Measuring function for medicare inpatient rehabilitation payment

Health Care Financing Review, Spring, 2003 by Grace M. Carter, Daniel A. Relles, Gregory K. Ridgeway, Carolyn M. Rimes

There were a small number of cases--roughly 0.1 of 1.0 percent of the sample--where the FIM[TM] data were incomplete. An additional 2.6 percent of matched cases were lost because we could not estimate case cost. In this article we predict cost only for typical cases discharged to the community --i.e., excluding in-hospital deaths, transfer cases, and atypically short-stay cases. We used the MEDPAR verified date of death to identify the 0.5 percent of cases that died in the hospital. We used the FIM[TM] discharge setting variable to identify the 21.4 percent of sample IRF cases that were transfers. We also excluded the 2 percent of cases discharged to the community with LOS less than or equal to 3 days. LOS was taken from the MEDPAR. In addition, we excluded a handful of pediatric cases and cases with extremely high age or long LOS. Finally, we excluded less than 0.3 percent of cases whose estimated cost was outside a 3-standard deviation interval of the mean for the RIC on a log scale. Our final sample for the analyses presented here covers 186,766 discharges.

METHODS

Separate models of cost were fit within each RIC. For the purposes of this article we will provide summary information across all RICs for each analysis. For the sake of brevity, we provide the details of some models only for the two largest RICs: stroke, and lower extremity joint replacement. (Additional details about other RICs are available on request from the authors.)

We use ordinary least squares regression (OLS) to examine the relationship between cost and individual FIM[TM] item responses. In an OLS model, a fixed amount of change in an independent variable, anywhere along its scale and no matter what the value of other variables, results in the same change in the prediction of the dependent variable. This is the simplest possible model and has parameters that are easily interpretable. It directly tests whether increasing functional independence is correlated with lower cost after controlling for other FIM[TM] items. Thus, it is a straightforward test of whether each item contributes to the prediction of cost in the expected way. For the items where this is not true, we looked more carefully at the FIM[TM] instructions and the consequences of including the variable in the FIM[TM] scales.

In order to demonstrate the relationship between cost and the FIM[TM] scales while controlling for age, we report the results of two models in addition to OLS. These are the generalized additive model (GAM) and classification and regression trees (CART). We construct graphs that allow us to interpret the results of these models.

The GAM approximates the relationship as a sum of smooth (rather than linear) functions of the independent variables (Hastie and Tibshirani, 1990). This means that a change in motor score from 20 to 21 might decrease predicted cost by a different percentage than a change from 60 to 61. GAM does not model interactions.

CART is the technique that was used to produce the FIM[TM]-FRGs that are the basis of the case-mix groups used for payment in the IRF PPS (Federal Register, 2001). It is a well-known technique for building patient classification models (Breiman et al., 1984) and was used in the construction of the original FRGs. CART requires a dependent variable (log cost), and it seeks to develop predictors of the dependent variable through a series of binary splits from a candidate set of independent variables (age, FIM[TM] motor score, and FIM[TM] cognitive score). CART is invariant to one-to-one monotonic transformations of the independent variable such as those produced by Rasch (1980) analysis. CART partitions the data into two groups using the independent variables. Such a partition might separate patients with motor score exceeding 50 from those with motor score less than 50. CART chooses the variable on which to split the data and the value of the variable at which to split so that the new partitions minimize the squared prediction error. CART then recursively splits each partition until it satisfies some stopping criteria. As a result CART is invariant to one-to-one monotonic transformations of the independent variable so that an analysis using age or log (age) as an independent variable would produce the same model. This is particularly useful for handling the ordinal FIM[TM] motor and cognitive scores. CART's final product is a set of groups, each of which contains all patients with a specified range of the independent variables. Payments are then set to be proportional to the expected cost of all patients in the group.