A. Interpret the coefficient of determination (R²) estimated for the nursing cost function.

B. Describe the economic and statistical significance of each estimated coefficient in the nursing cost function.

C. Average nursing costs for the eight for‑profit hospitals in the sample are only $318.52 per patient day, or $33.07 per patient day less than the $351.59 average cost experienced by the 32 not‑for‑profit hospitals. How can this fact be reconciled with the estimated coefficient of -39.156 for the for-profit status variable?

D. Would such an approach for nursing cost estimation have practical relevance for publicly-funded nursing cost reimbursement systems?

Cost estimation and cost containment are an important concern for a wide range of for-profit and not-for-profit organizations offering health-care services. For such organizations, the accurate measurement of costs per patient day (a measure of output) is necessary for effective management. Similarly, such cost estimates are of significant interest to public officials at the federal, state, and local government levels. For example, many state Medicaid reimbursement programs base their payment rates on historical accounting measures of average costs per unit of service. However, these historical average costs may or may not be relevant for hospital management decisions. During periods of substantial excess capacity, the overhead component of average costs may become irrelevant. When the facilities are fully used and facility expansion becomes necessary to increase services, then all costs, including overhead, are relevant. As a result, historical average costs provide a useful basis for planning purposes only if appropriate assumptions can be made about the relative length of periods of peak versus off-peak facility usage. From a public policy perspective, a further potential problem arises when hospital expense reimbursement programs are based on average costs per day, because the care needs and nursing costs of various patient groups can vary widely. For example, if the care received by the average publicly-supported Medicaid patient actually costs more than that received by non‑Medicaid patients, Medicaid reimbursement based on average costs would be inequitable to providers and could create access barriers for Medicaid patients.

As an alternative to accounting cost estimation methods, one might consider using engineering techniques to estimate nursing costs. For example, the labor cost of each type of service could be estimated as the product of an approximation of the time required to perform each service times the estimated wage rate per unit of time. Multiplying this figure by an estimate of the frequency of service gives an engineering estimate of the cost of the service. A possible limitation to the accuracy of this engineering cost estimation method is that treatment of a variety of illnesses often requires a combination of nursing services. To the extent that multiple services can be provided simultaneously, the engineering technique will tend to overstate actual costs unless the effect of service "packaging" is allowed for.

Cost estimation is also possible by means of a carefully designed regression based approach using variable cost and service data collected at the ward, unit, or facility level. Weekly labor costs for registered nurses (RNs), licensed practical nurses (LPNs), and nursing aides might be related to a variety of patient services performed during a given measurement period. With sufficient variability in cost and service levels over time, useful estimates of variable labor costs become possible for each type of service and for each patient category (Medicaid, non‑Medicaid, etc.). An important advantage of a regression based approach is that it explicitly allows for the effect of service packaging on variable costs. For example, if shots and wound dressing services are typically provided together, this will be reflected in the regression based estimates of variable costs per unit.

Long‑run costs per nursing facility can be estimated using either cross‑section or time‑series methods. By relating total facility costs to the service levels provided by a number of hospitals, nursing homes, or out‑patient care facilities during a specific period, useful cross‑section estimates of total service costs are possible. If case mixes were to vary dramatically according to type of facility, then the type of facility would have to be explicitly accounted for in the regression model analyzed. Similarly, if patient mix or service provider efficiency is expected to depend, at least in part, on the for-profit or not‑for‑profit organization status of the care facility, the regression model must also recognize this factor. These factors plus price level adjustments for inflation would be accounted for in a time series approach to nursing cost estimation.

To illustrate a regression‑based approach to nursing cost estimation, consider a hypothetical analysis of variable nursing costs conducted by the Southeast Association of Hospital Administrators (SAHA). Using confidential data provided by 40 regional hospitals, SAHA studied the relation between nursing costs per patient day and four typical categories of nursing services. These annual data appear in Table 8.2. The four categories of nursing services studied include shots, intravenous (IV) therapy, pulse taking and monitoring, and wound dressing. Each service is measured in terms of frequency per patient day. An output of 1.50 in the shots service category means that, on average, patients received one and one-half shots per day. Similarly, a value of 0.75 in the IV service category means that on average, patients received 0.75 units of IV therapy per day, and so on. In addition to four categories of nursing services, the not‑for‑profit or for‑profit status of each hospital is also indicated. Using a "dummy" (or binary) variable approach, the profit status variable equals 1 for the 8 for-profit hospitals included in the study and zero for the remaining 32 not‑for‑profit hospitals.

Cost estimation results for nursing costs per patient day derived using a regression-based approach are shown in Table 8.3.