Does prospective payment really contain nursing home costs? - Policy Impact - Statistical Data Included

Health Services Research, April, 2002 by Li-Wu Chen, Dennis G. Shea

Model Specification of the Nursing Home Cost Function

We used a hybrid functional form to estimate nursing home costs because the hybrid form combines the "economic rigor" and the specification flexibility of the translog form and the "intuitive appeal" of the ad hoc approach (Nyman 1988) (12)

In addition, the hybrid form allows for zero value for output variables and does not involve as many interaction terms for independent variables as a translog form does (Dor 1989; Grannemann, Brown, and Pauly 1986; Nyman 1988). The hybrid model used in this study was derived by modifying the equations in the studies by Dor (1989), Nyman (1988), and Grannemann, Brown, and Pauly (1986). The total cost function equation can be expressed as:

C = A [PI][P.sup.wj.sub.j][e.sup.f](Y,CM,Q)[e.sup.[epsilon]] and A = [e.sup.[CHI][theta]]

By taking the logarithm form for both sides of the above total cost function equation, the hybrid cost function is specified as follows:

ln C = [CHI][theta] [omega] ln P f(Y, CM, Q) [epsilon]

In this equation, C is the total operating cost of a nursing home facility in 1994, P is the input price of nursing home, X is a vector of variables that describe the nature and environments of nursing homes, and f is a function that describes the amount (output quantity Y) and the feature (case-mix CM and quality Q) of the outputs of a nursing home in 1994; f was specified as the following functional form:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where Y = yl y2 y3; and y1, y2, and y3 represent the instrumental measures for the 1994 Medicare days, Medicaid days, and private days served by a nursing home, respectively. CM is the patient case-mix score of a nursing home. Q1 through Q7 represent the seven quality indicator variables. Instrumental measures were used for the three quality of care process variables. To make sure that all quality indicator variables have the same direction so that higher number indicates higher quality, we transformed the values of three prevalence rate variables and the deficiency variable into negative values.

[summation over (3/ij=[1.sub.i[not equal to]j] [[alpha].sub.ij][[gamma].sub.i][[gamma].sub.j] [delta]Y(CM) [summation over (7/m=1)] [[gamma].sub.m] [YQ.sub.m]

X includes Medicaid payment methods, ownership indicators, the affiliation status (hospital-based and chain status), the interaction term variables between ownership and chain status, the market concentration indicator variable, the degree of environmental urbanization, and the geographic location of nursing homes. The OLS approach was used to estimate the nursing home hybrid cost function.

RESULTS

Table 2 shows the descriptive statistics for dependent and explanatory variables used in the regression analysis. Table 3 shows the results of regression.

According to the regression results in Table 3, quality of output is a strong predictor of cost, and higher quality predicts higher cost in nursing homes. Six of the seven quality-output interaction variables are statistically significant. The coefficients of these six variables all indicate that higher nursing home quality predicts higher costs, except for the physical restraint rate variable. These results confirm the importance of controlling for quality variation from various perspectives. The positive effects of nursing home quality on cost were calculated and listed in Table 4. The improvement in process-related quality indicators seems to cost more than that in structural indicator or regulatory compliance. In particular, the marginal increase by organizing a resident group or a family group would lead to an increase of $131,439 (3.8 percent) in the annual total cost for an average nursing home with 55,853 patient days in 1994. These findings on cost of quality improvement in nursing homes will provide useful information for the evaluation of cost-effectiveness of alterntive quality initiatives in this industry.