HHC more often than IRFs do. The acute hospital payments 

are higher for IRF patients. We have adjusted these payments with Medicare wage 

indices so these higher payments are probably due to the teaching and disproportionate 

share adjustments of the hospitals from which IRF patients are discharged. 

Standard Multivariate Results 

Table 3 reports the descriptive results and results from two different regression 

models. The first set of results “Unadjusted Models” reports the marginal effects for 

health outcomes and Medicare payments for patients whose first site of PAC was an IRF 

or SNF as compared to the reference group that received no institutional care. The second 

set of results, “Naïve Models”, report the marginal effects for the multivariate analysis

that controls for observable patient and hospital characteristics but does not control for 

selection into site of PAC based on unobservables. Finally, the results in the last set of 

columns, “IV models”, report the marginal effects from our instrumental variables 

models. As described earlier, the goal of these models is to control for selection in site of 

care based both on observable and unobservable characteristics.6

 

Health Outcomes 

Overall, the results show that patients whose first site of care is an IRF or SNF 

(compared to patients in the reference group who get home health care, other outpatient 

rehabilitation care, or no care) are more likely to have worse outcomes as measured by 

higher rates of mortality or care in an institutional setting 120 days after discharge from

acute care. However, the pattern of findings as we move from the unadjusted analyses to 

 

6

 The full set of regression results can be found in Appendix II. 

17
the IV models offers an excellent illustration of the need to control for selection into 

different PAC sites and to consider whether even our IV models succeed in controlling 

fully for selection. 

As shown, in the unadjusted model IRF patients are 0.6 percentage points more 

likely to be dead or institutionalized at post-discharge day 120 as compared to patients in 

the reference category. Controlling for observable differences in patient and hospital 

characteristics (the naïve model) reduces this marginal effect of IRF care by a third, to a 

difference of 0.43 percentage points. Accounting for patient selection on both observable 

and unobservable characteristics further reduces the IRF marginal effect to only 0.18 

percentage points, and this effect is only significantly different from zero at the 96% 

confidence level. 

A similar pattern emerges for the marginal effect of SNF use on the probability of 

death or institutionalization at day 120. The unadjusted model shows that SNF patients 

are 2.7 percentage points more likely to be to be dead or institutionalized at postdischarge day 120 as compared to patients in the reference category. The difference is 

reduced to 1.2 percentage points in the naïve model that controls for observable 

characteristics and to 0.46 percentage points in the IV model. The SNF effect in the IV

model is statistically significant at the 99% confidence level. Although the marginal 

effects of SNFs and IRFs are small in absolute terms they are large relative to the rate of

mortality or institutionalization experienced by the reference group that did not receive 

PAC in a SNF or IRF within 30 days of discharge from acute care. 

Notably, the results from the mortality only models show that after controlling for 

observable and unobservable patient and hospital characteristics (the IV model) there are 

no statistically significant differences in mortality rates across patients in different sites of

post-acute care. Thus the differences in mortality rates observed in the raw data are 

driven by differences in patient population. 

To summarize, our findings for health outcomes indicate that there is a great deal 

of selection into different sites of PAC based on patient characteristics. Patients who use 

IRF care are at higher risk of death or long-term institutionalization than those who use 

no institutional PAC, and those who use SNF care are at higher risk still. An important 

problem in assessing the causal effect of PAC on health outcomes is that this selection is 

based on both characteristics we observe and those we cannot observe. 

To control for both observable and unobservable patient differences, we estimated 

IV models. These analyses found no difference in mortality across PAC sites, but they 

did find that patients who used IRF or SNF care were slightly more likely than those in 

the reference group to be institutionalized at 120 days post-discharge. Thus, the marginal 

effects imply a relative risk ratio of 1.6 for IRFs and 2.5 for SNFs. In other words, the 

results from the IV model indicate that receiving post-acute care in an IRF increases the 

probability of death or institutionalization by 60% and seeking care in a SNF increases 

this probability by 150% compared with being sent home without institutional PAC. We 

conducted several indirect tests to assess the validity of our instruments and they seemed 

to perform well. Nonetheless, it is possible that our IV models did not fully purge our 

results of selection effects. For one, our tests of instrument validity are only indirect and 

suggestive; they are not conclusive. Additionally, even with valid instruments, IV 

estimates may retain some bias in the same direction as naïve estimates in finite samples 

(Staiger and Stock, 1997). 

18
Medicare Payments 

 In general, the results from the models show that episodes of post-acute care in an 

IRF or SNF are much more expensive (reflecting higher Medicare payments) than 

episodes of care for patients in the reference category. The results also show that 

Medicare payments for episodes of care beginning in IRFs are much higher than episodes 

of care beginning in a SNF, even after controlling for patient and discharging hospital 

characteristics. For example, the results from the IV model that accounts for selection 

both on observable and unobservable patient characteristics show that total Medicare 

payments (for 120 day episodes of care) for IRF and SNF patients were $8,023 and 

$3,578 respectively higher than Medicare payments for patients in the reference group. 

The results are similar when one compares total Medicare payments for post-acute care. 

Finally, these results also highlight the importance of controlling for patient selection, 

although controlling for selection had a smaller effect in the payment models compared 

to the outcome models. 

VII. Conclusions 

Our results indicate that there are differences in costs and possibly in outcomes 

across PAC sites for LEJR patients. Our models that control for both observable and 

unobservable selection suggest that IRF and SNF patients have a higher probability of 

being institutionalized 120 days post-discharge than patients who receive no institutional 

PAC. In particular, the results indicate that compared to patients at home, patients in 

IRFs and SNFs are more likely to be to be dead or institutionalized at post-discharge day 

120 by 0.18 percentage points and 0.46 percentage points respectively. Notably, neither 

IRFs nor SNFs have a significant effect on mortality alone, implying that the effect on

outcomes is operating exclusively through institutionalization. We reached similar 

conclusions about Medicare payments across sites of care. IRF payments for episodes 

following a LEJR were the highest, controlling for observable and unobservable 

characteristics, SNF patient episode payments were lower, and payments for patients not 

discharged to institutional PAC were the lowest. 

It is important in evaluating these findings to understand a key limitation of 

studies of health outcomes based on observational data: controlling fully for selection is 

extremely difficult. Our best estimates of the causal effect of PAC on outcomes are the 

IV models, but we cannot rule out the possibility that some selection remains in these 

estimates. Outcomes depend on many factors, including patients’ physical and cognitive 

abilities, underlying medical diseases, sensory and emotional factors, willingness to 

participate in care, and supportive environments. No risk-adjustment approach can 

control for every factor affecting outcomes of care (Iezzoni, 2004). While our choice of 

instrumental variables was carefully considered to address this problem, our estimates 

could be biased if our instruments are invalid. 

Another limitation of the study is that the outcomes we analyzed are not the ideal 

outcomes for LEJR patients. We would have preferred to examine functional status and 

changes therein, but we did not have the necessary data. Death and institutionalization at 

120 days are imperfect proxies for functional decline and are likely to be less closely 

related than functional status to the surgical procedure and the rehabilitation process. In 

19
addition, our outcome measures do not capture other dimensions of quality of life. The 

evidence from our unadjusted functional measures suggests that patients going to IRFs

and SNFs experience a short-term increase in functional status, with IRF patients 

beginning their stays with a lower level of functioning and achieving a higher level of 

functioning than SNF patients over a similar period of time. 

Finally, we underscore that our results do not apply to all patients who use IRFs 

or SNFs. Rather, our IV models show the effects of IRF and SNF use for marginal

patients. In this context, marginal patients are those whose decision to use IRF or SNF is 

swayed by the proximity and availability of these PAC sites. Thus our results apply to 

patients for whom, in a sense, the clinical decision is gray. They do not apply to patients 

who are ideal candidates for an IRF or who clearly require SNF care. Rather than being a 

limitation of our analysis, our focus on the marginal patient is an asset from a policy 

decision-making perspective since it is precisely these patients who will likely be affected 

by the reduced accessibility of IRF care as the 75 percent rule is enforced. 

Our analyses of costs have limitations as well. We have not captured the costs of 

physician, outpatient and hospice care. If patients not using institutional PAC rely more 

heavily on those types of care, then our findings overstate the degree to which IRF and 

SNF episodes of care are more expensive. If patients in IRFs and SNFs are using these 

services after their stay, our findings could understate costs for these patients. However, 

we do include costs of home health care, which is used at comparable rates by patients 

regardless of discharge destination. It seems reasonable to believe that use of outpatient 

and hospice care is likewise comparable across all categories of patients (i.e., those use 

institutional PAC and those who do not). 

What does this say about the wisdom of the 75 percent case-mix rule for IRFs? 

If, as CMS argued during its rulemaking process, the effect of the revised regulation will 

be to shift LEJR patients from IRFs to SNFs then Medicare payments will likely be 

reduced by the enforcement of the 75 percent rule. However, our findings indicate while 

expenditures would be reduced, the outcome measure used here indicates that there is a 

higher risk of institutionalization if patients are switched from IRFs to SNFs. 

However, in order to fully assess the impact of the 75 percent rule, we would need 

three additional types of information. First, we would ideally measure real resource use 

across sites of care rather than measuring only Medicare payments. Second, we would 

need a method for evaluating the trade-off between better outcomes and higher costs. 

Finally, we would need better measures of outcomes, including a measure of functional 

status that was captured consistently across all discharge settings. 

 

20
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25
Table 1: Patient Characteristics by PAC Site

Lower Extremity Joint Replacement Patients

January 2002 to June 2003

First Site of Post-Acute Care No IRF or SNF IRF SNF

Standard Standard Standard

Mean Deviation Mean Deviation Mean Deviation

Number of Observations 148,558 148,874 127,719 

Percent to Post-Acute Setting 34.94% 35.02% 30.04%

Demographics

Female 0.543 0.498 0.702 0.457 0.722 ** 0.448

White 0.942 0.234 0.899 0.302 0.933 ** 0.249

Black 0.033 0.178 0.068 ** 0.251 0.041 0.198

Hispanic 0.007 0.080 0.012 ** 0.110 0.008 0.090

Age 72.740 5.394 74.976 6.012 76.344 ** 6.353

Beneficiary is covered by Medicaid 0.052 0.223 0.092 0.288 0.101 ** 0.301

Lives in an MSA 0.651 0.477 0.777 ** 0.416 0.670 0.470

Lives adjacent to an MSA 0.182 0.386 0.126 0.332 0.181 ** 0.385

Complications

Post-operative pulmonary compromise 0.003 0.056 0.005 0.074 0.008 ** 0.087

Post-operative GI hemorrhage or ulceration 0.002 0.043 0.002 0.046 0.003 ** 0.057

Cellulitis or decubitus ulcer 0.003 0.057 0.005 0.067 0.008 ** 0.091

Septicemia 0.000 0.016 0.000 0.018 0.001 ** 0.027

Mechanical complications due to device or implant 0.009 0.095 0.012 0.107 0.017 ** 0.128

Miscellaneous complications 0.013 0.112 0.011 0.103 0.016 ** 0.124

Shock or cardiorespiratory arrest 0.001 0.027 0.001 0.032 0.002 ** 0.041

Post-op heart attack (AMI) 0.003 0.051 0.004 0.065 0.006 ** 0.076

Post-op cardiac abnormalities other than AMI 0.001 0.023 0.001 0.023 0.001 0.027

Procedure-related laceration or perforation 0.001 0.033 0.001 0.033 0.001 0.034

Venous thrombosis or pulmonary embolism 0.005 0.070 0.007 ** 0.085 0.006 0.077

Iatrogenic complications 0.034 0.182 0.040 0.196 0.047 ** 0.212

Sentinel Events 0.001 0.030 0.001 0.031 0.001 * 0.035

Comorbidities

Acute renal failure 0.003 0.057 0.007 0.082 0.008 ** 0.091

Delirium 0.007 0.086 0.014 0.119 0.020 ** 0.139

Cancer with a Poor Prognosis 0.003 0.053 0.003 0.056 0.003 0.059

Metastatic Cancer 0.001 0.026 0.001 0.028 0.001 * 0.034

Chronic Pulmonary Disease 0.091 0.288 0.112 0.315 0.118 ** 0.323

Coronary Artery Disease 0.155 0.362 0.178 * 0.382 0.173 0.378

Congestive Heart Failure 0.034 0.181 0.058 0.234 0.071 ** 0.257

Peripheral Vascular Disease 0.016 0.125 0.021 0.142 0.022 * 0.147

Severe Chronic Liver Disease 0.001 0.035 0.002 0.040 0.002 0.042

Diabetes with End Organ Damage 0.006 0.077 0.010 0.101 0.011 0.103

Chronic Renal Failure 0.001 0.035 0.002 0.040 0.002 ** 0.049

Nutritional Deficiencies 0.001 0.031 0.002 0.046 0.004 ** 0.062

Dementia 0.005 0.072 0.009 0.097 0.023 ** 0.151

Functional Impairment 0.005 0.068 0.011 0.103 0.010 0.102

Diabetes without End Organ Damage 0.122 0.328 0.152 0.359 0.151 0.358

Pneumonia 0.006 0.074 0.008 0.087 0.012 ** 0.110

Stroke 0.000 0.022 0.002 0.044 0.002 0.047

Notes: Patients who were in a custodial nursing home before their acute stay, in a custodial nursing home after

their acute stay, who used acute rehab (DRG 462), used long term care hospitals, or died in the first 30 days

after their acute discharge are excluded from this analysis. This excludes less than 3% of our sample.

A double asterisk (**) indicates a significant t-test for difference between IRF and SNF values at the 0.0001 level.

A single asterisk (*) indicates a significant difference at the 0.05 level. Asterisk is placed next to the higher of the two means.
Table 1: Patient Characteristics by PAC Site (continued)

Lower Extremity Joint Replacement Patients

January 2002 to June 2003

First Site of Post-Acute Care No IRF or SNF IRF SNF

Standard Standard Standard

Mean Deviation Mean Deviation Mean Deviation

Type of Replacement

Hip Replacement 0.312 0.463 0.361 0.480 0.400 ** 0.490

Total Hip Replacement 0.258 0.438 0.301 0.459 0.310 ** 0.463

Partial Hip Replacement 0.006 0.078 0.013 0.113 0.027 ** 0.163

Hip Revision 0.048 0.214 0.048 0.214 0.063 ** 0.243

Knee Replacement 0.685 0.465 0.639 ** 0.480 0.600 0.490

Total Knee Replacement 0.625 0.484 0.600 ** 0.490 0.558 0.497

Knee Revision 0.061 0.239 0.040 0.196 0.043 * 0.202

Bilateral Procedure 0.018 0.134 0.062 ** 0.241 0.040 0.195

Discharging Hospital Characteristics

Non-Profit Hospital 0.779 0.415 0.756 0.429 0.793 ** 0.405

Government Hospital 0.100 0.300 0.086 0.281 0.097 ** 0.296

Average Daily Census of Hospital 203.626 171.514 234.717 ** 181.666 190.566 177.802

Resident to ADC ratio of Hospital 0.118 0.220 0.144 ** 0.246 0.110 0.214

Percentage of Low Income Patients 0.123 0.080 0.125 ** 0.090 0.121 0.077

% Medicare days 0.472 0.121 0.471 0.118 0.485 ** 0.119

Case Mix Index of Hospital 1.532 0.240 1.548 ** 0.235 1.469 0.245

HMO Penetration Rate 8.609 12.278 10.090 12.399 10.307 * 12.915

IRFs within travel radius 10.573 12.264 12.769 ** 13.240 11.331 13.310

SNFs within travel radius 38.848 42.869 43.383 45.097 46.156 ** 48.029

No IRFs within travel radius 0.032 0.176 0.013 0.115 0.031 * 0.172

No SNFs within travel radius 0.001 0.036 0.001 ** 0.033 0.001 0.027

Distance to nearest SNF (miles) 2.586 5.421 1.909 4.467 2.033 ** 4.590

Distance to nearest IRF (miles) 17.535 22.714 10.842 23.800 17.831 ** 21.554

Distance to nearest SNF squared (miles) 36.076 262.525 23.601 214.603 25.198 219.340

Distance to nearest IRF squared (miles) 823.391 5,579.52 684.006 12,790.92 782.509 ** 4,389.06 

Notes: Patients who were in a custodial nursing home before their acute stay, in a custodial nursing home after

their acute stay, who used acute rehab (DRG 462), used long term care hospitals, or died in the first 30 days

after their acute discharge are excluded from this analysis. This excludes less than 3% of our sample.

A double asterisk (**) indicates a significant t-test for difference between IRF and SNF values at the 0.0001 level.

A single asterisk (*) indicates a significant difference at the 0.05 level. Asterisk is placed next to the higher of the two means.
Table 2: Outcomes by PAC Site

Lower Extremity Joint Replacement Patients

January 2002 to June 2003

First Site of Post-Acute Care No IRF or SNF IRF SNF

Standard Standard Standard

Mean Deviation Mean Deviation Mean Deviation

Functional Status

Admission/5-Day Barthel Index (0-90) -- -- 45.771 12.660 54.837 ** 16.012

Discharge/14-Day Barthel Index (0-90)1 -- -- 69.496 ** 57.686 13.741 18.887 

Admission Barthel Index for Those With 14+ Day Stay1 -- -- 34.562 11.257 47.493 ** 15.750

Discharge Barthel Index for Those With 14+ Day Stay1 -- -- 65.165 ** 57.686 16.173 18.887 

Observations with 14+ Day Stay -- -- 20,157 13.54% 39,304 30.77%

Walking Score at Admission (0-1)2 -- -- 0.101 0.302 0.204 ** 0.403

Walking Score at Discharge/14 Days (0-1)2 -- -- 0.850 ** 0.311 0.357 0.463 

Walking Score at Admission for Those With 14+ Day Stay1,2 -- -- 0.014 0.117 0.091 ** 0.287

Walking Score at Discharge/14 Days for Those With 14+ Day Stay(0-1)1,2 -- -- 0.760 ** 0.311 0.427 0.463 

Transfer Score at Admission (0-1)2 -- -- 0.107 0.310 0.157 ** 0.363

Transfer Score at Discharge/14 Days (0-1)2 -- -- 0.847 ** 0.301 0.360 0.458 

Transfer Score at Admission for Those With 14+ Day Stay1,2 -- -- 0.017 0.128 0.075 ** 0.264

Transfer Score at Discharge/14 Days for Those With 14+ Day Stay(0-1)1,2 -- -- 0.792 ** 0.301 0.406 0.458 

Health Outcomes

Rehospitalization Within 60 Days 0.070 0.255 0.103 ** 0.075 0.304 0.263 

Rehospitalization Within 120 Days 0.116 0.320 0.155 ** 0.135 0.362 0.342 

Custodial Nursing Home At 60 Days 0.000 0.015 0.001 0.039 0.010 ** 0.101

Custodial Nursing Home At 120 Days 0.000 0.019 0.003 0.056 0.018 ** 0.134

Mortality 30 to 60 Days 0.001 0.029 0.002 0.044 0.004 ** 0.066

Mortality Within 120 Days 0.002 0.048 0.005 0.073 0.011 ** 0.105

Dead or Custodial Nursing Home at 60 Days 0.001 0.032 0.003 0.059 0.015 ** 0.121

Dead or Custodial Nursing Home at 120 Days 0.003 0.051 0.008 0.092 0.029 ** 0.169

Independent in Community at 60 Days3 0.954 0.210 0.861 ** 0.808 0.346 0.394 

Independent in Community at 120 Days3 0.980 0.139 0.948 ** 0.922 0.222 0.268 

Independent in Community at 180 Days3 0.983 0.128 0.961 ** 0.942 0.194 0.234 

Length of Stay--60 Day Episodes

Initial Acute Length of Stay 4.242 2.045 4.067 2.176 4.660 ** 2.774

IRF Days 0.019 0.492 9.265 ** 0.145 4.680 1.512 

SNF Days 0.064 1.221 1.117 5.721 14.937 ** 12.537

HHC Days 15.764 16.193 14.857 16.742 15.393 ** 15.593

LTCH Days 0.006 0.385 0.049 ** 0.032 1.137 0.926 

Acute Readmission Days 0.440 2.212 0.825 3.227 0.982 ** 3.553

Total Post-Acute Days 16.294 16.522 26.113 18.888 31.489 ** 18.528

Total Days in Care 20.536 16.939 30.180 19.350 36.149 ** 19.265

Length of Stay--120 Day Episodes

Initial Acute Length of Stay 4.242 2.045 4.067 2.176 4.660 ** 2.774

IRF Days 0.048 0.858 9.467 ** 0.200 5.104 1.862 

SNF Days 0.154 2.377 1.662 8.717 16.333 ** 16.545

HHC Days 16.634 18.194 17.690 21.759 18.999 ** 20.845

LTCH Days 0.013 0.643 0.086 ** 0.064 1.795 1.568 

Acute Readmission Days 0.714 3.056 1.270 4.479 1.527 * 4.953

Total Post-Acute Days 17.563 19.262 30.175 26.598 37.123 ** 28.085

Total Days in Care 21.805 19.713 34.242 27.089 41.783 ** 28.895

Payments--60 Day Episodes

Acute Payments 9,508.18 1,940.18 9,753.34 ** 9,595.99 2,690.39 2,772.33 

IRF Payments-Simulated 100% PPS 20.21 553.15 8,878.63 ** 130.75 5,840.11 1,680.36 

SNF Payments 19.71 369.76 326.06 1,677.76 4,805.02 ** 3,757.91

HHC Payments 1,659.04 1,635.76 1,546.62 1,749.24 1,591.42 ** 1,663.22

LTCH Payments 5.01 340.90 32.18 * 22.63 861.70 701.94 

Acute Readmission Payments 594.28 3,293.39 916.46 3,998.27 1,054.85 ** 4,239.72

Total Post-Acute Payments 2,298.24 3,903.85 11,699.95 ** 7,604.66 8,178.34 6,339.15 

Total Episode Payments 11,806.42 4,460.53 21,453.29 ** 17,200.64 8,838.08 7,229.13 

Payments--120 Day Episodes

Acute Payments 9,508.18 1,940.18 9,753.34 ** 9,595.99 2,690.39 2,772.33 

IRF Payments-Simulated 100% PPS 51.46 1,288.96 9,078.37 ** 181.16 6,229.22 2,061.07 

SNF Payments 44.66 666.87 460.50 2,396.60 5,097.26 ** 4,516.75

HHC Payments 1,717.32 1,726.80 1,748.20 1,978.20 1,859.30 ** 1,900.89

LTCH Payments 9.94 576.28 53.01 * 39.93 1,222.12 1,083.21 

Acute Readmission Payments 984.32 4,401.34 1,426.31 5,428.50 1,658.11 ** 5,795.85

Total Post-Acute Payments 2,807.70 5,476.10 12,766.38 ** 8,835.75 10,294.68 8,870.10 

Total Episode Payments 12,315.88 5,924.22 22,519.73 ** 18,431.74 10,871.66 9,670.16 

Notes: Patients who were in a custodial nursing home before their acute stay, in a custodial nursing home after their acute stay, 

who used acute rehab (DRG 462), used long term care hospitals, or died in the first 30 days after their acute discharge are excluded

from this analysis. This excludes less than 3% of our sample. If payments were 0, we correspondingly set days of care to 0.

A double asterisk (**) indicates a significant t-test for difference between IRF and SNF values at the 0.0001 level.

A single asterisk (*) indicates a significant difference at the 0.05 level. Asterisk is placed next to the higher of the two means. 1 SNF patients only have a follow-up assessment if they have a 14-Day stay or more. 2 This dichotomous variable indicates whether the person can walk or transfer on their own (with or without supervision) or not. 3 Defined as not receiving any acute, PAC, or custodial nursing home care.
Table 3: Regression Output

Lower Extremity Joint Replacement Patients

January 2002 to June 2003

Unadjusted Characteristics Naïve/exogenous Probit Joint Mu

Probit (for outcom

Outcome

Marginal Effect Marginal Effect Std. Error P-value Marginal Effect 

Dead or institutionalized at post-discharge day 120

IRF vs. no Medicare-paid institutional care 0.0058 0.0043 0.0004 0.00 ** 0.0018 

SNF vs. no Medicare-paid institutional care 0.0267 0.0120 0.0005 0.00 ** 0.0046 

Dead at post-discharge day 120

IRF vs. no Medicare-paid institutional care 0.0030 0.0020 0.0003 0.00 ** 0.0016 

SNF vs. no Medicare-paid institutional care 0.0089 0.0038 0.0003 0.00 ** 0.0023 

Total PAC payments to post-discharge day 120

IRF vs. no Medicare-paid institutional care 9,958.68 9,050.13 31.3061 0.00 ** 8,297.52 

SNF vs. no Medicare-paid institutional care 6,028.05 4,684.61 33.0433 0.00 ** 3,704.12 

Total Payments (PAC payments + Acute Stay) to post-discharge day 120

IRF vs. no Medicare-paid institutional care 10,203.85 8,871.21 32.7081 0.00 ** 8,023.00 

SNF vs. no Medicare-paid institutional care 6,115.86 4,590.17 34.5231 0.00 ** 3,577.86 

Notes: A double asterisk (**) indicates significance at the 0.001 level.

A single asterisk (*) indicates significance at the 0.05 level.
Appendix I

1. Formulation and Estimation of the Joint Model of Site of Care and

Outcomes

We begin by presenting a general representation of our model which has two modules, a

choice of site of care (“No IRF or SNF”, IRF, and SNF) module and a outcome module.

The formulation, estimation methods and exposition borrows heavily from Deb and

Trivedi (2004). In this model, the choice of site of care and outcome modules are linked

because site of care choices are regressors in the outcome module and because there are

common unobservable (latent) factors.

Let y

∗

i

denote the propensity underlying the observed values of outcome, yi (in the

case of payments, y

∗

i = yi). Let dj be a binary variables representing receipt of the

j

th site of care, with j = 0, 1, 2 (corresponding to “No IRF or SNF”, IRF, and SNF

respectively) and with “No IRF or SNF” as the baseline choice.

The outcome equation for individual i, i = 1, ..., N, is formulated as

y

∗

i = x

′

iβ + γ1d1i + γ2d2i +

X

j

λj lji + εi (1)

where xiis a set of exogenous covariates and β, γ1, and γ2 are parameters associated

with the exogenous covariates and site of care variables. The error term is partitioned

into εi, an independently distributed random error, and latent factors lji which denote

unobserved characteristics common to individual i’s choice of site of care j and outcome

of that individual. The λj , factor loadings, are parameters associated with the latent

factors.

The transformation from y

∗

i

given in (1) to the observed random variable yiis

through an appropriate distribution function f such that

Pr(Yi = yi|xi, d1i,d2i, lji) = f(x

′

iβ + γ1d1i + γ2d2i +

X

j

λj lji). (2)

1
In the case of the binary outcome, f is assumed to be the normal distribution function,

i.e, the outcome equation is a probit model. In the linear case f is the identity link.

Following the random utility framework (McFadden, 1980, p. S15), the propensity

to select site of care j, j = 0, 1, 2, is formulated as

U

∗

ji = z

′

iαj + δj lji + ηji. (3)

where zi denotes exogenous covariates, αj the associated parameters and ηji are random

error terms assumed to be independent of εi. Once again, lji are latent factors and δj

are associated factor loadings. The transformation from the latent variable formulation

to the observed multinomial choices is via a distribution function g such that

Pr(dji = 1|zi, lji) = g(z

′

iαj + δj lji), j = 0, 1, 2. (4)

We denote covariates in this site-choice module by z and covariates in the outcome

module by x to highlight the fact that they contain different variables in the empirical

analysis. In this study, we use the extreme value distribution for g so that the model

for site of care is a multinomial logit.

Because the latent factors lji enter both choice of site of care (4) and outcome (2)

equations, they capture the individual-specific factors that induce self-selection into site

of care through unobservables on outcomes.

Under these assumptions, the joint distribution of selection and outcome variables,

conditional on the common latent factors, can be written as

Pr(Yi = yi, dji = 1|xi, zi, lji) = f(x

′

iβ + γ1d1i + γ2d2i +

P

j

λj lji)

×g(z

′

iαj + δj lji)

. (5)

The problem in estimation arises because the lji are unknown. We assume that the

distribution of lji, hj , is known (normally distributed) and can therefore be integrated

out of the joint density, i.e.,

Pr(Yi = yi, dji = 1|xi, zi) = R

h

f(x

′

iβ + γ1d1i + γ2d2i +

P

j

λj lji)

×g(z

′

iαj + δj lji)] hj (lji)dlji

. (6)

2
Cast in this form, the unknown parameters of the model may be estimated by maximum

likelihood.

The main computational problem, given suitable specifications for f, g and hj , is

that the integral (6)does not have, in general, a closed form solution. But this difficulty

can be addressed using simulation-based estimation (Gourieroux and Monfort, 1996) by

noting that

Pr(Yi = yi, dji = 1|xi, zi) = Ehf(x

′

iβ + γ1d1i + γ2d2i +

P

j

λj lji)

×g(z

′

iαj + δj lji)]

≈

1

S

P

S

s=1

h

f(x

′

iβ + γ1d1i + γ2d2i +

P

j

λj

eljis)

×g(z

′

iαj + δj

eljis)

i

, (7)

where eljis is the s

th draw (from a total of S draws) of a pseudo-random number from the

density hj and Pr denotes the simulated probability. A simulated likeliho f od function

for the data can then be defined. The MSL estimator maximizes the average simulated

log likelihood. Because of the complexity of our model, standard simulation methods

are quite slow. Therefore, we adapt an acceleration technique that uses quasi-random

draws based on Halton sequences (Bhat, 2001; Train, 2002).We maximize the simulated

likelihood using a quasi-Newton algorithm.

3
References

Bhat, C.R. (2001) “Quasi-random Maximum Simulated Likelihood Estimation of the

Mixed Multinomial Logit Model”, Transportation Research: Part B, 35, 677-693.

Deb, P., and P.K. Trivedi (1997), “Demand for Medical Care by the Elderly in the

United States: A Finite Mixture Approach”, Journal of Applied Econometrics,

12, 313-336.

Gouri ́eroux, C. and A. Monfort (1996), Simulation Based Econometrics Methods, New

York: Oxford University Press.

McFadden, D. (1980) “Econometric Models for Probabilistic Choice among Products”,

Journal of Business, 53, S13-S29.

McFadden, D. and K. Train (2000), “Mixed MNL Models for Discrete Response”,

Journal of Applied Econometrics, 15, 447-470.

Train, K. (2002). Discrete Choice Methods with Simulation, New York: Cambridge

University Press.

White, H. (1982), “Maximum Likelihood Estimation of Misspecified Models”, Econometrica, 50, 1-25.

4
Appendix II: Regression Results for Outcomes and Payments (Probit Models)

Lower Extremity Joint Replacement Patients

January 2002 to June 2003

Outcomes Measured at 120 Days

Dependent Variable Dead or Institutionalized Dead Post-Acute Payments 

Marginal Standard Marginal Standard Marginal Standard 

Effect Error T-Statistic Effect Error T-Statistic Effect Error T-Statistic 

Independent Variable ($thousands) IRF Effect 0.002 0.001 2.01 0.002 0.001 1.36 8.298 0.068 121.90 SNF Effect 0.005 0.001 6.11 0.002 0.001 1.88 3.704 0.061 61.10 Age -0.023 0.042 -0.55 -0.011 0.038 -0.29 -97.437 6.062 -16.07 Age Squared 0.050 0.027 1.84 0.029 0.025 1.17 74.140 3.952 18.76 Female 0.003 0.063 0.05 0.001 0.095 0.01 -8.323 2.790 -2.98 Female*Age -0.011 0.050 -0.21 0.000 0.047 -0.01 22.699 7.295 3.11 Female*Age Squared 0.007 0.031 0.22 -0.003 0.029 -0.12 -14.414 4.747 -3.04 Black -0.001 0.000 -2.13 0.001 0.000 1.52 1.045 0.046 22.49 Hispanic -0.003 0.000 -7.79 -0.001 0.001 -1.20 0.174 0.106 1.64 Other Race -0.002 0.000 -6.53 -0.001 0.000 -2.81 -0.323 0.081 -3.99 Beneficiary is covered by Medicaid 0.014 0.001 17.96 0.001 0.000 3.19 2.202 0.035 62.96 Lives in an MSA 0.000 0.000 0.35 0.000 0.000 1.34 0.081 0.036 2.26 Lives adjacent to an MSA 0.000 0.000 -0.52 0.000 0.000 0.31 0.167 0.040 4.17 Post-operative pulmonary compromise 0.006 0.001 3.88 0.003 0.001 2.34 2.139 0.095 22.54 Post-operative GI hemorrhage or ulceration 0.003 0.002 1.76 0.001 0.001 0.80 2.283 0.154 14.78 Cellulitis or decubitus ulcer 0.018 0.002 7.75 0.009 0.002 4.84 4.168 0.096 43.21 Septicemia 0.003 0.005 0.69 -0.001 0.004 -0.16 4.588 0.271 16.93 Mechanical complications due to device or implant 0.005 0.001 5.73 0.002 0.001 3.13 2.537 0.068 37.35 Miscellaneous complications 0.000 0.001 0.16 -0.001 0.000 -1.27 -0.120 0.083 -1.44 Shock or cardiorespiratory arrest 0.005 0.002 1.90 0.001 0.002 0.45 3.649 0.174 20.98 Post-op heart attack (AMI) 0.005 0.001 3.50 0.004 0.001 3.04 5.962 0.085 69.83 Post-op cardiac abnormalities other than AMI -0.002 0.002 -1.34 0.000 0.003 0.07 0.892 0.290 3.08 Procedure-related laceration or perforation 0.001 0.002 0.45 0.002 0.003 0.89 0.705 0.266 2.65 Venous thrombosis or pulmonary embolism 0.002 0.001 1.94 0.002 0.001 1.41 1.155 0.114 10.14 Iatrogenic complications 0.001 0.000 2.05 0.001 0.000 1.43 0.475 0.048 9.89 Sentinel Events 0.006 0.004 1.70 0.005 0.004 1.31 2.528 0.210 12.04 Acute renal failure 0.005 0.001 3.83 0.004 0.001 3.27 3.373 0.086 39.23 Delirium 0.004 0.001 4.29 0.002 0.001 2.35 1.507 0.072 20.81 Cancer with a Poor Prognosis 0.011 0.003 4.46 0.012 0.003 4.29 1.149 0.149 7.73 Metastatic Cancer 0.065 0.011 5.74 0.074 0.013 5.77 1.632 0.255 6.40 Chronic Pulmonary Disease 0.002 0.000 7.49 0.002 0.000 6.51 0.710 0.032 22.52 Coronary Artery Disease 0.000 0.000 2.07 0.000 0.000 2.02 0.562 0.027 20.89 Congestive Heart Failure 0.005 0.000 11.47 0.004 0.001 8.16 1.853 0.036 51.32 Peripheral Vascular Disease 0.002 0.001 2.53 0.001 0.001 1.84 0.831 0.064 12.98 Severe Chronic Liver Disease 0.016 0.004 4.01 0.020 0.005 3.98 3.040 0.196 15.55 Diabetes with End Organ Damage 0.007 0.001 4.93 0.004 0.001 3.38 2.651 0.083 31.95 Chronic Renal Failure 0.022 0.004 5.00 0.024 0.005 4.83 3.925 0.151 25.93 Nutritional Deficiencies 0.012 0.003 4.71 0.007 0.002 3.10 2.733 0.144 18.92 Dementia 0.037 0.002 15.67 0.007 0.001 6.26 2.862 0.075 38.01 Functional Impairment 0.010 0.001 6.75 0.003 0.001 2.96 3.000 0.081 36.90 Diabetes without End Organ Damage 0.002 0.000 6.97 0.001 0.000 4.09 0.899 0.029 31.18 Pneumonia 0.007 0.001 5.85 0.004 0.001 3.86 2.169 0.080 27.20 Stroke 0.030 0.006 4.95 0.009 0.004 2.42 9.458 0.138 68.55 
Appendix II: Regression Results for Outcomes and Payments (Probit Models)

Lower Extremity Joint Replacement Patients

January 2002 to June 2003

Outcomes Measured at 120 Days

Dependent Variable Dead or Institutionalized Dead Post-Acute Payments 

Marginal Standard Marginal Standard Marginal Standard 

Effect Error T-Statistic Effect Error T-Statistic Effect Error T-Statistic 

Independent Variable ($thousands) 

Hip Replacement 0.008 0.005 1.61 0.003 0.004 0.61 2.686 0.370 7.25 Total Hip Replacement -0.003 0.002 -1.85 -0.002 0.002 -0.98 -1.520 0.297 -5.12 Partial Hip Replacement 0.012 0.007 1.75 0.007 0.007 0.90 1.943 0.303 6.41 Hip Revision 0.003 0.003 0.97 0.001 0.003 0.22 0.714 0.296 2.41 Knee Replacement 0.004 0.003 1.35 0.000 0.006 0.08 2.369 0.389 6.09 Total Knee Replacement -0.003 0.004 -0.92 -0.002 0.006 -0.27 -1.983 0.322 -6.15 Knee Revision 0.000 0.004 0.13 0.001 0.008 0.07 -0.682 0.320 -2.13 Bilateral Procedure 0.000 0.001 0.61 0.000 0.000 -0.96 0.841 0.058 14.50 Non-Profit Hospital 0.000 0.000 0.26 0.000 0.000 -1.71 -0.948 0.032 -29.38 Government Hospital 0.000 0.000 0.01 0.000 0.000 -0.80 -0.727 0.045 -16.00 Average Daily Census of Hospital 0.000 0.000 -0.66 0.000 0.000 -0.30 0.186 0.008 24.64 Resident to ADC ratio of Hospital 0.001 0.000 2.05 0.000 0.000 -0.08 0.925 0.052 17.68 Percentage of Low Income Patients 0.002 0.001 1.68 0.003 0.001 2.54 1.522 0.137 11.13 % Medicare days 0.001 0.001 1.57 0.000 0.001 -0.02 2.252 0.116 19.48 Case Mix Index of Hospital -0.002 0.000 -4.72 -0.001 0.000 -1.91 -1.042 0.057 -18.18 HMO Penetration Rate 0.000 0.000 -1.87 0.000 0.000 -0.53 0.011 0.001 10.63 
Appendix II: Regression Results for Choice of PAC Site (Multinomial Logit)

Lower Extremity Joint Replacement Patients

January 2002 to June 2003

Total Payments -- 120 Day Episodes

Dependent Variable No IRF or SNF IRF Care 

Marginal Standard Marginal Standard Margin

Effect Error T-Statistic Effect Error T-Statistic Effec

Independent VariableAge 0.067 0.501 0.134 3.094 0.508 6.091 -Age Squared -1.339 0.340 -3.935 -1.635 0.318 -5.141 Female 0.523 0.119 4.402 0.131 0.171 0.770 -Female*Age -2.359 0.644 -3.663 0.178 0.609 0.293 Female*Age Squared 1.626 0.418 3.893 -0.174 0.404 -0.432 -Black -0.078 0.003 -22.538 0.104 0.004 27.208 -Hispanic -0.019 0.009 -2.181 0.078 0.009 8.733 -Other Race -0.009 0.006 -1.638 0.034 0.006 5.934 -Beneficiary is covered by Medicaid -0.100 0.003 -35.224 0.027 0.003 8.439 Lives in an MSA -0.157 0.004 -39.413 0.079 0.004 21.435 Lives adjacent to an MSA -0.088 0.003 -29.760 0.032 0.004 9.011 Post-operative pulmonary compromise -0.074 0.011 -6.734 0.000 0.011 0.019 Post-operative GI hemorrhage or ulceration -0.031 0.017 -1.789 -0.032 0.016 -1.961 Cellulitis or decubitus ulcer -0.072 0.011 -6.708 -0.046 0.010 -4.425 Septicemia -0.159 0.031 -5.124 -0.073 0.036 -2.036 Mechanical complications due to device or implant -0.061 0.007 -8.357 -0.006 0.007 -0.813 Miscellaneous complications -0.005 0.007 -0.777 -0.039 0.007 -5.502 Shock or cardiorespiratory arrest -0.066 0.024 -2.700 -0.018 0.023 -0.782 Post-op heart attack (AMI) -0.020 0.014 -1.487 -0.002 0.012 -0.170 Post-op cardiac abnormalities other than AMI 0.035 0.036 0.961 -0.032 0.032 -1.024 -Procedure-related laceration or perforation 0.033 0.025 1.315 -0.023 0.023 -1.003 -Venous thrombosis or pulmonary embolism -0.025 0.010 -2.483 0.031 0.010 3.148 -Iatrogenic complications -0.036 0.004 -9.148 0.007 0.004 1.710 Sentinel Events -0.025 0.023 -1.065 -0.014 0.024 -0.593 Acute renal failure -0.116 0.010 -11.946 0.039 0.010 3.843 Delirium -0.127 0.006 -21.125 0.028 0.007 4.073 Cancer with a Poor Prognosis -0.008 0.014 -0.608 0.007 0.013 0.550 Metastatic Cancer -0.023 0.026 -0.899 -0.026 0.025 -1.024 Chronic Pulmonary Disease -0.051 0.002 -20.698 0.020 0.003 7.786 Coronary Artery Disease -0.037 0.002 -18.196 0.030 0.002 14.155 Congestive Heart Failure -0.081 0.004 -22.902 0.024 0.004 6.469 Peripheral Vascular Disease -0.043 0.006 -7.663 0.018 0.006 3.040 Severe Chronic Liver Disease -0.084 0.018 -4.721 0.024 0.019 1.253 
Appendix II: Regression Results for Choice of PAC Site (Multinomial Logit)

Lower Extremity Joint Replacement Patients

January 2002 to June 2003

Total Payments -- 120 Day Episodes

Dependent Variable No IRF or SNF IRF Care 

Marginal Standard Marginal Standard Margin

Effect Error T-Statistic Effect Error T-Statistic Effec

Independent Variable

Diabetes with End Organ Damage -0.137 0.007 -20.513 0.053 0.008 6.280 Chronic Renal Failure -0.039 0.019 -2.032 -0.027 0.017 -1.519 Nutritional Deficiencies -0.130 0.015 -8.507 -0.008 0.016 -0.491 Dementia -0.125 0.007 -18.096 -0.071 0.007 -10.581 Functional Impairment -0.145 0.007 -21.069 0.091 0.008 10.713 Diabetes without End Organ Damage -0.077 0.002 -36.529 0.031 0.002 13.324 Pneumonia -0.058 0.009 -6.654 -0.021 0.009 -2.383 Stroke -0.197 0.017 -11.952 0.111 0.022 5.094 Hip Replacement -0.513 0.025 -20.923 0.388 0.038 10.302 Total Hip Replacement 0.278 0.037 7.475 -0.179 0.029 -6.073 -Partial Hip Replacement 0.198 0.038 5.163 -0.185 0.024 -7.819 -Hip Revision 0.331 0.036 9.100 -0.219 0.022 -9.922 -Knee Replacement -0.286 0.041 -6.920 0.194 0.033 5.819 Total Knee Replacement -0.017 0.035 -0.474 0.040 0.027 1.463 -Knee Revision 0.067 0.038 1.762 -0.027 0.028 -0.958 -Bilateral Procedure -0.248 0.002 -101.486 0.215 0.004 49.102 Non-Profit Hospital 0.055 0.002 24.913 -0.110 0.002 -45.035 Government Hospital 0.057 0.004 14.996 -0.089 0.003 -28.460 Average Daily Census of Hospital -0.014 0.001 -25.084 0.015 0.001 27.895 Resident to ADC ratio of Hospital -0.045 0.004 -10.472 -0.001 0.004 -0.248 Percentage of Low Income Patients -0.080 0.010 -7.645 0.159 0.010 16.253 -% Medicare days -0.263 0.008 -31.659 0.106 0.008 13.016 Case Mix Index of Hospital 0.136 0.004 31.996 0.109 0.004 26.213 -HMO Penetration Rate -0.001 0.000 -17.121 -0.002 0.000 -22.277 IRFs within travel radius (00) -0.214 0.012 -17.300 0.917 0.013 73.337 -SNFs within travel radius (00) -0.038 0.003 -11.214 -0.182 0.004 -51.303 Distance to nearest SNF (00 miles) 0.242 0.022 10.990 0.279 0.022 12.896 -Distance to nearest IRF (00 miles) 0.050 0.007 6.945 -0.619 0.007 -82.606 No IRFs within travel radius (00) 0.069 0.006 11.045 -0.026 0.006 -4.065 -No SNFs within travel radius (00) 0.010 0.026 0.404 0.048 0.027 1.795 -Distance to nearest SNF squared (00 miles) -0.766 0.039 -19.777 0.351 0.033 10.648 Distance to nearest IRF squared (00 miles) 0.034 0.002 19.521 0.147 0.001 99.889 -
Appendix II: Regression Results for Choice of PAC Site (Multinomial Logit)

Lower Extremity Joint Replacement Patients

January 2002 to June 2003

Total PAC Payments -- 120 Day Episodes

Dependent Variable No IRF or SNF IRF Care 

Marginal Standard Marginal Standard Margin

Effect Error T-Statistic Effect Error T-Statistic Effec

Independent VariableAge 0.068 0.501 0.135 3.094 0.508 6.092 -Age Squared -1.339 0.340 -3.937 -1.635 0.318 -5.143 Female 0.523 0.119 4.402 0.132 0.171 0.771 -Female*Age -2.359 0.644 -3.664 0.178 0.609 0.292 Female*Age Squared 1.626 0.418 3.893 -0.174 0.404 -0.431 -Black -0.078 0.003 -22.530 0.104 0.004 27.201 -Hispanic -0.019 0.009 -2.178 0.078 0.009 8.733 -Other Race -0.009 0.006 -1.637 0.034 0.006 5.933 -Beneficiary is covered by Medicaid -0.100 0.003 -35.232 0.027 0.003 8.426 Lives in an MSA -0.157 0.004 -39.410 0.079 0.004 21.433 Lives adjacent to an MSA -0.088 0.003 -29.765 0.032 0.004 9.001 Post-operative pulmonary compromise -0.074 0.011 -6.774 0.000 0.011 0.018 Post-operative GI hemorrhage or ulceration -0.031 0.017 -1.789 -0.032 0.016 -1.961 Cellulitis or decubitus ulcer -0.072 0.011 -6.707 -0.046 0.010 -4.433 Septicemia -0.159 0.031 -5.134 -0.073 0.036 -2.038 Mechanical complications due to device or implant -0.061 0.007 -8.367 -0.006 0.007 -0.815 Miscellaneous complications -0.005 0.007 -0.779 -0.039 0.007 -5.503 Shock or cardiorespiratory arrest -0.066 0.024 -2.723 -0.018 0.023 -0.786 Post-op heart attack (AMI) -0.020 0.014 -1.491 -0.002 0.012 -0.171 Post-op cardiac abnormalities other than AMI 0.035 0.036 0.964 -0.032 0.032 -1.017 -Procedure-related laceration or perforation 0.033 0.025 1.316 -0.023 0.023 -1.006 -Venous thrombosis or pulmonary embolism -0.025 0.010 -2.484 0.031 0.010 3.150 -Iatrogenic complications -0.036 0.004 -9.155 0.007 0.004 1.710 Sentinel Events -0.025 0.023 -1.067 -0.014 0.024 -0.593 Acute renal failure -0.116 0.010 -11.990 0.039 0.010 3.845 Delirium -0.127 0.006 -21.143 0.028 0.007 4.072 Cancer with a Poor Prognosis -0.008 0.014 -0.608 0.007 0.013 0.550 Metastatic Cancer -0.023 0.026 -0.898 -0.026 0.025 -1.024 Chronic Pulmonary Disease -0.051 0.002 -20.707 0.019 0.003 7.776 Coronary Artery Disease -0.037 0.002 -18.206 0.030 0.002 14.161 Congestive Heart Failure -0.081 0.004 -22.915 0.024 0.004 6.463 Peripheral Vascular Disease -0.043 0.006 -7.662 0.018 0.006 3.037 Severe Chronic Liver Disease -0.084 0.018 -4.719 0.024 0.019 1.250 
Appendix II: Regression Results for Choice of PAC Site (Multinomial Logit)

Lower Extremity Joint Replacement Patients

January 2002 to June 2003

Total PAC Payments -- 120 Day Episodes

Dependent Variable No IRF or SNF IRF Care 

Marginal Standard Marginal Standard Margin

Effect Error T-Statistic Effect Error T-Statistic Effec

Independent Variable

Diabetes with End Organ Damage -0.137 0.007 -20.525 0.053 0.008 6.277 Chronic Renal Failure -0.039 0.019 -2.044 -0.027 0.017 -1.524 Nutritional Deficiencies -0.130 0.015 -8.515 -0.008 0.016 -0.494 Dementia -0.125 0.007 -18.108 -0.071 0.007 -10.590 Functional Impairment -0.145 0.007 -21.072 0.091 0.008 10.711 Diabetes without End Organ Damage -0.077 0.002 -36.540 0.031 0.002 13.323 Pneumonia -0.058 0.009 -6.661 -0.021 0.009 -2.385 Stroke -0.197 0.016 -12.064 0.111 0.022 5.103 Hip Replacement -0.513 0.024 -20.948 0.388 0.038 10.293 Total Hip Replacement 0.278 0.037 7.502 -0.179 0.029 -6.068 -Partial Hip Replacement 0.198 0.038 5.182 -0.185 0.024 -7.815 -Hip Revision 0.331 0.036 9.134 -0.219 0.022 -9.919 -Knee Replacement -0.286 0.041 -6.916 0.194 0.033 5.819 Total Knee Replacement -0.017 0.035 -0.473 0.040 0.027 1.462 -Knee Revision 0.067 0.038 1.762 -0.027 0.028 -0.958 -Bilateral Procedure -0.248 0.002 -101.494 0.214 0.004 49.075 Non-Profit Hospital 0.055 0.002 24.900 -0.110 0.002 -45.042 Government Hospital 0.057 0.004 14.993 -0.089 0.003 -28.463 Average Daily Census of Hospital -0.015 0.001 -25.139 0.015 0.001 27.908 Resident to ADC ratio of Hospital -0.045 0.004 -10.472 -0.001 0.004 -0.248 Percentage of Low Income Patients -0.080 0.010 -7.643 0.159 0.010 16.258 -% Medicare days -0.263 0.008 -31.663 0.106 0.008 13.011 Case Mix Index of Hospital 0.136 0.004 31.992 0.109 0.004 26.212 -HMO Penetration Rate -0.001 0.000 -16.931 -0.002 0.000 -22.139 IRFs within travel radius (00) -0.213 0.012 -17.288 0.917 0.013 73.333 -SNFs within travel radius (00) -0.038 0.003 -11.215 -0.182 0.004 -51.304 Distance to nearest SNF (00 miles) 0.243 0.022 10.993 0.279 0.022 12.900 -Distance to nearest IRF (00 miles) 0.050 0.007 6.923 -0.620 0.007 -82.617 No IRFs within travel radius (00) 0.069 0.006 11.049 -0.026 0.006 -4.064 -No SNFs within travel radius (00) 0.010 0.026 0.404 0.048 0.027 1.795 -Distance to nearest SNF squared (00 miles) -0.766 0.039 -19.763 0.351 0.033 10.640 Distance to nearest IRF squared (00 miles) 0.034 0.002 19.526 0.147 0.001 99.779 -
Appendix II: Regression Results for Choice of PAC Site (Multinomial Logit)

Lower Extremity Joint Replacement Patients

January 2002 to June 2003

Dead or Institutionalized at 120 Days

Dependent Variable No IRF or SNF IRF Care 

Marginal Standard Marginal Standard Margin

Effect Error T-Statistic Effect Error T-Statistic Effec

Independent VariableAge 0.065 0.517 0.126 3.093 0.498 6.217 -Age Squared -1.338 0.328 -4.080 -1.633 0.328 -4.971 Female 0.523 0.130 4.033 0.131 0.175 0.748 -Female*Age -2.360 0.617 -3.826 0.180 0.597 0.302 Female*Age Squared 1.626 0.414 3.927 -0.176 0.396 -0.443 -Black -0.078 0.003 -22.546 0.104 0.004 27.487 -Hispanic -0.019 0.009 -2.195 0.078 0.009 8.717 -Other Race -0.009 0.006 -1.698 0.034 0.006 6.037 -Beneficiary is covered by Medicaid -0.100 0.003 -36.185 0.027 0.003 8.701 Lives in an MSA -0.157 0.004 -40.283 0.079 0.004 20.586 Lives adjacent to an MSA -0.088 0.003 -29.586 0.032 0.004 8.783 Post-operative pulmonary compromise -0.074 0.011 -6.813 0.000 0.011 0.026 Post-operative GI hemorrhage or ulceration -0.031 0.017 -1.779 -0.032 0.016 -2.009 Cellulitis or decubitus ulcer -0.072 0.011 -6.745 -0.046 0.010 -4.352 Septicemia -0.159 0.030 -5.282 -0.073 0.035 -2.089 Mechanical complications due to device or implant -0.061 0.007 -8.447 -0.006 0.007 -0.815 Miscellaneous complications -0.005 0.007 -0.746 -0.039 0.007 -5.445 Shock or cardiorespiratory arrest -0.066 0.024 -2.774 -0.018 0.023 -0.805 Post-op heart attack (AMI) -0.020 0.013 -1.594 -0.002 0.012 -0.169 Post-op cardiac abnormalities other than AMI 0.035 0.035 1.004 -0.032 0.031 -1.053 -Procedure-related laceration or perforation 0.033 0.023 1.417 -0.023 0.022 -1.065 -Venous thrombosis or pulmonary embolism -0.025 0.010 -2.574 0.031 0.010 3.082 -Iatrogenic complications -0.036 0.004 -8.746 0.007 0.004 1.705 Sentinel Events -0.025 0.024 -1.034 -0.014 0.024 -0.579 Acute renal failure -0.116 0.009 -12.796 0.039 0.010 3.856 Delirium -0.128 0.006 -20.463 0.028 0.007 4.051 Cancer with a Poor Prognosis -0.008 0.014 -0.586 0.007 0.014 0.536 Metastatic Cancer -0.023 0.026 -0.917 -0.026 0.026 -1.003 Chronic Pulmonary Disease -0.051 0.002 -20.907 0.020 0.003 7.620 Coronary Artery Disease -0.037 0.002 -17.285 0.030 0.002 13.816 Congestive Heart Failure -0.081 0.003 -23.434 0.024 0.004 6.766 Peripheral Vascular Disease -0.043 0.006 -7.665 0.018 0.006 3.086 Severe Chronic Liver Disease -0.084 0.017 -4.993 0.024 0.018 1.308 
Appendix II: Regression Results for Choice of PAC Site (Multinomial Logit)

Lower Extremity Joint Replacement Patients

January 2002 to June 2003

Dead or Institutionalized at 120 Days

Dependent Variable No IRF or SNF IRF Care 

Marginal Standard Marginal Standard Margin

Effect Error T-Statistic Effect Error T-Statistic Effec

Independent Variable

Diabetes with End Organ Damage -0.138 0.007 -20.193 0.053 0.008 6.374 Chronic Renal Failure -0.039 0.019 -2.061 -0.027 0.018 -1.487 Nutritional Deficiencies -0.130 0.016 -8.277 -0.008 0.017 -0.457 Dementia -0.125 0.007 -17.339 -0.071 0.007 -10.804 Functional Impairment -0.145 0.007 -20.688 0.091 0.009 10.563 Diabetes without End Organ Damage -0.077 0.002 -37.972 0.031 0.002 13.605 Pneumonia -0.058 0.009 -6.396 -0.021 0.009 -2.350 Stroke -0.198 0.016 -12.188 0.111 0.021 5.332 Hip Replacement -0.513 0.025 -20.419 0.389 0.038 10.288 Total Hip Replacement 0.278 0.038 7.320 -0.179 0.030 -5.955 -Partial Hip Replacement 0.198 0.039 5.022 -0.185 0.024 -7.616 -Hip Revision 0.331 0.035 9.410 -0.219 0.023 -9.623 -Knee Replacement -0.286 0.040 -7.075 0.194 0.033 5.870 Total Knee Replacement -0.017 0.035 -0.482 0.040 0.028 1.412 -Knee Revision 0.067 0.038 1.776 -0.027 0.028 -0.954 -Bilateral Procedure -0.248 0.002 -105.010 0.215 0.004 51.344 Non-Profit Hospital 0.055 0.002 24.000 -0.110 0.003 -44.002 Government Hospital 0.057 0.004 15.536 -0.089 0.003 -27.517 Average Daily Census of Hospital -0.014 0.001 -24.505 0.015 0.001 27.807 Resident to ADC ratio of Hospital -0.045 0.004 -10.369 -0.001 0.004 -0.226 Percentage of Low Income Patients -0.080 0.011 -7.355 0.159 0.010 16.041 -% Medicare days -0.263 0.008 -31.443 0.106 0.008 12.831 Case Mix Index of Hospital 0.136 0.004 34.182 0.109 0.004 27.839 -HMO Penetration Rate -0.001 0.000 -17.030 -0.002 0.000 -21.465 IRFs within travel radius (00) -0.214 0.012 -17.390 0.917 0.012 74.064 -SNFs within travel radius (00) -0.038 0.004 -10.824 -0.182 0.004 -49.217 Distance to nearest SNF (00 miles) 0.242 0.023 10.766 0.279 0.022 12.529 -Distance to nearest IRF (00 miles) 0.050 0.007 7.048 -0.620 0.007 -86.989 No IRFs within travel radius (00) 0.069 0.006 11.862 -0.026 0.006 -4.136 -No SNFs within travel radius (00) 0.010 0.025 0.407 0.048 0.028 1.750 -Distance to nearest SNF squared (00 miles) -0.767 0.039 -19.582 0.352 0.032 10.863 Distance to nearest IRF squared (00 miles) 0.034 0.002 18.438 0.147 0.001 102.546 -
Appendix II: Regression Results for Choice of PAC Site (Multinomial Logit)

Lower Extremity Joint Replacement Patients

January 2002 to June 2003

Dead at 120 Days

Dependent Variable No IRF or SNF IRF Care 

Marginal Standard Marginal Standard Margin

Effect Error T-Statistic Effect Error T-Statistic Effec

Independent VariableAge 0.073 0.517 0.140 3.085 0.498 6.200 -Age Squared -1.338 0.328 -4.082 -1.629 0.329 -4.957 Female 0.525 0.129 4.058 0.132 0.175 0.755 -Female*Age -2.359 0.617 -3.825 0.175 0.597 0.293 Female*Age Squared 1.619 0.414 3.910 -0.169 0.396 -0.427 -Black -0.077 0.003 -22.431 0.103 0.004 27.352 -Hispanic -0.019 0.009 -2.247 0.077 0.009 8.617 -Other Race -0.010 0.006 -1.762 0.034 0.006 6.105 -Beneficiary is covered by Medicaid -0.100 0.003 -36.160 0.027 0.003 8.701 Lives in an MSA -0.157 0.004 -40.253 0.079 0.004 20.525 Lives adjacent to an MSA -0.088 0.003 -29.750 0.032 0.004 8.789 Post-operative pulmonary compromise -0.074 0.011 -6.855 0.001 0.011 0.069 Post-operative GI hemorrhage or ulceration -0.032 0.017 -1.860 -0.033 0.016 -2.106 Cellulitis or decubitus ulcer -0.072 0.011 -6.811 -0.046 0.010 -4.370 Septicemia -0.156 0.030 -5.130 -0.069 0.035 -1.953 Mechanical complications due to device or implant -0.061 0.007 -8.462 -0.006 0.007 -0.785 Miscellaneous complications -0.005 0.007 -0.628 -0.039 0.007 -5.500 Shock or cardiorespiratory arrest -0.065 0.024 -2.742 -0.017 0.023 -0.760 Post-op heart attack (AMI) -0.021 0.013 -1.631 -0.001 0.012 -0.106 Post-op cardiac abnormalities other than AMI 0.035 0.035 1.004 -0.032 0.031 -1.026 -Procedure-related laceration or perforation 0.032 0.023 1.388 -0.023 0.022 -1.040 -Venous thrombosis or pulmonary embolism -0.026 0.010 -2.590 0.032 0.010 3.174 -Iatrogenic complications -0.036 0.004 -8.675 0.007 0.004 1.640 Sentinel Events -0.025 0.024 -1.017 -0.013 0.024 -0.547 Acute renal failure -0.117 0.009 -12.863 0.039 0.010 3.863 Delirium -0.127 0.006 -20.246 0.028 0.007 4.023 Cancer with a Poor Prognosis -0.008 0.014 -0.556 0.007 0.014 0.511 Metastatic Cancer -0.023 0.026 -0.899 -0.025 0.026 -0.963 Chronic Pulmonary Disease -0.051 0.002 -20.949 0.020 0.003 7.618 Coronary Artery Disease -0.037 0.002 -17.305 0.030 0.002 13.793 Congestive Heart Failure -0.080 0.003 -23.325 0.024 0.004 6.703 Peripheral Vascular Disease -0.043 0.006 -7.695 0.018 0.006 3.071 Severe Chronic Liver Disease -0.083 0.017 -4.976 0.024 0.018 1.309 
Appendix II: Regression Results for Choice of PAC Site (Multinomial Logit)

Lower Extremity Joint Replacement Patients

January 2002 to June 2003

Dead at 120 Days

Dependent Variable No IRF or SNF IRF Care 

Marginal Standard Marginal Standard Margin

Effect Error T-Statistic Effect Error T-Statistic Effec

Independent Variable

Diabetes with End Organ Damage -0.138 0.007 -20.315 0.054 0.008 6.426 Chronic Renal Failure -0.039 0.019 -2.078 -0.027 0.018 -1.527 Nutritional Deficiencies -0.130 0.016 -8.247 -0.011 0.017 -0.632 Dementia -0.125 0.007 -17.335 -0.072 0.007 -11.013 Functional Impairment -0.146 0.007 -20.988 0.091 0.009 10.606 Diabetes without End Organ Damage -0.077 0.002 -38.022 0.031 0.002 13.620 Pneumonia -0.058 0.009 -6.470 -0.020 0.009 -2.271 Stroke -0.197 0.016 -12.078 0.111 0.021 5.326 Hip Replacement -0.514 0.025 -20.508 0.388 0.038 10.296 Total Hip Replacement 0.277 0.038 7.268 -0.181 0.030 -6.029 -Partial Hip Replacement 0.195 0.039 4.939 -0.186 0.024 -7.710 -Hip Revision 0.328 0.035 9.326 -0.220 0.023 -9.718 -Knee Replacement -0.288 0.040 -7.124 0.194 0.033 5.872 Total Knee Replacement -0.019 0.035 -0.537 0.038 0.028 1.352 -Knee Revision 0.065 0.038 1.730 -0.029 0.028 -1.012 -Bilateral Procedure -0.248 0.002 -104.935 0.214 0.004 51.256 Non-Profit Hospital 0.055 0.002 23.970 -0.111 0.003 -44.070 Government Hospital 0.057 0.004 15.426 -0.088 0.003 -27.476 Average Daily Census of Hospital -0.014 0.001 -24.606 0.015 0.001 27.886 Resident to ADC ratio of Hospital -0.044 0.004 -10.313 -0.001 0.004 -0.272 Percentage of Low Income Patients -0.080 0.011 -7.337 0.162 0.010 16.331 -% Medicare days -0.265 0.008 -31.734 0.109 0.008 13.159 Case Mix Index of Hospital 0.136 0.004 34.005 0.110 0.004 28.069 -HMO Penetration Rate -0.001 0.000 -16.835 -0.002 0.000 -21.390 IRFs within travel radius (00) -0.209 0.012 -17.005 0.909 0.012 73.429 -SNFs within travel radius (00) -0.039 0.004 -11.260 -0.180 0.004 -48.686 Distance to nearest SNF (00 miles) 0.237 0.023 10.514 0.289 0.022 12.987 -Distance to nearest IRF (00 miles) 0.057 0.007 7.955 -0.620 0.007 -87.042 No IRFs within travel radius (00) 0.069 0.006 11.835 -0.026 0.006 -4.095 -No SNFs within travel radius (00) 0.008 0.025 0.330 0.054 0.028 1.946 -Distance to nearest SNF squared (00 miles) -0.760 0.039 -19.437 0.356 0.032 11.064 Distance to nearest IRF squared (00 miles) 0.029 0.002 15.809 0.144 0.001 100.523 -