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

DISCUSSION

Standard linear regression has been widely used for setting payment rates for prospective payment systems. The importance of obtaining regression parameter estimates that are robust to statistical outlier IREs is clear given the size of PPS expenditures; a shift from 19.1 percent to 17.9 percent for the rural adjustment would result in a redistribution of $3.5 million to nonrural IRFs. It is important that the best possible approach be used to derive payment adjustments and to confirm that existing standard approaches yield reasonable results. Our simulation study showed that the coefficient estimates obtained using the Bayesian outlier accommodation model are less sensitive to extreme observations than either the standard linear or robust regression approaches, thus making it less likely that a policy analyst will be misled by statistical outliers. The Bayesian outlier accommodation model provides at the very least a useful approach to assess the sensitivity of parameter estimates to the normality assumption and statistical outliers. Skewness and non-normality are commonly found in cost data, and linear regression coefficient estimates can be extremely sensitive to departures from normality (O'Hagan and Stevens 2003). While the standard practice of specifying the average cost per case outcome variable in the logged form is helpful for determining payment adjustors, our analysis shows that this may not fully solve the problem of developing the most suitable model in the context of developing facility payment adjustments in prospective payment systems. O'Hagan and Stevens (2003) argue that using methods that rely on asymptotic normality for the analysis of case-level health care cost data may be nonrobust if the data are highly nonnormal; our analysis shows that non-normality of cost data can also be an issue at the facility level. The Bayesian outlier accommodation model fit here does not rely on assumptions about asymptotically normally distributed errors.

The Bayesian outlier accommodation model retains the basic structure and interpretability of the commonly used standard linear regression approach, which should be appealing to practitioners who have used standard linear regression for decades to derive facility payment adjustments. We have also shown that the Bayesian framework can be used to formally test hypotheses about the suitability of various models as part of the analysis; in this case, we showed that the data overwhelmingly support the use of the Bayesian outlier accommodation model.