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Optimal Long-Term Care Nurse-Staffing Levels.

The purpose of this study was to investigate the effect of nursing inputs on the production of quality in nursing homes. By including the price (wages) of nurses, the "optimal" levels of staffing are considered. Staffing "intensity" and "mix" refer to the quantity of nurse hires and the ratio of hires for each nurse category. These include registered nurses (RNs), licensed practical nurses (LPNs), and nurses' aides (NAs). The prevalence of decubitus ulcers is chosen as a quality indicator because good estimates of treatment cost of decubitus exist in the literature.

The production of quality in nursing homes has been a topic of great interest in recent years. From a policy perspective, the goal is to produce the most appropriate level of quality. Optimal in this sense minimizes cost. A primary determinant of nursing home cost is nurse wages. Coupled with this is the fact that nurse staffing directly affects outcomes. Do nursing home owners minimize costs at the expense of quality because they do not bear responsibility for lower quality? If nursing home owners value cheaper inputs over quality outcomes, do they substitute for lower cost inputs in a way that is socially inefficient?

Subject to licensing constraints, nursing homes have the option to substitute NAs for LPNs and LPNs and/or NAs for RNs to reduce costs. RNs are able to perform all LPN and NA tasks and LPNs can accomplish those of NAs. The reverse is not true. If RNs provide better quality care than LPNs and LPNs perform better quality care than NAs, the substitution of inferior inputs can result in a lower-quality product at a reduced price. However, inferior inputs may not, in fact, cost less. Bad outcomes obviously increase cost to someone. Because outcomes come at a price, they are not simply quality indicators but, rather, quality at a price. For example, a patient suffering from an infection may be administered an expensive antibiotic and hospitalized, whereas a noninfected patient does not require this care. The added cost of caring for the infected person becomes an additional production cost. In cases like this, the substitution of inferior nursing inputs may lead to an overall increase in the total cost of care. This increase may be borne by the nursing home or it may be passed on to Medicare, Medicaid, the patient, or society at large. If the nursing home bears the cost of treatment for bad outcomes, it does not save money by substituting inferior nursing inputs at the front end of the process. On the other hand, if the nursing home does not bear the added cost it will have an incentive to overproduce bad outcomes. Viewed in this manner, nursing staff is not only an input but, inexorably, affects output. In production terms, it would be valuable to identify nurse-staffing inputs that provide the most "efficient" nursing home output bundle.

Background

Increased demand. America is aging and, therefore, the services used by the elderly (over age 65) are increasingly in demand. One of these services is nursing home care with demographics the primary driver of these costs. In 1986, 22% of nursing home residents were over the age of 85. Because this population is projected to expand rapidly, nursing home demand will continue to put increased pressure on these costs (Swan & Harrington, 1986). For example, from 1987 to 1995, per-capita health care spending increased only 3% for the population-at-large but grew 6% for the elderly (Rhoades, 1998).

The prospective payment system (PPS) instituted in 1983 for acute care hospitals is also placing increased demand on nursing homes. The PPS has had the effect of decreasing hospital lengths of stay and increasing the case mix intensity of patients admitted to long-term care facilities (Shaughnessy & Kramer, 1990). This has effectively substituted long term for acute care and, consequently, nursing homes are increasingly caring for patients with greater clinical needs. The combination of an aging population and the substitution from hospital to nursing home has resulted in nursing home patients who are frailer, have greater clinical problems, and require more care, both skilled and unskilled.

Quality. This trend of increasing acuity for nursing home residents raises the question of whether these residents are receiving quality care. Society has attempted, through regulations, to assure nursing home quality by requiring inspections, licensure, certification, personnel regulations, and ombudsman programs (Rantz et al., 1997). Despite these efforts, the Institute of Medicine (IOM) has reported unsatisfactory nursing home quality. In 1986, the IOM recommended that patient outcomes should be assessed as part of quality improvement efforts (IOM, 1986). Since this report, the development and use of patient outcome indicators has been an important focus in the long-term care research arena. According to the IOM Committee on the Adequacy of Nurse Staffing in Hospitals and Nursing Homes, RN coverage is "essential" to the quality of care in nursing homes (Kane, 1995). It is in this vein that some have called for nurse staffing research to standardize the concepts of staffing level and skill mix to optimize quality output (Clancy, Amende, & Geolot, 1997).

Investigators have found that the intensity of nursing care is a significant indicator of long-term care quality (Braun, 1991; Johnson-Pawlson, 1996; Rantz et al., 1997). These studies define "intensity" as the ratio of nursing hours to resident days and has been significantly associated with a decrease in decubitus ulcers, restraint use (Braun, 1991; Rantz et al., 1997), weight loss (Rantz et al., 1997), catheterizations, urinary tract infections, antibiotic use (Cherry, 1991), regulatory deficiencies (Johnson-Pawlson, 1996), and reduced mortality (Braun, 1991; Cherry, 1991).

"Nurse staffing mix" refers to the ratio of the various categories of "nurses" employed by the nursing home. Mortality (Linn, Gurel, & Linn, 1977), weight loss, incontinence (Munroe, 1990), restraint use (Graber & Sloane, 1995), pressure ulcers, and regulatory deficiencies (Munroe, 1990) were significantly reduced with a relatively increased mix of "better" nursing inputs. In addition, increased RN hours have been associated with improved functional status (Linn et al., 1977) and resident discharges to the community (Braun, 1991).

Other factors associated with nursing home outcome include ownership, occupancy rate, case mix, facility size, per capita income, percent of residents over 85, nursing home beds per capita, percent private pay (Zinn & Aaronson, 1993), and percent Medicaid (Munroe, 1990). Many of these variables were used in this study. Previous studies associating staffing to outcomes have not addressed the questions of optimal staffing levels or the consequences of "inadequate" staffing. This study begins to fill this void.

Theoretical Framework

The theoretical framework of this thesis is the production function of the firm. Nursing homes, like other firms, make choices about input efficiency as they produce and supply patient care. These choices are made through a basic production function. That is, Q= f(K,L,M, ...), where Q represents outputs of patient care, and K, L, and M represent capital, labor, and other factors respectively (Nicholson, 1995, p. 311). The definition of patient care outputs includes care provided at a given level of quality. This basic model is used to determine nursing home output given inputs K, L, and M. In this inquiry, labor hours represent nursing staff and outputs represent resident outcomes. The basic model can be simplified by holding various terms constant. By controlling for certain nursing home inputs (beds, case-mix, etc.), the specific impact of nurse staffing on output was examined.

The nursing home can substitute inputs to increase efficiency. The rate of technical substitution quantifies how one input can be used to substitute for another. In nursing homes, for example, LPN and NA labor perform many identical tasks. Although LPNs independently dispense medications and implement care, both LPNs and NAs provide supportive care and basic hygiene. Therefore, the nursing home can hire different combinations of LPNs and NAs and keep output constant. Depending on other input choices the nursing homes make, LPNs and NAs are, at some level, substitutable. Total cost and revenue are a function of the choices the nursing home makes about input mix and quantity. For example, LPNs earn higher wages than NAs. To justify these wages LPNs must either provide more valuable care or a greater quantity of care than NAs. The nursing home firm balances the higher wages paid to LPNs with increased productivity. Intuitively, because any single input can be used too much, the rational nursing home prefers an optimal LPN and NA mix to provide increased flexibility and minimum economic cost.

Research Questions

Nursing homes produce an output of patient days at some level of quality. The first research question examines the optimal staff required to minimize decubitus ulcer costs. Hypothesis 1: There exists an optimal level of nurse staffing that minimizes the cost of decubitus ulcers.

The next question addresses inefficiency. Specifically, if as expected, the optimal staff described in question one differs from current staffing levels in the nursing home, inefficiencies exist. Either the nursing home is providing too much staff or too little. If the staffing levels are less than optimal, too much decubitus cost is produced. Conversely, if staffing levels exceed the optimal, resources are wasted through additional staffing costs. In either event, a welfare loss affects society. Hypothesis 2: There exists an identifiable societal welfare loss when staffing levels fall outside the optima.

Data

The basic unit and year of analysis was the nursing home in 1994. Two secondary data sets were used: Area Resource File (ARF) and the 1994 Online Survey Certification and Reporting System (OSCAR). ARF is county-level data that summarizes population, health, and social resources. (Due to the nature of the ARF, not all data are from 1994. Therefore, the closest calendar year is used as a proxy for the 1994 numbers. These proxies pertain only to the stratification of the county population by age [1990] and. the number of nursing home beds [1991]. The assumption is that the demography will change little during these relatively short periods of time. All other ARF data are from 1994). The OSCAR is obtained through self-reported surveys and contains aggregate nursing home facility information obtained through the nursing home certification process. These two sources of data are merged and a cost optimization analyses performed at the facility level (unit of inquiry). In addition to OSCAR and ARF, three additional pieces of information are used. The first two, nursing wages (all categories) and medical inflation rates, are obtained from the United States Bureau of Labor Statistics (USBLS, 1998). The third, the cost of decubitus ulcers, is estimated from the prior work of Xakellis and Frantz (1996).

After using county variables to merge the 1994 OSCAR and ARF, 14,449 nursing home cases are obtained. After assessing each facility for data completeness, 14,422 facilities remain. (Several geographic areas were dropped due to missing ARF variables of interest: Washington DC [n=18], Puerto Rico In =2], Virgin Islands [n=1]. Five facilities reported a zero census and were excluded. Finally, one case was excluded due to a missing state and county identifier). All variables of interest were evaluated for significant deviation from the mean and outliers were excluded. (All cases in excess of three standard deviations are excluded. These include RN cost [n=361], LPN cost [n=297], NA cost [n=220], and case-mix [n=229]). An additional 1,306 cases were dropped for negative decubitus data. (The decubitus ulcers present on admission were subtracted from the total decubiti before dollar values were assessed; 1,306 cases resulted in a negative value after this adjustment.) At the conclusion of this process, 12,128 cases remain, representing 85% of the original merged data. Using an independent samples t-test, the excluded cases (n=2,321) were compared to the final analytic sample and found to be from the same population. (Since all variables in the final analytic sample contain at least one value that lies within the 95% confidence interval of the excluded sample [available upon request], the analytic and excluded samples are considered "the same" [Neter, Wasserman, & Kutner, 1990, p. 15; Pindyck & Rubinfeld, 1998, p. 42]).

Variables

Decubitus cost. The OSCAR only counts residents with breaks in their skin (stage 2, 3, and 4) as having a decubitus ulcer. Therefore, a resident with reddened skin (stage 1) is not considered a decubitus "count" for study purposes. To identify cost, a dollar amount is coupled with the count. The inflation-adjusted decubitus ulcer costs per resident day is estimated at $12.28 (excluding hospitalization). (Various studies have estimated treatment cost of and prevention of decubitus ulcers in the long-term and acute care settings. Some estimate the mean cost of treatment per ulcer and per patient [Xakellis & Frantz, 1996]. Others estimate the cost of an ulcer-free day and total cost to the facility for prevention interventions over a 3-month [Xakellis, Frantz, & Lewis, 1995] or

5-year [Frantz, Gardner, Harvey, & Specht, 1991] period. This study uses the cost figures of Xakellis and Frantz [1996] because costs are calculated on a per-patient level and the costs are for treating new and existing decubitus ulcers, rather than preventive costs.) The dependent variable Decub is calculated by multiplying the daily cost per decubitus ulcer by the total number of facility decubitus days. Decub represents total facility decubitus cost.

Independent Variables

This model measures optimal output and minimum costs of nursing homes by using production inputs and a number of controls as explanatory variables. These include a vector of variables describing the local environment of the nursing home and a vector of variables related to the specific production inputs the nursing home chooses. Many of these variables were significant in previous nursing home quality studies while others were added based on theory. The basic inquiry delved into the relationship between nurse staffing and output. Therefore, for every nursing home the staffing levels of the three categories of nurse are included.

OSCAR reports full-time equivalency (FTE) (each FTE represents 40 hours of labor per week) numbers for RNs, LPNs, and NAs. Normalized values are obtained by dividing the total FTEs in each nurse category by the census at the time of the survey for the respective facility. To measure optimal production, input nursing costs are included. State wage rates for each nurse category provide these costs. (The BLS provides hourly state wage rates for each category of nurse. Because decubitus cost data are presented as an annual cost, these hourly wage rates are converted to an annual wage rate [hourly rate, 40 hours, 52 weeks]. However, the current BLS reports wages for 1997 and this inquiry uses 1994 costs. This necessitated a downward adjustment of the 1997 wage rates through the use of the medical care professional services inflation index [USBLS, 1998] from the 1997 to the 1994 rates. This analysis is available upon request from the author).

By multiplying the normalized FTEs by the adjusted wage rates, the nurse staffing cost variables used in this inquiry are created. Three additional squared variables are created to facilitate optimization (see Figure 1). In addition to the nurse staffing impact variables, other variables may have influenced both cost and output. These are included as controls (see Table 1).
Figure 1.
Variables to Facilitate Optimization

RN = (RN1)(RN_Wage) = Facility RN cost per
  resident                                     [RN.sup.2] = (RN)(RN)
LPN = (LPN1)(LPN_Wage) = Facility LPN cost
  per resident                                 [LPN.sup.2] = (LPN)(LPN)
NA = (NA1)(NA_Wage) = Facility NA cost per
  resident                                     [NA.sup.2] = (NA)(NA)
Table 1.
Operationalized Variables

Variable          Definition
Decub             Annual nursing home decubitus cost
RN                Facility RN cost per resident
LPN2              Facility LPN cost per resident
NA                Facility NA cost per resident
RN2               Facility RN cost per resident squared
LPN2              Facility LPN cost per resident squared
NA2               Facility NA cost per resident squared
Case_Mix          Severity of illness continuum (0 to 4)
Size              Number of beds in the nursing home
Occ_rate          census / beds
Medicaid          Medicaid residents / census
FP                For-profit indicator (1 = FP, 0 = NFP or government)
NFP               Not-for-profit indicator (1 = not-for-profit, 0 = FP
                  or government)
Chain             Part of a chain (1 = chain, 0 = not part of a chain)
Hosp_bas          Hospital-based facility (1 = hospital-based, 0 = not
                  hospital-based facility)
Therapy           (Activity therapy FTEs / resident) + (Dietitians FTEs
                  / resident) + (Medication aide FTEs / resident) +
                  (Mental health therapy FTEs / resident) +
                  (Occupational therapy FTEs / resident) + (Physical
                  therapy FTEs / resident)
Admin             FTE administrative staff per resident
Hosp_bed          total hospital beds in the county
NH_beds           number of county nursing home beds
Mgd_care          number of managed care enrollees in the county
Urb_Rur           County population continuum (0 = greater than 1
                  million through 9 = less than 2500)
GT65LT85          County population number over age 65 and less than 85
GT85              County population number over age 85.
PCI               County per capita income.
Alabama through   1 = Alabama, 0 = not Alabama
Wyoming           1 = Wyoming, 0 = not Wyoming.


Methodology and Model

The data contain a cross-section of multiple observations at a point in time (1994) for all United States nursing homes. The central limit theorem suggests that larger samples lead to a mean estimate that is closer, on average, to the population mean; in fact, if large enough, the sample mean should be identical to the population mean. In this inquiry, all federally certified skilled and intermediate nursing facilities were included in the sample. A visual examination of histograms with superimposed normal curves confirms an essentially normal distribution for the variables included in the model.

An important property of normal distributions is that they can be fully described by their mean and variance. With a large, normally distributed sample, the sample mean approaches the population mean and the predicted value of the estimator is unbiased. Furthermore, as the sample size increases, the probability that the sample estimator will differ from the population becomes very small. Thus, due to the large sample properties and normal distribution of the sample, ordinary least squares (OLS) estimation gives unbiased and consistent results (Pindyck & Rubinfeld, 1998, p. 31) (see Figure 2).

Figure 2.

The Basic Model

[Y.sub.i] = [[Beta].sub.1]+[[Beta].sub.2][X.sub.2i]+[[Beta].sub.3][X.sub.31]+ ....+[[Beta].sub.k][X.sub.ki]+[[Epsilon].sub.i]

Y = dependent variable (decubitus ulcer cost)

X = independent variables, as described above

[Epsilon] = error term

i = number of observations

k = number of independent variables.

Initially, the interest is in nursing home inputs that minimize the cost of decubitus ulcers. Therefore, Decub = f (RN + [RN.sup.2] + LPN + [LPN.sup.2] + NA + [NA.sup.2] + controls). An additional consideration is the optimal efficiency level of the nursing home in terms of nurse staffing. The difference between the optimal staff mix and the staffing levels actually chosen by nursing homes is a measure of nursing home operating inefficiencies. To find optima, the model results for each of the staffing level coefficients were differentiated, the result equal to zero was set, and solved (see Figure 3).

Figure 3.

Calculation for Optimal Staff Mix and Staffing Levels

[Delta] Decub / [[Delta].sub.3]RN = [[Beta].sub.1]RN + [[Beta].sub.2][RN.sup.2] = 0 RN = +/- [[Beta].sub.1]/2[[Beta].sub.2] and [Delta] Decub / [Delta]LPN = [[Beta].sub.3]LPN + [[Beta].sub.4][LPN.sup.2] = 0 LPN = +/- [[Beta].sub.3]/2[[Beta].sub.4, and [Delta] Decub / [Delta]NA = [[Beta].sub.5]NA + [[Beta].sub.6][NA.sup.2] = 0 NA = +/- [[Beta].sub.5]/2[[Beta].sub.6]

This yields optimal staffing cost levels per resident for nursing home cost minimization. Nursing home efficiency is assessed by comparing these optimal levels to the staffing decisions the nursing home operator makes. Inefficiency represents a welfare loss to society.

Results

A summary of descriptive and frequency data is provided in Tables 2 and 3. The sample reflects a predominance of proprietary ownership (62%), chain affiliation (54.7%), and stand-alone facilities (98%). The typical facility had 115 beds, an occupancy rate of 87.53%, and received the greatest proportion of its income from Medicaid (67.7%). The average nursing home spent $2,606.45, $1,607.94, and $569.98 per resident on the inputs of RNs, LPNs, and NAs respectively. The average county of residency had 2,805 hospital beds, 3,436 nursing home beds, and a population of 658,126, consisting of 65,884 aged 65 to 85 and another 7,231 over age 85. Additionally, 260,991 persons are enrolled in managed care plans.
Table 2.
Descriptive Statistics
(N=12,128)

Variable   Minimum   Maximum    Mean      Standard Deviation
Decub      4482      748527     33945     33291
RN         288.08    11603.85   2606.5    1708
LPN        23.74     6639.49    1607.94   1218.75
NA         16.76     2132.15    569.98    219.45
Admin      0         712.02     5.50      11.61
Case_mix   .05       2.28       1.15      .3699
Size       6         1082       114.56    69.26
Occ_rate   .01       1.00       .8753     .1434
Therapy    0         2285       5.09      28.61
Medicaid   0         1.00       .677      .2218
Hosp_bed   0         33028      2805.05   6066.68
NH_beds    0         36386      3436.18   6905.54
Mgd_care   0         5737889    260991    930573
Urb_Rur    0         9          3.07      2.82
PCI        6583      53189      20314     4773
GT65LT85   34        775160     65884     139816
GT85       7         85427      7231      15246
Table 3.
Variable Frequencies
(N=12,128)

Variable   Label                Frequency   Percent
Chain      Chain                6636        54.7
           Not chain            5492        45.3
Hosp_bas   Hospital-based       243         2
           Not hospital-based   11885       98
FP         For-profit           7575        62.5
           NFP or government    4553        37.5
NFP        Not-for-profit       1652        13.6
           FP or government     10476       86.4


Regression analysis. Table 4 displays the results of multiple regression analysis describing the predictors of decubitus ulcer cost (Decub). This model explains 46.8% of decubitus cost variance and is clearly superior to a random predictor of this variation (F=149.108, p=.000).
Table 4.
Regression Analysis of Decubitus Costs
(Excluding Hospitalization Costs)

Variable   Estimate     t-value        Standard
                                       Estimate
Constant   -48596       -15.12 (***)
RN         -1.659       -2.342  (**)   -.085
RN2        .000277      1.665    (*)   .113
LPN        4.544        4.217  (***)   .166
LPN2       -.000699     -1.856   (*)   .130
NA         -7.334       -2.117  (**)   -.048
NA2        .0002004     .909           .020
Admin      -.869        -.045          .000
Case_mix   5456.583     8.336  (***)   .061
Size       291.608      81.128 (***)   .607
Occ_rate   36226.8      19.140 (***)   .156
Chain      2600.678     5.368  (***)   .039
Hosp_bas   5389.401     2.894  (***)   .023
FP         1680.417     2.808  (***)   .024
NFP        -1288.46     -1.672   (*)   -.013
Therapy    4.068        .518           .003
Medicaid   4875.585     3.912  (***)   .032
Urb_Rur    -430.782     -4.024 (***)   -.037
Hosp_bed   1.225        5.176  (***)   .223
NH_beds    -.889        -4.248 (***)   -.184
Pop        -.005016     -4.605 (***)   -.235
GT65LT85   -.188        6.453  (***)   .789
GT85       -1.161       -4.711 (***)   -.532
Alabama    10344.47     4.343  (***)   .037
Alaska     5813.79      .574           .004
Arizona    -674.326     -.220          -.002
Arkansas   6694.25      2.877  (***)   .026
Calif      8342.915     4.389  (***)   .066
Colorado   2544.656     1.046          .009
Conn       -1907.57     -.769          -.007
Delaware   1555.249     .354           .003
Florida    7344.566     3.702  (***)   .042
Georgia    9876.963     4.699  (***)   .044
Hawaii     -9373.26     -1.56          -.011
Idaho      3346.464     .864           .006
Illinois   8254.486     4.530  (***)   .053
Indiana    5220.861     2.774  (***)   .030
Iowa       2533.754     1.291          .013
Kansas     4633.819     2.032   (**)   .018
Kentucky   10791.3      4.814  (***)   .042
Louisana   2227.561     1.028          .010
Maine      4254.416     1.514          .012
Maryland   8904.128     3.698  (***)   .031
Massachu   6851.79      3.569  (***)   .037
Michigan   13805.45     7.181  (***)   .071
Minesota   -4322.98     -2.116  (**)   -.020
Missippi   10190.08     4.100  (***)   .034
Missouri   4949.457     2.543   (**)   .026
Montana    2207.659     .708           .005
Nebraska   3517.979     1.465          .012
Nevada     9234.956     1.926    (*)   .014
N_Hamp     1737.66      .496           .004
N_Jersey   10751.2      5.034  (***)   .046
N_Mexico   6873.349     1.941    (*)   .014
New_York   4802.049     2.599  (***)   .029
N_Car      8838.244     4.153  (***)   .037
N_Dakota   -2462.8      -.727          -.005
Ohio       5073.233     3.015  (***)   .037
Oklahoma   8955.848     4.345  (***)   .044
Oregon     6153.494     2.325   (**)   .018
Penn       11539.76     6.343  (***)   .068
R_Island   -3890.50     -1.116         -.008
S_Car      1354.939     .501           .004
S_Dakota   4285.097     1.434          .011
Tennesee   5163.127     2.459          .023
Texas      6797.868     3.854  (***)   .057
Utah       399.423      .117           .001
Vermont    3923.914     .501           .003
Virginia   10655.63     4.942  (***)   .044
Wash       2467.192     1.075          .009
W_Vir      18207.48     6.826  (***)   .054
Wyoming    1800.571     .341           .002

R-square= .468 Adjusted R-square = .464

(*) p < .10; (**) < .05; (***) < .01


Impact variables. Per-resident annual RN wages are negatively associated with annual facility decubitus cost ([Beta]=-1.659, p=.019). This indicates that increased facility spending on RN inputs decreases decubitus costs because these facilities operate at greater levels of nursing expertise. This was the expected result and is consistent with previous studies associating nursing expertise with decreased long-term care negative outcomes (Braun, 1991; Graber & Sloane, 1995; Linn et al., 1977; Munroe, 1990).

Per-resident annual wages paid to LPNs is positively associated with annual facility decubitus ulcer cost ([Beta]=4.544, p=.000). This result defines a relationship of increased LPN spending with increased decubitus costs. This is unexpected but there is a possible explanation. Although LPN labor has greater expertise relative to NAs, it is lower than RNs, and nursing homes may be substituting LPNs for RNs. Previous research associates higher ratios of RN to LPN hours with better resident outcomes (Munroe, 1990). In this light, increased LPN wages resulted in a net decrease in expertise relative to RNs.

Finally, per-resident annual wages paid to NAs is negatively associated with annual facility decubitus ulcer cost ([Beta]=-26.838, p=.000). Rather than increasing expertise, NAs provide intensity; they also are a relatively cheap and efficient investment. The large negative coefficient signals a strong impact on decreased decubitus cost. This was the expected result and is consistent with many studies associating increased nursing intensity with improved outcomes (Braun, 1991; Cherry, 1991; Johnson-Pawlson, 1996; Munroe, 1990; Rantz et al., 1997).

Other independent variables. Nursing home decubitus ulcer cost is positively associated with the case-mix severity of the resident population ([Beta]=19,780, p=.000) and the percentage of residents receiving Medicaid ([Beta]=17,427, p=.000). It is not surprising that more deteriorated residents have more decubitus ulcers and, as a result, increased costs. The Medicaid finding is consistent with previous works (Munroe, 1990; Nyman, 1987; Weissert & Scanlon, 1985; Zinn & Aaronson, 1993). Larger facilities ([Beta]=291.608, p=.000) and greater occupancy rates ([Beta]=36,266, p-.000) predict increased decubitus costs. The affiliation of a nursing home with either other nursing homes (Chain; [Beta]=9,410, p=.000) or hospitals (Hosp bas; [Beta]=19,548, p=.004) is also positively associated with decubitus costs. It was not surprising that larger facilities (less supervision), chain affiliation (staffing guidelines), and higher case-mix severity would increase decubitus cost. It is also not surprising that as the percentage of Medicaid residents increases, decubitus cost also increases. However, it was expected that hospital-based nursing homes would have less decubitus cost because they would internalize their externalities. This was not the case. Possibly, the affiliation with a hospital attracts residents more likely to require hospitalization and, thus, more expensive treatment, including decubitus ulcers.

Compared to the government facility reference group, not-for-profit facilities (NFP; [Beta]= - 4665.9, p=.094) have a large negative influence on decubitus ulcer cost, while for-profit facilities (FP; [Beta]=6,085, p=.005) exhibit a positive one. However, due to significant correlation between FP and NFP (-.512), these results should be viewed with some caution, even though previous work associates profit status with outcomes (O'Brien, Saxberg, & Smith, 1983; Riportella-Muller & Slesinger, 1982; Zinn & Aaronson, 1993). Some geographic and demographic variables (Urb_Rur, Hosp bed, NH_beds, Pop, GT65LT85, GT85) and many qualitative indicator state variables are significant predictors of decubitus cost (see Table 4). A large negative influence on decubitus ulcers is the location of the facility in an urban or a rural setting (Urb Rur; [Beta] = -1560.005, p-.000). Rural counties have fewer decubitus ulcer costs. Two other controls have significant negative influences on decubitus cost. More nursing home beds in the county (NH_beds) also predict fewer decubitus costs ([Beta] = -3.218, p=.000). This is not surprising because nursing home operators may compete on quality in areas with increased nursing home bed availability. A county population over age 85 (GT85) was also inversely related to decubitus ulcer cost ([Beta]= -4.204, p=.000). The number of administrators per resident (Admin) was in the expected direction (negative) but not statistically significant. Many state variables (the reference group was Wisconsin) are significant predictors of decubitus cost. This is expected because individual state regulation and reimbursement policies affect nursing homes.

Optimal staffing. Staffing coefficients for both models are displayed in Table 5. To find the optima, the model results were differentiated for each staffing level coefficient, the result equal to zero was set, and the optimal level of staffing was solved. Optimal levels for the nursing home operator (excluding hospital costs) are found in Figure 4.

Figure 4.

Calculation for Optimal Levels for the Nursing Home Operator

[Delta] Decub 2 / [Delta]RN = [[Beta].sub.1]RN + [[Beta].sub.2][RN.sup.2] = 0 RN = [[Beta].sub.1]/2[[Beta].sub.2] = 1.659 / 2 (.0002778) = 2983.81 [Delta] Decub 2 / [Delta]LPN = [[Beta].sub.3]LPN + [[Beta].sub.4] [LPN.sup.2] = 0 LPN = [[Beta].sub.3]/2[[Beta].sub.4] = 4.544 / 2 (- .000699) = 3250.36 [Delta] Decub 2 / [Delta]NA = [[Beta].sub.5]NA + [[Beta].sub.6][NA.sup.2] = 0 NA = [[Beta].sub.5]/2[[Beta].sub.6] = - 7.334 / 2(.002004) = 1829.84
Table 5.
Staff Impact Coefficients

                          RN                  LPN

Model             [Beta]1   [Beta]2    [Beta]3   [Beta]4

Nursing home      -1.659    .0002778    4.544    .000699
decubitus costs

                          NA

Model             [Beta]5   [Beta]6

Nursing home      -7.334    .002004
decubitus costs


To predict a minimum, the second derivative of the coefficient ([[Beta].sub.1], [[Beta].sub.3, [[Beta].sub.5]) must be negative. The model estimates staffing cost per resident levels for RNs and NAs that minimize (negative sign) the cost of decubitus ulcers. The positive LPN estimator means that it cannot be used as a definer of minimum decubitus cost. In fact, the model shows a positive relationship between LPN staff spending and decubitus cost. Therefore, all research questions addressing staffing levels can only be answered for RNs and NAs.

Research Questions

The first question asked was, "What is the optimal nurse staffing level that minimizes the cost of decubitus ulcers to the nursing home?" The hypothesis was that this optimal existed. The nursing home operator minimizes decubitus costs by spending $2,983.81 and $1,829.84 per resident per year for RN and NA labor, respectively (see Table 5). The second question addressed inefficiency. Welfare loss occurs if a nursing home staffs either above (excessive staff costs) or below (excessive decubitus costs) the optimal.

In 1994, very few nursing homes were at this optimal, especially for NA inputs (see Table 6). Of the 12,128 sampled facilities, only four nursing homes were at optimal (+/- 5%) for both RNs and NAs, and only 326 were within 50% of optimal. This indicates substantial welfare loss.
Table 6.
Percentage of Current Staffing Levels at Optimal
(N=12,128)

Staffing Optima               +/- 5% (%)    +/- 10% (%)
RN (Optimal = $2983.81)       N=1090 (9%)   N=2026 (16.7%)
NA (Optimal = $1829.842)      N=16 (.13%)   N=31 (.26%)
RN and NA (Both at Optimal)   N=4 (.032%)   N=4 (.032%)

Staffing Optima               +/- 25% (%)      +/- 50% (%)
RN (Optimal = $2983.81)       N=3957 (32.6%)   N=7057 (58.2%)
NA (Optimal = $1829.842)      N=95 (.78%)      N=684 (5.6%)
RN and NA (Both at Optimal)   N=15 (.12%)      N=326 (2.6%)


Optimal decubitus cost is calculated by solving the optimal equation from the model. A new variable (Op_decub) was created which specifies optimal decubitus cost while controlling for all other independent variables in the model and then comparing it to the actual estimated cost (Decub) incurred by each facility. (This level was estimated by creating a new variable [Op_decub]. Because the staffing optimals are a per-resident estimate, the coefficients of RN, [RN.sup.2], LPN, [LPN.sup.2], NA and [NA.sup.2] were multiplied by the facility census. The controls were then multiplied by their coefficients and added together with the optimal staffing levels per resident and solved for decubitus cost. Thus, Op_decub = [-1.659 * residents] + [.000277 * residents] + [4.544 * residents] + [-.000699 * residents] + [7.334 * residents] + [.0002004 * residents] + [control coefficients * control values]).

To quantify nursing home inefficiencies, a 95% confidence interval was created that is considered within optimal standards (see Table 7). The vast majority of nursing homes (N=11,338) fall outside the optimal level (+/-5%) for decubitus costs. There are 4,811 facilities with greater than optimal (+5%) decubitus costs, equaling $84,085,167. Another 6,427 have lower than optimal (-5%) decubitus costs, equaling $83,230,463, for a total societal welfare loss of $167,315,630.
Table 7.
Total Societal Welfare Loss

Variable                 Min    Max          Mean

Op_Decub (n = 12,1280)   0      294,724.9    34,184.56
Op_Decub +5% (n= 4811)   3.79   495,581.6    17,477.69
Op_Decub -5% (n = 6527)  4.48   158,969.25   12,751
Total Welfare Loss (above and below optimal)

Variable                                       Welfare Loss (sum of all
                                               facilities)
Op_Decub (n = 12,1280)
Op_Decub +5% (n= 4811)                         $84,085,167
Op_Decub -5% (n = 6527)                        $83,230,463
Total Welfare Loss (above and below optimal)   $167,315,630


The results of this inquiry demonstrate that NAs have substantially more impact than RNs on minimizing long-term care decubitus costs, but both were significant. However, increased LPN staffing did not move these costs toward a minimum. The model was a good model and explained 46.4% of the variation of decubitus and most variables were significant at very strong levels, including all of the impact staffing variables. Optimal RN and NA levels per resident per year are defined and the number of facilities above and below these optima is specified. Finally, the total societal welfare loss due to excessive decubitus ulcer costs and excessive staffing is quantified at $167,315,630.

Discussion and Conclusions

There is an optimal level of staffing that minimizes decubitus ulcer cost in nursing homes. Hypothesis #1 is confirmed. The study provides important findings in the area of nursing home efficiency. These results imply that there are measurable levels of nurse staffing in the long-term care setting that minimize decubitus ulcer cost. The optimal level of RN and NA spending is $2,983.81 and $1,829.84 per resident per year, respectively. The average nursing home operator would have to increase annual RN inputs by approximately $380 per resident, more than triple NA inputs from $569.98 to $1,830.32 per resident, and reduce or possibly eliminate LPN inputs.

The 1994 mean hourly wage for RNs, LPNs, and NAs was $17.37, $11.53, and $7.06 respectively. This equated to annual wages of $34,730 (RN), $23,066 (LPN), and $14,112 (NA). At 1994 per-resident staffing levels, the average nursing home hires one RN for every 13.32 residents and one NA for every 24.76 residents. To be at optimal, the average nursing home operator would have to increase staffing to one RN for every 11.63 residents and one NA for every 7.71 residents. Conversely, the positive LPN coefficient is a signal to reduce LPN inputs. In effect, the more nursing home operators increase LPN wage inputs at the expense of other inputs, the greater the cost of decubitus ulcers to both the nursing home and society. By spending scarce resources on LPNs, the nursing home makes a choice not to increase hires for the other nurse categories. Society would be better off with either increased NA or RN inputs.

The level of inefficiency attributable to nursing homes operating at nonoptimal levels is substantial. Hypothesis #2 is confirmed. In terms of the nursing home optimal, many facilities operate at a staffing level greater than optimal, and many others operate at a level less than optimal. There were 3,851 facilities" that were staffed too high for RNs, 11 facilities staffed too high for NAs, 7,185 facilities that were staffed too low for RNs, and 12,101 facilities that were staffed too low for NAs. Nursing homes that produce excessive decubitus ulcers due to insufficient staffing essentially waste scarce resources used to treat decubitus ulcers. Excessive treatment costs in facilities that are staffed too low is $84,085,167. Facilities that staffed at excessive levels reduce decubitus ulcers below a level that is efficient. The resources spent on excessive staff could be used more efficiently elsewhere due to diminishing returns on the labor inputs. The cost of excessive staff (or other factors) in facilities that are staffed too high is $83,230,463. Thus, more optimal staffing would have improved economic efficiency on a national level by $167,315,630.

Implications

This study advances understanding of the relationship between nursing home staffing and outcomes. Previous studies generally found that increasing the number of nurses has a positive impact on the incidence of most outcomes; however, these studies did not address the question of optimal staffing based on outcome cost. For example, if society or a nursing home operator chose to assign one RN to every nursing home resident, bad outcomes would probably decrease (although even there, only to a point). However, this is implausible because of the cost of RN inputs. Unlike prior studies, this inquiry indicates that more nurses are good but only to a point and it indicates where that point is. Where other studies have concluded that increasing numbers of nurses reduce bad outcomes, this study attempts to balance the additional cost of increasing nurse inputs with the savings resulting from fewer bad outcomes. This balance of cost and outcome leads to an estimate of an efficient optimum.

The results indicate that nursing homes should increase RN and NA hires. RNs may bring a theoretical framework and superior clinical skills to the nursing home. NAs have the most contact with nursing home residents and are responsible for performing many of the tasks that are essential in preventing and treating many chronic conditions, in this case, decubitus ulcers. NAs are an efficient input of nursing home production because they provide a greater presence at relatively low cost. At 1994 prices, the nursing home operator could purchase approximately five NAs for the price of three LPNs. NAs have a limited knowledge base but with proper guidance, leadership, and direction, they can positively influence patient outcomes. The results of this inquiry support the need for additional low-cost nursing home labor inputs.

It is, perhaps, surprising that nursing home operators were operating at such a high degree of inefficiency. However, there are several possible explanations.

Profit orientation. Nursing homes are under pressure to show a profit. Even nonprofit nursing home operators must have some level of profit to continue to operate. In an effort to drive profits, operators may not consider the cost of bad outcomes.

Insufficient information. There is a paucity of research that quantifies the cost of bad outcomes in terms of facility resource requirements. Without this knowledge, the nursing home may choose its staff levels based primarily on wages. Since RNs cost more, facility operators may want to use fewer RNs. Because prior studies fail to demonstrate that using fewer RNs will lead to increased facility costs, most operators may not understand the relationship between facility costs and staffing levels.

Recruitment and retention of RNs. Another possible explanation may be an inability to recruit and retain RNs. Nursing home RNs spend most of their time on administrative functions and less than 10% on direct resident care. Additionally, nursing home RNs are paid substantially less than their hospital-based colleagues and retention may be linked to salary (Kanda & Mezey, 1991). It is also possible that a nursing home may be willing to hire additional RNs at current wages but would be unwilling to raise that wage since the perceived benefit of additional RNs is outweighed by the increased wages the nursing home would have to pay the existing workforce. At existing wages, therefore, a shortage of nurses occurs. This inquiry balances differences between hospital-based and nursing home RNs by using state wage rates. In fact, by overestimating nursing home RN cost, the positive impact of RNs on optimal costs is underestimated.

Regulations. A final explanation of nursing home staffing inefficiency may be compliance with federal and state RN staffing requirements. The intention of staffing regulations is to set a quality floor, not an optimum. However, federal and state requirements meant to merely specify minimum staffing levels can be used by nursing homes to justify less than optimal staffing. They are, after all, in compliance.

Limitations

This study examines only one nursing home output, decubitus ulcer cost. The interpretation of these results should, therefore, be viewed with some caution. There are many other adverse outcomes occurring in long-term care facilities and the optimal staffing level for one is not necessarily the same for another. Therefore, this inquiry should only be viewed as a first step. Additional research is required, including not only various adverse outcomes (including cost) but nursing home profitability.

The data are taken from 1994. However, other event(s), occurring during 1994 and not included in the study after 1994, may have influenced the nursing homes input decisions. Also, the long-term care environment has changed since 1994, and nursing homes may have altered their production input in response to these factors.

Measurement issues and estimation may also create issues. The wage variables were based on state indexes deflated from 1998 to 1994 levels. A more accurate wage measurement would have been to use actual 1994 facility wages. This would entail obtaining nursing home financial statements from 1994 which was not practical. The cost of decubitus ulcers is also an estimate based on previously analyzed data at a large nursing home and inflated from 1991 to 1994 dollars. A more accurate measurement would employ individual decubitus ulcer costs at each facility; however, this information could not be obtained.

OSCAR data are based on questionnaires completed by nursing home administrators. In other words, the data are based on responses and not objective observations, and it is likely that some of the nursing home operators did not provide accurate information. This type of response bias is always a potential problem when using reported data.

Another important issue is that of unknown factors that are not included in the model due to the lack of information or improper formulation of theory. Omitting a significant variable(s) leads to biased estimators. An example of a missing factor in this study could be the number of nurses that attended specialty courses in decubitus ulcer care. However, the [R.sup.2] of 46.4% coupled with robust coefficients, indicates that the impact of omitted variable bias may not be a large problem. This suggests a lack of bias.

Conclusions

Ideally, this study should be replicated for other outcomes. However, the results contain important implications for nursing home operators. The traditional nursing home staffing model includes RN input(s) that have little, if any, daily patient contact. The LPN acts essentially as a charge nurse who passes out medications, performs treatments, and supervises NAs. NAs perform the majority of the required routine tasks. The results of this study suggest the need to reconsider this model, at least in the context of minimizing decubitus ulcer cost and, if similar results are found for other negative nursing home outcomes, the current staffing model and patterns may be fully inappropriate.

RNs bring a level of quality to the nursing home that LPNs do not. It is possible that an RN's educational preparation, which includes a basis in theory, results in an increased understanding of disease processes that leads to increased savings through higher-quality care. The positive relationship between LPNs and decubitus costs presents more questions than answers. In particular, should there be any LPNs in long-term care? The results raise some doubts about LPN's value, at least in the context of minimizing decubitus costs. This study's results clearly suggest that NAs are an efficient nursing home production factor for minimizing decubitus costs because they are relatively inexpensive and are capable of performing many labor-intensive tasks without extensive training or education. Thus, it is possible that the most efficient staffing model involves the exclusive use of RNs and NAs. By reducing LPN inputs, more NAs can be hired, increasing the total number of workers available to turn, reposition, walk, bathe, and feed long-term care residents. For many debilitating conditions (not just decubitus), these activities are important. Perhaps the results of this study suggest that more RNs are needed to function as supervisors and trainers of nursing assistants.

Future research should examine other adverse outcomes in the long-term care setting and optimize each. These outcomes might include depression, patient falls, diabetes, contractures, nosocomial infections, and the like. As each becomes optimized, a bundle develops and an increasingly efficient staffing model ensues. In that the majority of nursing homes remain proprietary, another research thread should include nursing home revenue maximization minus the cost of bad outcomes. Examining staffing levels and efficiencies in the nursing home from a perspective that focuses on outcomes can lead to more efficient staffing decisions and more effective use of long-term care facility resources.

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THOMAS J. HENDRIX, PhD, RN, is Assistant Professor, College of Nursing, University of Utah, Salt Lake City, UT.

STEPHEN E. FOREMAN, JD, PhD, is Assistant Professor, Health Policy and Administration, The Pennsylvania State University, Philadelphia, PA.
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Date:Jul 1, 2001
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