Identifying and accommodating statistical outliers when setting prospective payment rates for inpatient rehabilitation facilities

Health Services Research, Dec, 2004 by Susan M. Paddock, Barbara O. Wynn, Grace M. Carter, Melinda Beeuwkes Buntin

As part of the Balanced Budget Act of 1997, the U.S. Congress mandated that the Centers for Medicare and Medicaid Services (CMS) implement a prospective payment system (PPS) for hospital inpatient rehabilitation facilities (IRF) who care for Medicare beneficiaries. In 1999, Medicare's payments for inpatient rehabilitation care were $4.2 billion. This new IRF PPS was implemented on January 1, 2002. Under the new IRF PPS, inpatient rehabilitation facilities are compensated for providing inpatient rehabilitation care based on a predetermined amount per case according to the patient's impairment, age, level of function, and comorbid conditions. As is the case for hospitals under the acute care PPS, some cost differences among IRFs are due to factors other than patient characteristics, such as wage differences across geographic areas, and the fact that payment under the new IRE PPS is also a function of facility-specific factors.

A standard method for adjusting payment rates for facility cost differences in Medicare prospective payment systems is to use standard linear regression to model the average case-mix-adjusted cost per case at a facility as a function of facility characteristics that are related to cost. Functions of the resulting coefficients are used as payment adjustors (Lave 1984; Sheingold 1990). Several features of these "payment regressions" have been discussed in the literature. For example, Sheingold (1990) focuses on the use of linear regression in developing payment adjustments for the Medicare acute hospital PPS, stating that the variables included in the payment regression must not only be related to cost, but must also be beyond the control of the facilities so as not to introduce inappropriate incentives into the payment system. Other authors have focused on the impact of various transformations of predictor variables in the payment model; Rogowski and Newhouse (1999) and Dalton and Norton (2000) discuss the impact of the specification of the indirect teaching variable on Medicare's acute PPS.

A key assumption of standard linear regression is that regression error terms are normally distributed; the linear regression framework might be inappropriate for payment adjustments if this assumption is violated. This article focuses on the validity of the assumption of normally distributed errors using the derivation of facility payment adjustments for the IRE PPS as an example. The article is structured as follows. First, background is provided on the IRE PPS and the role of facility payment adjustments within this payment system. An overview of the standard method for deriving facility payment adjustments is given, followed by an illustration using the data that were used to derive the facility payment adjustments for the IRF PPS. We show that the assumption of normally distributed regression errors is questionable and discuss alternative statistical approaches to address this issue. In particular, we propose using a Bayesian outlier accommodation model to develop payment adjustments. The Bayesian outlier accommodation model relaxes the assumption of normally distributed errors, thus accommodating potentially unduly influential IRFs in the analysis. We show that it is structurally similar to the standard linear regression model, thus readily fitting into the existing paradigm for developing facility payment adjustments. Our discussion focuses on the IRF PPS, but the issues raised here also apply to the linear regression models used to set facility payment adjustments in other prospective payment systems.

Note that the term "statistical outlier" is used throughout this paper to denote IRFs that are identified as being highly unusual relative to other IRFs that are part of the statistical analysis. The statistical outlier IRFs that are discussed here have nothing to do with Medicare's outlier payment policies, which pertain not to facilities but rather to cases that have unusually high costs as determined by criteria that are specific to Medicare's various payment systems.

DESCRIPTION OF THE IRF PPS

The unit of payment in the IKF PPS is a Medicare covered hospital stay, beginning with an admission to the rehabilitation hospital or a rehabilitation unit of an acute care hospital and ending with discharge from that facility. Each case is classified into one of 380 case-mix groups. The case-mix groups (CMGs) are based on cause of impairment, age, functional status as measured by items based on the FIM[TM] instrument (Uniform Data System for Medical Rehabilitation 1997), and comorbid condition, with additional groups constructed for deaths and atypically short-stay cases. A weight is associated with each CMG that reflects the relative costliness of a case within that CMG. The payment for a rehabilitation stay under the IKF PPS is a product of three factors: a national baseline payment; the weight assigned to the patient's case-mix group that adjusts the national baseline payment for the relative costliness of the patient; and a facility adjustment to compensate IRFs for factors associated with increased costs that are beyond the control of the IRFs. In addition, the payment is adjusted for outlier cases and short stay transfer cases. The development of the standard baseline payment, case weights, and rules for payment of unusual cases are further detailed in Carter et al. (2002).